U.S. patent application number 16/636313 was filed with the patent office on 2022-09-29 for verification of interactions system and method.
The applicant listed for this patent is Visa International Service Association. Invention is credited to Karl Benedikt Bunz, Lucianna Kiffer, Loi Luu, Mahdi Zamani.
Application Number | 20220311619 16/636313 |
Document ID | / |
Family ID | 1000006588958 |
Filed Date | 2022-09-29 |
United States Patent
Application |
20220311619 |
Kind Code |
A9 |
Zamani; Mahdi ; et
al. |
September 29, 2022 |
VERIFICATION OF INTERACTIONS SYSTEM AND METHOD
Abstract
A system and method is disclosed. The method comprises a client
device receiving a verification request comprising an interaction
identifier. The client device can then query a full node for a
random sampling of block headers from the full node. The client
device can receive the random sampling of block headers from the
full node, and verify the random sampling of block headers. The
client device can then determine that the blockchain maintained by
the full node is valid after verifying the random sampling of block
headers.
Inventors: |
Zamani; Mahdi; (Palo Alto,
CA) ; Kiffer; Lucianna; (San Francisco, CA) ;
Luu; Loi; (Mountain View, CA) ; Bunz; Karl
Benedikt; (Palo Alto, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Visa International Service Association |
San Francisco |
CA |
US |
|
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 20220116223 A1 |
April 14, 2022 |
|
|
Family ID: |
1000006588958 |
Appl. No.: |
16/636313 |
Filed: |
August 9, 2018 |
PCT Filed: |
August 9, 2018 |
PCT NO: |
PCT/US2018/046101 |
371 Date: |
February 3, 2020 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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62543259 |
Aug 9, 2017 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H04L 9/3265 20130101;
H04L 2209/56 20130101; H04L 9/50 20220501; H04L 9/3247 20130101;
H04L 9/3239 20130101 |
International
Class: |
H04L 9/32 20060101
H04L009/32 |
Claims
1. A method comprising: receiving, by a client device, a
verification request comprising an interaction identifier; in
response to receiving the verification request, querying, by the
client device, a full node for a random sampling of block headers
from the full node; receiving, by the client device, the random
sampling of block headers from the full node; verifying, by the
client device, the random sampling of block headers; determining
that a blockchain maintained by the full node is valid after
verifying the random sampling of block headers; and verifying, by
the client device, that the interaction identifier is in a valid
block in the blockchain.
2. The method of claim 1 further comprising: querying, by the
client device, a plurality of full nodes for current heights of
blockchains maintained by the full nodes; receiving, by the client
device, a plurality of current heights for the blockchains
maintained by the full nodes; and determining, by the client
device, the full node from among the plurality of full nodes.
3. The method of claim 2, wherein determining the full node further
comprises: determining, by the client device, a most frequent
height of the plurality of current heights; and selecting, by the
client device, the full node of the plurality of full nodes that
reported a current height comparable to the most frequent
height.
4. The method of claim 1, wherein the verification request includes
a Merkle proof comprising a first path and a first plurality of
sibling graph nodes, the first path including a first plurality of
graph nodes in a Merkle tree from a Merkle root to a first graph
node, the first graph node associated with the interaction
identifier, and wherein the verification request includes a Merkle
mountain range proof comprising a second path and a second
plurality of sibling graph nodes, the second path including a
second plurality of graph nodes in a Merkle mountain range from a
Merkle mountain range root to a second graph node, the second graph
node associated with a block header containing the interaction
identifier.
5. The method of claim 4 further comprising: verifying, by the
client device, the Merkle proof; verifying, by the client device,
the Merkle mountain range proof, determining, by the client device,
if the interaction identifier corresponds to a valid interaction
based on verification of the Merkle proof and the Merkle mountain
range proof; and transmitting, by the client device, a verification
response indicating whether or not the interaction identifier
corresponds to the valid interaction.
6. The method of claim 1, wherein after verifying the random
sampling of block headers the method further comprises: repeating,
by the client device, the querying, receiving, and verifying steps,
for a predetermined number of rounds.
7. The method of claim 1, wherein querying the full node for a
random sampling of block headers from the full node further
comprises: transmitting, by the client device, a random number to
the full node, wherein the full node partitions the blockchain
maintained by the full node into substantially equally sized number
of partitions, selects the random sampling of block headers from a
most recent partition based on the random number, and transmits the
random sampling of block headers to the client device.
8. The method of claim 7, wherein the full node determines a
plurality of Merkle mountain range proofs associated with the
random sampling of block headers from the full node and transmit
the plurality of Merkle mountain range proofs to the client
device.
9. The method of claim 1 further comprising: performing, by the
client device, additional processing based on an interaction
associated with the interaction identifier, wherein the additional
processing includes performing an action or operation as indicated
in the interaction or transferring assets between the client device
and a prover as outlined in the interaction.
10. The method of claim 1, wherein each block header of the random
sampling of block headers comprises a previous hash value, a nonce,
a timestamp, a Merkle root, and a Merkle mountain range root.
11. The method of claim 10 further comprising: obtaining, by the
client device, a plurality of Merkle mountain range proofs
associated with the random sampling of block headers from the full
node; and wherein verifying the random sampling of block headers
further comprises: verifying, by the client device, validity of the
previous hash value and the nonce; and verifying, by the client
device, the plurality of Merkle mountain range proofs.
12. A client device comprising: a processor; a memory; and a
computer readable medium coupled to the processor, the computer
readable medium comprising code, executable by the processor, for
implementing a method comprising: receiving a verification request
comprising an interaction identifier; in response to receiving the
verification request, querying a full node for a random sampling of
block headers from the full node; receiving the random sampling of
block headers from the full node; verifying the random sampling of
block headers; determining that a blockchain maintained by the full
node is valid after verifying the random sampling of block headers;
and verifying that the interaction identifier is in a valid block
in the blockchain.
13. The client device of claim 12, wherein the method further
comprises: querying a plurality of full nodes for current heights
of blockchains maintained by the full nodes; receiving a plurality
of current heights for the blockchains maintained by the full
nodes; and determining the full node from among the plurality of
full nodes.
14. The client device of claim 13, wherein determining the full
node further comprises: determining, by the client device, a most
frequent height of the plurality of current heights; and selecting,
by the client device, the full node of the plurality of full nodes
that reported a current height comparable to the most frequent
height.
15. (canceled)
16. (canceled)
17. (canceled)
18. (canceled)
19. (canceled)
20. (canceled)
21. (canceled)
22. (canceled)
23. A method comprising: receiving, by a full node, a query for a
random sampling of block headers including a random number from a
client device; selecting, by the full node, the random sampling of
block headers from a blockchain; determining, by the full node, a
plurality of verification proofs associated with the random
sampling of block headers; and transmitting, by the full node, the
random sampling of block headers and the plurality of verification
proofs to the client device, wherein the client device verifies the
random sampling of block headers and the plurality of verification
proofs.
24. The method of claim 23, wherein the plurality of verification
proofs are a plurality of Merkle mountain range proofs.
25. The method of claim 23, wherein the method further comprises:
partitioning, by the full node, the blockchain into partitions
including a most recent partition comprising a latest block header,
wherein the random sampling of block headers are selected from the
most recent partition.
26. The method of claim 25, wherein the blockchain is partitioned
into the partitions based on a number of queries received.
27. The method of claim 25 further comprising: determining, by the
full node, that a number of blocks in the most recent partition is
substantially equivalent to a number of block headers included in
the random sampling of block headers.
28. The method of claim 23 further comprising: receiving, by the
full node, a query for a current height of the blockchain from the
client device; determining, by the full node, the current height of
the blockchain; and transmitting, by the full node, the current
height of the blockchain to the client device, wherein the client
device determines if the current height of the blockchain is
substantially equivalent to a plurality of current heights received
from a plurality of full nodes.
29. (canceled)
30. (canceled)
31. (canceled)
32. (canceled)
33. (canceled)
34. (canceled)
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is a PCT application claiming priority to
U.S. Provisional Application No. 62/543,259 filed Aug. 9, 2017,
which is herein incorporated by reference in its entirety.
BACKGROUND
[0002] To ensure the validity of interactions, verification
networks rely on a mechanism to verify if particular interactions
are included in a blockchain. A node in the verification network
can check if an interaction is recorded in the blockchain and that
the block belongs to the longest chain (i.e., correct chain), in
case of a fork in the blockchain. To perform these checks, the node
downloads all blocks in the blockchain and verifies all of them.
Blockchains like Ethereum [Vitalik Buterin. Ethereum's white paper.
https://github.com/ethereum/wiki/wiki/White-Paper 2014] and Bitcoin
[Satoshi Nakamoto. Bitcoin: A peer-to-peer electronic cash system,
2008. Available at https://bitcoin.org/bitcoin.pdf] rely on
proof-of-work (PoW) [Cynthia Dwork and Moni Naor. Pricing via
processing or combatting junk mail. In Advances in
Cryptology--CRYPTO '92: 12th Annual International Cryptology
Conference Santa Barbara, Calif., USA Aug. 16-20, 1992 Proceedings,
pages 139-147, Berlin, Heidelberg, 1993. Springer Berlin
Heidelberg] to reach agreement on blocks of transactions added to
their blockchains. In Bitcoin and Ethereum, syncing all of these
blocks requires a node to send and receive hundreds of gigabytes of
data (about 160 GB in Bitcoin, see [Blockchain charts: Bitcoin's
blockchain size, July 2018. Available at
https://blockchain.info/charts/blocks-size], and 650 GB in
Ethereum, see [Bitinfocharts: Ethereum blockchain size, July 2018.
Available at https://bitinfocharts.com/ethereum]), taking days for
both downloading and verification.
[0003] Having all blocks allows a node to verify the inclusion of
any past transaction on the blockchain. Such a requirement
especially imposes a significant burden on resource-limited
clients, often known as light or thin clients, such as smartphones
and Internet-of-things devices that typically have access to
limited bandwidth, storage, and computation resources, but still
want to verify the inclusion of transactions on the blockchain.
[0004] Bitcoin has a synchronization mechanism, called simplified
payment verification (SPV), that allows clients with limited
resources, such as mobile phones and tablets, to verify
transactions without downloading the entire blocks. In SPV, instead
of downloading all blocks from a full node, an SPV client can
download all block headers, which have a much smaller size than the
blocks (e.g., 80 bytes per block header vs 1 MB per block in
Bitcoin), but still contain enough information to correctly verify
that a transaction is included in some block and verify that the
block is included at a certain position in the blockchain. Each
block header contains the root of a Merkle tree, see [Ralph C.
Merkle. A digital signature based on a conventional encryption
function. In A Conference on the Theory and Applications of
Cryptographic Techniques on Advances in Cryptology, CRYPTO '87,
pages 369-378, London, UK, UK, 1988. Springer-Verlag], that is
constructed over all transactions in the block. The Merkle root,
along with a Merkle proof sent by the full node for any given
transaction, allows the light client to verify the inclusion of the
transaction in the block. Due to the hash of the previous block
included in each header, the client can also check the validity of
every header on the chain one-by-one. This ensures that the header
corresponds to a valid block at a certain position in a blockchain
of the same length, which the full node has never sent to the light
client in full.
[0005] SPV clients are the most popular clients in the Bitcoin
ecosystem and enable various applications to a broad class of
users. This is mainly due to the fact that not many people can
afford the technical and physical resources needed to run a full
node. For example, Bitcoin's blockchain was recently used to build
notary services by allowing users to verify the validity and
integrity of documents with SPV clients, see [Open timestamps.
https://opentimestamps.org/, 2018] and [Stampery.
https://stampery.com/, 2018]. Also, in a recent work known as
Catena, see [Alin Tomescu and Srivinas Devadas. Catena: Efficient
non-equivocation via bitcoin. In 2017 IEEE Symposium on Security
and Privacy (SP), pages 393-409, May 2017], an authenticated log
system leverages Bitcoin's blockchain to allow Internet browsers to
fetch and validate HTTPS certificates. Thus, light-weight
verification clients are in great demand. SPV proofs can also be
used in applications that require cross-ledger verification of
transactions, e.g., transferring assets to sidechains, see [Dashjr
et al, Enabling blockchain innovations with pegged sidechains,
2014. https://www.blockstream.com/sidechains.pdf] and [Kiayias et
al, Non-interactive proofs of proof-of-work. 2017], and
sharding-based blockchain protocols, see [Luu et al, A secure
sharding protocol for open blockchains. In Proceedings of the 2016
ACM SIGSAC Conference on Computer and Communications Security, CCS
'16, pages 17-30, New York, N.Y., USA, 2016. ACM], [Kokoris-Kogias
at al, OmniLedger: A secure, scale-out, decentralized ledger via
sharding. In 2018 IEEE Symposium on Security and Privacy (S&P),
pages 19-34, 2018], and [Mahdi Zamani, Mahnush Movahedi, and
Mariana Raykova. RapidChain: Scaling blockchains via full sharding.
In 2018 ACM Conference on Computer and Communications Security
(CCS), 2018].
[0006] As the number of block headers increases linearly with the
size of the blockchain, the resource constraints for current light
clients also increase. For example, as of mid-2018, the Ethereum
blockchain has more than 6 million blocks, see [Bitinfocharts:
Ethereum blockchain size, July 2018. Available at
https://bitinfocharts.com/ethereum]. Given that each block header
is of size 528 bytes, an SPV client in Ethereum would have to
download and store more than 3 GB of data to be able to verify all
events on the Ethereum blockchain. As such, current light clients
cannot handle the large amounts of data needed to verify
interactions on blockchains as the length of the blockchains
increase.
[0007] Embodiments of the invention address these and other
problems individually and collectively.
BRIEF SUMMARY
[0008] Embodiments of the invention are directed to methods and
systems of efficiently determining that a full node maintains a
valid longest blockchain as well as verifying an that interaction
is valid and stored in the blockchain.
[0009] One embodiment of the invention is directed to a method. The
method comprises a client device receiving a verification request
comprising an interaction identifier; querying, by the client
device, a full node for a random sampling of block headers from the
full node; receiving, by the client device, the random sampling of
block headers from the full node; verifying, by the client device,
the random sampling of block headers; and determining that the
blockchain maintained by the full node is valid after verifying the
random sampling of block headers.
[0010] Another embodiment of the invention is directed to the
client device comprising: a processor, a memory; and a computer
readable medium coupled to the processor, the computer readable
medium comprising code, executable by the processor, for
implementing a method comprising: receiving a verification request
comprising an interaction identifier; querying a full node for a
random sampling of block headers from the full node; receiving the
random sampling of block headers from the full node; verifying the
random sampling of block headers; and determining that the
blockchain maintained by the full node is valid after verifying the
random sampling of block headers.
[0011] Another embodiment is directed to a method. The method
comprising: receiving, by a full node, a query for a random
sampling of block headers including a random number from a client
device; selecting, by the full node, the random sampling of block
headers from a blockchain; determining, by the full node, a
plurality of Merkle mountain range proofs associated with the
random sampling of block headers; and transmitting, by the full
node, the random sampling of block headers and the plurality of
Merkle mountain range proofs to the client device.
[0012] Another embodiment of the invention is directed to the
client device comprising: a processor, a memory; and a computer
readable medium coupled to the processor, the computer readable
medium comprising code, executable by the processor, for
implementing a method comprising: receiving a query for a random
sampling of block headers including a random number from a client
device; selecting the random sampling of block headers from a
blockchain; determining a plurality of Merkle mountain range proofs
associated with the random sampling of block headers; and
transmitting the random sampling of block headers and the plurality
of Merkle mountain range proofs to the client device.
[0013] Another embodiment is directed to a method. The method
comprising: receiving, by a full node, a query for a random
sampling of block headers including a random number from a client
device; selecting, by the full node, the random sampling of block
headers from a blockchain; determining, by the full node, a
plurality of verification proofs associated with the random
sampling of block headers; and transmitting, by the full node, the
random sampling of block headers and the plurality of verification
proofs to the client device, wherein the client device verifies the
random sampling of block headers and the plurality of verification
proofs.
[0014] Another embodiment of the invention is directed to the full
node comprising: a processor, a memory; and a computer readable
medium coupled to the processor, the computer readable medium
comprising code, executable by the processor, for implementing a
method comprising: receiving a query for a random sampling of block
headers including a random number from a client device; selecting
the random sampling of block headers from a blockchain; determining
a plurality of verification proofs associated with the random
sampling of block headers; and transmitting the random sampling of
block headers and the plurality of verification proofs to the
client device, wherein the client device verifies the random
sampling of block headers and the plurality of verification
proofs.
[0015] Further details regarding embodiments of the invention can
be found in the Detailed Description and the Figures.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] FIG. 1 shows a system according to embodiments of the
invention.
[0017] FIG. 2 shows components of a client device according to an
embodiment of the invention.
[0018] FIG. 3 shows an example blockchain format.
[0019] FIG. 4 shows an example of updating a Merkle mountain range
when new data entries are appended as new leaves of the Merkle
mountain range according to embodiments of the invention.
[0020] FIG. 5 shows a blockchain structure according to embodiments
of the invention.
[0021] FIG. 6 shows a flowchart of a longest chain verification
method according to embodiments of the invention.
[0022] FIG. 7 shows a flowchart of a longest chain verification
method performed by a full node according to embodiments of the
invention.
[0023] FIG. 8 shows a flowchart of an interaction verification
method according to embodiments of the invention.
[0024] FIG. 9 shows a flow diagram of verifying a longest chain and
an interaction according to embodiments of the invention.
[0025] FIG. 10 shows a Merkle tree according to embodiments of the
invention.
DETAILED DESCRIPTION
[0026] Prior to discussing embodiments of the invention, some terms
can be described in further detail.
[0027] A "user" may include an individual. In some embodiments, a
user may be associated with one or more personal accounts and/or
mobile devices. The user may also be referred to as a cardholder,
account holder, or consumer in some embodiments.
[0028] A "client device" may be a computing device capable of
transmitting and/or receiving data. Examples of client devices may
include a mobile phone, a smart phone, a personal digital assistant
(PDA), a laptop computer, a desktop computer, a server computer, a
vehicle such as an automobile, a light client device, a tablet PC,
etc. Additionally, user devices may be any type of wearable
technology device, such as a watch, earpiece, glasses, etc. The
user device may include one or more processors capable of
processing user input. The user device may also include one or more
input sensors for receiving user input. The user device may
comprise any electronic device that may be operated by a user,
which may also provide remote communication capabilities to a
network. Examples of remote communication capabilities include
using a mobile phone (wireless) network, wireless data network
(e.g., 3G, 4G or similar networks), Wi-Fi, Wi-Max, or any other
communication medium that may provide access to a network such as
the Internet or a private network.
[0029] A "light client" may be an application or software capable
of communicating with a verification network. The light client may,
for example, be present on a client device. In some embodiments, a
light client may communicate with a verification network and verify
a longest blockchain and an interaction.
[0030] A "verification network" may be any set of nodes (computer
systems and components) configured to provide verification for an
interaction. The verification network may comprise a distributed
computing environment utilizing several nodes that are
interconnected via communication links, using one or more computer
networks or direct connections. The verification network may be
implemented over any appropriate network, including an intranet,
the Internet, a cellular network, a local area network or any other
such network or combination thereof. Components used for such a
system can depend at least in part upon the type of network and/or
environment selected. Protocols and components for communicating
via such a network are well known and will not be discussed herein
in detail. Communication over the verification network can be
enabled by wired or wireless connections and combinations thereof.
Nodes may be independently operated by third parties and may be
added to, or removed from, the verification network on a continuous
basis. In some embodiments, a node in a verification network may be
a full node.
[0031] A "node" may be a point at which lines or pathways intersect
or branch or can be a central or connecting point. A node can be a
"graph node," which can be a data value in a Merkle tree or a
Merkle mountain range. A graph node can include data such as a hash
value, which can be equivalent to child graph nodes of the graph
node hashed together. A graph node at the bottom of a Merkle tree
or a Merkle mountain range can be referred to as a leaf node. A
graph node at the top of a Merkle tree or a Merkle mountain range
can be referred to as a root node.
[0032] A node can also be a "computer node," which can be any
computer or device that connects to the verification network. A
node that can fully verify each block and interaction in the
blockchain can be a full node. A "full node" can store the full
blockchain (i.e., each block and each interaction). A "client
device" may be a computer node in the verification network. The use
of a node as being a graph node or a computer node will be apparent
according to the context in which it is used.
[0033] The term "verification" and its derivatives may refer to a
process that utilizes information to determine whether an
underlying subject is valid under a given set of circumstances.
Verification may include any comparison of information to ensure
some data or information is correct, valid, accurate, legitimate,
and/or in good standing.
[0034] A "verification request" can be a request message requesting
verification. A verification request can comprise an interaction
identifier. A verification request can request verification of an
interaction identifier. In some embodiments, the verification
request can also comprise a Merkle proof as well as a Merkle
mountain range proof. The Merkle proof and the Merkle mountain
range proof can be associated with the interaction identifier
included in the verification request.
[0035] A "verification proof" can be a data item that can be used
to verify the truth of a statement. A verification proof can be
included in a verification request regarding an interaction. A
verification proof can be a Merkle proof or a Merkle mountain range
proof.
[0036] A "Merkle tree" can be a data structure that can encode
interaction data. A Merkle tree can be a balanced binary tree where
the leaf nodes of the tree hold some value, and each non-leaf node
can store a hash of a concatenation of the values of both children
nodes. When a new leaf is added to a Merkle tree, the entire tree
can be recomputed. For example, each node in the Merkle tree can be
determined to be the hash of both children nodes.
[0037] A "Merkle proof" can be a proof that an interaction is
included in a Merkle tree. A Merkle proof can include a path from a
Merkle root of a Merkle tree to a node associated with an
interaction identifier as well as sibling nodes of each node in the
path. The path can include each node connecting the Merkle root
node to the node associated with the interaction identifier.
[0038] A "Merkle mountain range" can be a data structure that can
encode block headers. For example, a Merkle mountain range can be a
type of Merkle tree. A Merkle mountain range M can be a binary hash
tree with n leaves, a root r, and the following properties: 1) M
can be a hash tree; 2) M can have a depth [log.sub.2 n]; and 3) if
n>1, the number of leaves n=2.sup.i+j for a maximum integer i
such that 2.sup.1<n, wherein r.left can be a Merkle mountain
range with 2.sup.i leaves and wherein r.right can be a Merkle
mountain range with j leaves. A Merkle mountain range can allow for
new leafs to be appended to the Merkle mountain range without
recomputing the entire Merkle mountain range. A small number of
nodes are recomputed when appending a new leaf to a Merkle mountain
range.
[0039] A "Merkle mountain range proof" can be a proof that a block
header is included in a Merkle mountain range. For example, a
Merkle mountain range proof can include a path from a Merkle
mountain range root to a node associated with a block header. The
path can include each node connecting the root node to the node
associated with the block header The Merkle mountain range proof
can also include the sibling nodes of each node in the path.
[0040] A "sibling node" can denote a relationship between nodes. A
node's sibling node can be a node that is in a same hierarchical
level under the same parent node in either a Merkle tree or a
Merkle mountain range. For example, a node that is a parent node
can have two child nodes that are on a lower hierarchical level
than the parent node. The two child nodes can be sibling nodes.
[0041] A "Merkel root" and a "Merkle mountain range root" can be a
node at the highest hierarchical level in a Merkle tree or a Merkle
mountain range, respectively. A Merkle root and a Merkle mountain
range root do not have any sibling nodes or parent nodes. A Merkle
root and a Merkle mountain range root can connect to child
nodes.
[0042] A "blockchain" can be a distributed database that maintains
a continuously-growing list of records secured from tampering and
revision. A blockchain may include a number of blocks of
interaction records. Each block in the blockchain can contain also
include a timestamp and a link to a previous block. Stated
differently, interaction records in a blockchain may be stored as a
series of "blocks," or permanent files that include a record of a
number of interactions occurring over a given period of time.
Blocks may be appended to a blockchain by an appropriate node after
it completes the block and the block is validated. Each block can
be associated with a block header. In embodiments of the invention,
a blockchain may be distributed, and a copy of the blockchain may
be maintained at each full node in a verification network. Any node
within the verification network may subsequently use the blockchain
to verify interactions.
[0043] A "block header" can be a header including information
regarding a block. A block header can be used to identify a
particular block an a blockchain. A block header can comprise any
suitable information, such as a previous hash, a Merkle root, a
timestamp, a nonce, and a Merkle mountain range root. In some
embodiments, a block header can also include a difficulty
value.
[0044] An "interaction" may refer to a reciprocal action or
influence. An interaction can include a communication, contact, or
exchange between parties, devices, and/or entities. Example
interactions include a transaction between two parties and a data
exchange between two devices. Interactions can also be agreements,
contracts, and the like.
[0045] A "server computer" may include a powerful computer or
cluster of computers. For example, the server computer can be a
large mainframe, a minicomputer cluster, or a group of servers
functioning as a unit. In one example, the server computer may be a
database server coupled to a Web server. The server computer may
comprise one or more computational apparatuses and may use any of a
variety of computing structures, arrangements, and compilations for
servicing the requests from one or more client computers.
[0046] A "resource provider" may be an entity that can provide a
resource such as goods, services, information, and/or access.
Examples of resource providers includes merchants, access devices,
secure data access points, data providers, transit agencies,
governmental entities, venue and dwelling operators, etc. A
resource provider may operate a client device. A merchant may
typically be an entity that engages in transactions and can sell
goods or services, or provide access to goods or services.
[0047] A "merchant" may typically be an entity that engages in
transactions and can sell goods or services, or provide access to
goods or services.
[0048] A "processor" may refer to any suitable data computation
device or devices. A processor may comprise one or more
microprocessors working together to accomplish a desired function.
The processor may include a CPU comprising at least one high-speed
data processor adequate to execute program components for executing
user and/or system-generated requests. The CPU may be a
microprocessor such as AMD's Athlon, Duron and/or Opteron; IBM
and/or Motorola's PowerPC; IBM's and Sony's Cell processor; Intel's
Celeron, Itanium, Pentium, Xeon, and/or XScale; and/or the like
processor(s).
[0049] A "memory" may be any suitable device or devices that can
store electronic data. A suitable memory may comprise a
non-transitory computer readable medium that stores instructions
that can be executed by a processor to implement a desired method.
Examples of memories may comprise one or more memory chips, disk
drives, etc. Such memories may operate using any suitable
electrical, optical, and/or magnetic mode of operation.
[0050] Details of some embodiments of the present invention will
now be described.
I. INTRODUCTION
[0051] Embodiments of the invention allow for an interaction
verification protocol for light clients in blockchain protocols
that grow based on the longest chain principle. In embodiments of
the invention, a verifier operating a client device can download
and store a logarithmic (rather than a linear) number of block
headers to verify any interaction stored on a blockchain.
Embodiments of the invention can utilize a non-interactive
probabilistic protocol to sample a small (e.g., logarithmic) set of
random block headers from a full node to limit the likelihood of an
adversarial full node cheating in the longest-chain verification
process, given the adversary's limited computational power in
creating valid blocks. A data structure called a Merkle mountain
range (MMR) can allow client devices to verify any interaction in a
blockchain with a minimal amount of information. The Merkle
mountain range can include a Merkle mountain range root that can be
stored in the block headers. Further, embodiments of the invention
can be implemented in current Bitcoin and/or Ethereum networks via
a soft fork.
[0052] Reducing the number of block headers that a client device
has to download from a full node is a security challenge. By
downloading the entire chain of block headers, the client device
can verify that the events proved by the full node are actually
recorded on the longest chain. Without being required to send all
block headers to the client device, a malicious prover can take
advantage of the client device's smaller computational power
(relative to the combined computational power of honest nodes) to
create and send only a small (but valid) number of fake blocks
tricking the client device to accept a smaller fake chain. Existing
solutions for handling this challenge are inefficient, complex, and
require significant changes to the design of already-established
blockchains.
A. Prior Work
[0053] Current blockchain technologies, such as Bitcoin and
Ethereum, maintain an append-only ledger in a network. The ledger
includes a list of blocks of transaction data, the blocks are
cryptographically chained together as depicted in FIG. 3. A block
is created by a computationally intensive process called
proof-of-work in which valid blocks need to demonstrate a
sufficient "difficulty" (i.e., sufficient computation power to
create on average). If there are more than one available chains of
blocks, then network participants, i.e., nodes, need to download
all blocks in all chains and follow the chain which has the highest
total difficulty. This mechanism guarantees that, in the long run,
the network will agree on a single and valid chain, see [Garay et
al, The Bitcoin backbone protocol: Analysis and applications. In
Advances in Cryptology--EUROCRYPT 2015, pages 281-310, 2015],
[Bitcoin Website. http://www.bitcoin.org/], and [Rafael Pass, Lior
Seeman, and Abhi Shelat. Analysis of the blockchain protocol in
asynchronous networks. In Jean-Sebastien Coron and Jesper Buus
Nielsen, editors, Advances in Cryptology--EUROCRYPT 2017, pages
643-673, Cham, 2017. Springer International Publishing.].
[0054] Nakamoto [Bitcoin Website. http://www.bitcoin.org/] proposes
a simplified payment verification (SPV) protocol to verify Bitcoin
transactions with minimal trust on some full nodes. Specifically, a
client device downloads all block headers rather than the full
blocks, which are much smaller in size. A block header contains a
hash of a Merkle root that commits all transactions in the block.
Therefore, after downloading all block headers in the blockchain, a
client device can verify the existence of any transaction in any
block, given that a prover provides a Merkle proof of size logs
hashes to the client device, in which s is the number of
transactions in the block. For further details on light clients in
Bitcoin see [socrates1024. The high-value-hash highway.
https://bitcointalk.orgfindex.php?topic=98986.0, 2012].
[0055] FIG. 3 shows an example blockchain format. For example, the
blockchain format shown in FIG. 3 can be used in Bitcoin. A
blockchain 300 can comprise a plurality of blocks, for example,
block 302A and block 302B. Each block can comprise a block header,
e.g., block 302A comprises block header 304. The block header 304
can include multiple data elements, such as a previous header hash
306 and a Merkle root 308. The previous header hash 306 can be a
hash of the previous block's header. The Merkle root 308 can be a
root of a Merkle tree which is a tree in which every leaf node is
labelled with the hash of a data block, for example a transaction
310-314. Each leaf of the Merkle tree can represent one of the
transactions 310-314.
[0056] There are two additional solutions to SPVs proposed by
Kiayias et. al., see [Kiayias et al, Proofs of Proofs of Work with
Sublinear Complexity, pages 61-78. Springer Berlin Heidelberg,
Berlin, Heidelberg, 2016] and [Kiayias et al, Non-interactive
proofs of proof-of-work. 2017]). They propose an SPV protocol,
called proofs of proof-of-work (PoPoW), which reduces the required
resources of an SPV client to a logarithmic number of blocks. The
protocol is based on the observation that a certain number of lucky
blocks called superblocks are expected to exist in a proof-of-work
(PoW) chain if it has been created honestly. A superblock is a rare
block that has a PoW output value (i.e., the block ID) containing
more leading zeros than the other valid blocks, and hence, can be
used to show that enough work has been done when the chain
containing that block was created. It can be shown that, by
verifying the validity of a logarithmic number of superblocks, a
client device can ensure the validity of the entire chain it
receives from a full node with high probability. Inspired by a skip
list data structure, PoPoW changes the blockchain structure in such
a way that each block, instead of having one reference to the
immediate previous block, stores multiple references to previous
blocks including the superblocks.
[0057] However, PoPoW requires significant modifications to the
blockchain structure which can limit its adoption in existing
blockchains. Moreover, the practicality of the PoPoW approach is
yet to be shown, as the constant factors in the protocol's overhead
seems to be large. Each transaction inclusion proof in PoPoW is
increased by m log(n)log(log(n)) in size to prove that the block
that contains the transaction belongs to the correct chain, where m
is a security parameter and where n is the number of blocks in the
blockchain. Furthermore, PoPoW increases the size of each proof by
a log n factor. In addition, PoPoW is interactive, meaning that the
client device has to communicate over multiple sequential rounds
with the client device to obtain a validity proof. This incurs a
high latency and communication cost for both the client device and
the full node.
[0058] In a later work, Kiayias et. al., see [Kiayias et al,
Non-interactive proofs of proof-of-work. 2017], present an attack
against PoPoW, where an adversary can double-spend bitcoins even if
it controls a minority of the hashing power. They also propose a
non-interactive proofs of proof-of-work (NIPoPoW) protocol that
allows succinct (i.e., logarithmic-size) proofs but with the same
proof complexity as in PoPoW.
[0059] However, the PoPoW and NIPoPoW protocols are vulnerable to a
bribing attack, where an attacker offers an incentive to miners in
the network who will be lucky and find superblocks, in exchange for
not publishing their blocks to the network. The attacker then
builds a fake chain containing the superblocks of the bribed
miner's superblocks and uses it to pretend possession of the
longest chain using a valid PoPoW proof. Such an attack is possible
in any protocol that differentiates between mined blocks in a
deterministic way, because the adversary knows in advance the type
of blocks that it is willing to bribe. The adversary can advertise
for the superblocks before the superblocks are mined and published
to the network. To prove block inclusion, vector commitments can be
employed as described in https://eprint.iacr.org/2011/495.pdf.
B. Problem Definition
[0060] Consider a blockchain protocol that grows a chain based on
the longest (i.e., most difficult) chain rule of PoW-mined blocks
(see [Garay et al, The bitcoin backbone protocol: Analysis and
applications. In Annual International Conference on the Theory and
Applications of Cryptographic Techniques, pages 281-310. Springer,
2015]), where honest miners eventually agree on the chain that
requires the largest combined mining power to be created. Also,
consider an adversary that owns at most a one half fraction of the
mining power (e.g., f<1/2) in the verification network. As shown
in FIG. 1, an SPV protocol can be executed between a prover, a
client device (i.e., a verifier), and a group of full nodes. The
full nodes can claim to hold a valid copy of the blockchain. An
adversarial full node may store a non-valid copy of the blockchain.
The prover wants to convince the client device that a previously
performed interaction is valid and has already been recorded on the
blockchain. Embodiments of the invention allow the client device to
verify the validity of the interaction with the help of the full
nodes. Less than half of the full nodes may be controlled by the
adversary, and thus collude with a malicious prover. An interaction
is said to be valid if it is included in a correctly-mined block of
interactions that belongs to the longest chain.
[0061] Embodiments of the invention can provide for the following
security, client efficiency, and non-interactiveness properties.
The security property means that the client device can accept an
interaction if the interaction is valid (i.e., is an interaction
included in a correctly-mined block that belongs to the longest
chain with high probability). The client efficiency property means
that the client can download and verify a small (e.g., sublinear)
number of block headers from a full node, rather than download all
block headers in the blockchain. The non-interactiveness property
means that no subsequent interactions between the prover, the
client, and the full nodes are needed.
[0062] To achieve the first property of security, the client device
can participate in the process with the prover as well as the full
nodes to obtain a proof, denoted by .pi..sub.tx, that provides the
following guarantees: 1) proof of inclusion: the interaction is
included in some correctly-mined block B on a chain C; and 2) proof
of chain: C is the longest (e.g., most difficult) chain agreed upon
by a majority of the nodes in the verification network.
[0063] Given that the adversary that can control at most an f
fraction of the mining power, the proof .pi..sub.tx can provide the
following properties: 1) completeness: at the end of the process,
the client device can determine that the interaction is valid and
2) soundness: the adversary cannot convince the client device that
the interaction is valid.
C. Overview of Embodiments of the Invention
[0064] Embodiments of the invention allow for a non-interactive SPV
protocol for a client device. In embodiments of the invention, a
client device can download and store a logarithmic number of blocks
using a probabilistic verification method as well as using a
structure called Merkle mountain range (MMR), see [Peter Todd.
Merkle mountain range.
https://github.com/opentimestamps/opentimestamps-server/blob/master/doc/m-
erkle-mountain-range.md]. An MMR allows small inclusion proofs,
while including an additive logarithmic factor in addition to the
current inclusion proof in Bitcoin and Ethereum. Embodiments of the
invention use an extra hash (i.e., the MMR root) in the block
headers which can be added to existing blockchains (e.g., Bitcoin)
via a soft-fork.
[0065] Theorem 1: there exists a protocol that can provide the
completeness and soundness properties, described above, with high
probability as well as the following performance guarantees: 1) let
n denote the number of blocks in the longest chain, and s denote
the number of interactions in the block B. .pi..sub.rec(tx) has
size O(log s) and .pi..sub.B has size O(log n). 2) The client
device can verify .pi..sub.tx efficiently with an O(log s+log n)
computation overhead.
[0066] Consider a prover (i.e., a full node) that wants to convince
a verifier (i.e., a client device) that an interaction tx is
recorded properly in some block B.sub.x on a blockchain of length
n, where x.di-elect cons.[1,n]. To achieve this, the prover can
provide the client device with a proof of inclusion which consists
of two cryptographic proofs. The proof of inclusion can include a
proof of longest chain and a proof of interaction. The proof of
longest chain can be that the block B.sub.x is located at height x
of the correct (i.e., longest) chain. The proof of interaction can
be that the interaction tx is recorded properly in the block
B.sub.x. The client device can verify that the interaction is
included in a block as well as verify that the block is in the
longest chain.
[0067] To commit to the entire chain of blocks, the prover can
maintain a Merkle mountain range over all blocks added to the
blockchain so far. In addition to being a Merkle tree, MMR allows
for efficient appends at the prover side and efficient block
inclusion verifications at the verifier side. At every block height
i, the full node appends the hash of B.sub.i-1 to the most recent
MMR and records the new MMR root, denoted by M.sub.i-1, in the
header of B.sub.i (see FIG. 5). As a result, each MMR root stored
at every block height can be seen as a commitment by the full node
to the blockchain at that specific height.
[0068] An MMR tree can allow the client device to efficiently
verify any blockchain event (i.e., an interaction) with the latest
block header. MMR allows all previous blocks to be efficiently
committed to the latest block header in a single hash. The original
Merkle tree structure can be used to achieve the same goal,
however, updating the Merkle trees with new block headers as the
leaves is not efficient. The entire Merkle tree either needs to be
restructured, which is inefficient, or the system can use an
"unbalanced" tree which may yield a proof size of much larger than
log n hashes. MMR is a variant of the original Merkle tree that
allows a much more efficient update process, thus the overhead for
full nodes when processing blocks becomes negligible. Further,
introducing MMR into current blockchain protocols only needs a mild
modification.
[0069] Given any two blockchains of the same length, one of which
is maintained by an adversary with less than one half fraction
(i.e., f<1/2) of mining power, embodiments of the invention
allow client devices to determine, with high probability, which
chain is valid and longer by downloading a small (i.e., log n)
number of block headers from each chain. In embodiments of the
invention, this can be done using a novel probabilistic
verification protocol in which O(log n) block headers are
downloaded by the client device from each chain and verified. Here
the concept of length is used to mean the number of blocks, for
ease of explanation. Below the problem can be formulated to include
the concept of total difficulty, to match with the actual
implementation in Bitcoin and Ethereum.
[0070] Next, two phases will be discussed. The first phase can be
prove, while the second phase is verify. The prove phase can be an
interactive protocol performed between the prover and the verifier
over O(log n) rounds to submit the proof of inclusion to the
verifier for a given interaction tx. In some embodiments, the prove
phase can be a non-interactive protocol to minimize latency, which
is described in further detail herein. The verify phase can be
executed locally by the verifier and does not require any
interaction between the prover and the verifier.
[0071] To generate a proof of longest chain, the two parties (i.e.,
the full node and the verifier) can participate in m=O(log n)
rounds of a probabilistic block sampling protocol. In each round
j.di-elect cons.[1,m], the verifier can send a random number
r.sub.j to the full node to request k random blocks from a certain
part of the full node's header chain. In some embodiments, the k
random blocks can be k=O(1), in other words, k can be a constant
number of blocks sampled in each round. The k random blocks can be
determined based on the random number r.sub.j. For example, if the
random number is equal to a value of 001002008010, then the full
node can select the four block headers of blocks 1, 2, 8, and 10.
As another example, the random number r.sub.j can be equal to a
value of 3469. The full node can select the blocks 3, 4, 6, and 9
based on the random number r.sub.j. The random number r.sub.j can
be in any suitable format. In other embodiments, the full node can
use the random value as an input to a function. The full node can
then select a number of random block headers based on the output of
the function.
[0072] If any of the k blocks are invalid, then the client device
can abort the process and blacklist the full node. In some
embodiments, the client device can verify that it received the
correct block headers based on the random number r.sub.j, for
example, block headers 3, 4, 6, and 9 when the random number
r.sub.j is 3469. Otherwise, the client device can proceed to the
next round of requests. In round j, the full node can split its
chain to 2.sup.j-1 equal-sized partitions. The full node can sample
k headers from the last partition, i.e., from the header at
height
n - n 2 j - 1 ##EQU00001##
to the header at height n. For example, if it is the second round,
j=2, and the current height of the blockchain is n=100, then the
full node can partition the blockchain into 2.sup.2-1=2 partitions.
The full node can sample k headers from the most recent partition,
i.e., the second partition, ranging from the height
1 .times. 0 .times. 0 - 1 .times. 0 .times. 0 2 2 - 1 = 5 .times. 0
##EQU00002##
the header at height n=100.
[0073] The benefit of sampling random block headers from
increasingly small partitions of the blockchain, allow the client
device to determine that the full node is not controlled by an
adversary. As the partitions decrease in size, the full node
selects random block headers that are more recent. In this way, the
client device, upon receiving the random block headers, can verify
more recent block headers than old block headers, thus preventing
adversaries from creating small falsified sidechains (e.g., at a
forking point in the blockchain).
[0074] To verify each block header, the client device can receive
an MMR proof from the full node and can then verify the proof using
the latest MMR root, M.sub.n-1, recorded in the header of the last
block, B.sub.n. To obtain the last proof (i.e., that the block has
been included in the longest chain), the client device can verify
an MMR proof which can be obtained from the last block header of
the longest chain (which is already proved). To obtain a proof that
the interaction was included in some block, the client device can
verify the Merkle proof provided by the full node against the root
of the interaction Merkle tree included the block header. This is
described in further detail below.
[0075] The intuition behind the probabilistic verification protocol
is that given any two blockchains of the same length, one of which
is maintained by an adversary with f<1/2 fraction of the honest
mining power, the probability that the adversary can mine the same
number of blocks as the honest miners reduces exponentially as the
valid chain grows. Thus, if the adversary has mined a certain
number of valid blocks in any partition and both chains have equal
lengths, the adversary must include a sufficient number of fake
blocks to "lengthen" the malicious chain.
[0076] Additionally, in some embodiments, a Fiat-Shamir heuristic
[Amos Fiat and Adi Shamir. How to prove yourself: Practical
solutions to identification and signature problems. In Conference
on the Theory and Application of Cryptographic Techniques, pages
186-194. Springer, 1986.] using the random oracle assumption can
make the probabilistic verification protocol non-interactive. In
the non-interactive protocol, the client device no longer sends a
random number in every round for the sampling of k block headers,
yet it is computationally intractable for the adversary to cheat
the client device. The non-interactiveness makes the process more
practical since (1) the full nodes can send the same proof to many
client devices without any recalculation; and (2) the client device
can forward the proof to other new client devices, which can safely
verify the correctness of the proof. This reduces both the
computation and bandwidth overheads for client devices and full
nodes.
[0077] The valid chain is the chain that requires more work to
find, e.g., the highest total block difficulty. The longest chain
rule is a simplified way of determining which chain is valid. In
what follows, for ease of explanation, it can be assumed that each
block has the same difficulty. However, it is understood that, in
some embodiments, each block can have a different difficulty.
D. System
[0078] FIG. 1 shows a system 100 comprising a number of components.
The system 100 comprises a client device 102, a full node 104, and
a prover 106. The client device 102 can be in operative
communication with the full node 104 and the prover 106. In some
embodiments, the client device 102 can be in operative
communication with any suitable number of full nodes, for example,
1, 2, 10, or 100 full nodes. However, for simplicity of
illustration, a certain number of components are shown in FIG. 1.
It is understood, however, that embodiments of the invention may
include more than one of each component.
[0079] The components in FIG. 1 may be in operative communication
with each other through any suitable communication channel or
communications network. Suitable communications networks may be any
one and/or the combination of the following: a direct
interconnection; the Internet; a Local Area Network (LAN); a
Metropolitan Area Network (MAN); an Operating Missions as Nodes on
the Internet (OMNI); a secured custom connection; a Wide Area
Network (WAN); a wireless network (e.g., employing protocols such
as, but not limited to a Wireless Application Protocol (WAP),
I-mode, and/or the like); and/or the like. Messages between the
computers, networks, and devices may be transmitted using a secure
communications protocols such as, but not limited to, File Transfer
Protocol (FTP); HyperText Transfer Protocol (HTTP); Secure
Hypertext Transfer Protocol (HTTPS), Secure Socket Layer (SSL), ISO
(e.g., ISO 8583) and/or the like.
[0080] The client device 102 can be a device capable of
communicating with a verification network. In some embodiments, the
client device 102 may be operated by a resource provider, and the
client device 102 may be a verifier. The client device 102 may also
be capable of receiving a verification request comprising an
interaction identifier from a prover 106. The client device 102 can
also determine a full node 104 that holds the longest blockchain,
and can verify that the interaction identifier is in a valid block
in the longest blockchain using information, such as an MMR root in
the latest block header, from the full node. The client device 102
can also verify that an interaction associated with the interaction
identifier is valid, and can transmit a verification response to
the prover 106 regarding the validity of the interaction.
[0081] The client device 102 can then perform additional processing
based on the interaction. Additional processing can include
performing an action or operation as indicated in the interaction
and/or transferring assets, physical and digital, between the
verifier and the prover as outlined in the interaction. For
example, the interaction can be a transaction between a resource
provider and a customer. The interaction can indicate that the
customer transferred assets, physical or digital, to the resource
prover. Upon verifying the interaction, as described herein, the
resource prover can provide a resource, as described in the
interaction, to the customer.
[0082] Any computer or device that connects to the verification
network can be referred to as a node. A node that can fully verify
each block and interaction in the blockchain can be a full node.
The full node 104 can store the full blockchain (i.e., each block
and each interaction) in a memory, and can be capable of proving
that it holds the longest blockchain. The full node 104 can also
receive queries for a current height of the blockchain and
subsequently determine and return the current height of the
blockchain. In some embodiments, the full node 104 can be capable
of partitioning the blockchain into a number of partitions and can
select random block headers from a particular partition.
[0083] In some embodiments, the prover 106 can be a client device
operated by a user. It could be, but need not be, a full node in
some embodiments. The prover 106 may transmit a verification
request regarding a previously performed interaction that was
stored on the blockchain to the client device 102. As an example,
the prover 106 can be a user or customer that wants to provide an
interaction identifier associated with a valid interaction to a
resource provider operating a client device 102 in order to prove
that the interaction occurred and is valid.
[0084] FIG. 2 shows a block diagram of a client device 200
according to some embodiments of the invention. The exemplary
client device 200 may comprise a processor 202. The processor 202
may be coupled to a non-transitory computer readable medium 204
comprising an interaction verification module 204A, a one or more
output elements 206, one or more input elements 208, a network
interface 210, and a secure memory 212.
[0085] The computer readable medium 204 may comprise code,
executable by the processor 202, to implement a method comprising:
receiving a verification request comprising an interaction
identifier; querying a full node for a random sampling of block
headers from the full node; receiving the random sampling of block
headers from the full node; verifying the random sampling of block
headers; and determining that the blockchain maintained by the full
node is valid after verifying the random sampling of block
headers.
[0086] The interaction verification module 204A may comprise
software code for verifying an Interaction. It may comprise
software code executable by the processor 202, to implement a
method comprising: verifying a Merkle proof received from a prover;
verifying a Merkle mountain range proof received from a prover;
determining if an interaction identifier corresponds to a valid
interaction based on verification of the Merkle proof and the
Merkle mountain range proof; and transmitting a verification
response indicating whether or not the interaction identifier
corresponds to the valid interaction.
[0087] The one or more output elements 206 may comprise any
suitable device(s) that may output data. Examples of output
elements 206 may include display screens, speakers, and data
transmission devices.
[0088] The one or more input elements 208 may include any suitable
device(s) capable of inputting data into the client device 200.
Examples of input devices include buttons, touchscreens, touch
pads, microphones, etc.
[0089] The network interface 210 may include an interface that can
allow the client device 200 to communicate with external computers.
The network interface 210 may enable the client device 200 to
communicate data to and from another device (e.g., resource
provider computer, authorization computer, etc.). Some examples of
the network interface 210 may include a modem, a physical network
interface (such as an Ethernet card or other Network Interface Card
(NIC)), a virtual network interface, a communications port, a
Personal Computer Memory Card International Association (PCMCIA)
slot and card, or the like. The wireless protocols enabled by the
network interface 210 may include Wi-Fi.TM..
[0090] Data transferred via the network interface 210 may be in the
form of signals which may be electrical, electromagnetic, optical,
or any other signal capable of being received by the external
communications interface (collectively referred to as "electronic
signals" or "electronic messages"). These electronic messages that
may comprise data or instructions may be provided between the
network interface 210 and other devices via a communications path
or channel. As noted above, any suitable communication path or
channel may be used such as, for Instance, a wire or cable, fiber
optics, a telephone line, a cellular link, a radio frequency (RF)
link, a WAN or LAN network, the Internet, or any other suitable
medium.
[0091] The secure memory 212 may store encrypted access data, key
identifiers, public keys, and any other relevant data securely. The
secure memory 212 may be in the form of a secure element, a
hardware security module, or any other suitable form of secure data
storage. In some embodiments, the client device 200 can store
information regarding a genesis block (i.e., the first block in a
blockchain).
E. Threat Model
[0092] An adversary may be present in the verification network
according to embodiments of the invention. The adversary may be an
adaptive (or rushing) adversary. As such, the adversary can choose
which full nodes in a verification network to corrupt and which
blocks to falsify in the blockchain. The mining power of the
adversary can be bounded by a known fraction, e.g.,
f(0<f<1/2).
[0093] In some embodiments, it can be assumed that the client
device is connected to at least one full node which has the correct
view of the blockchain. This assumption is equivalent to assuming
that the client device is not vulnerable to eclipse attacks.
Defending against such attacks is orthogonal of this work and has
been done by recent papers, see [Heilman et al, Eclipse attacks on
bitcoin's peer-topeer network. In 24th USENIX Security Symposium
(USENIX Security 15), pages 129-144, Washington, D.C., 2015. USENIX
Association] and [Gervais et al, Tampering with the delivery of
blocks and transactions in bitcoin. In Proceedings of the 22Nd ACM
SIGSAC Conference on Computer and Communications Security, CCS '15,
pages 692-705, New York, N.Y., USA, 2015. ACM.]. In some
embodiments, it can be assumed that the adversary cannot drop or
tamper with messages transmitted between the client device and full
nodes. The client device is not assumed to know any state in the
chain, except the genesis block (i.e., the first block).
II. MERKLE MOUNTAIN RANGE
[0094] A data structure called a Merkle mountain range (MMR) can be
leveraged to allow a client device to verify any previous
interaction using the latest block header. Merkle trees and Merkle
mountain ranges will be discussed next.
[0095] The need to download all block headers in prior work is, in
part, due to the verifications of interactions or events in all
previous blocks. After the longest chain has been verified and
accepted, with a few block headers downloaded, verification of an
interaction in some previous block may include verifying that the
block actually belongs to the longest chain. The naive approach is
to download all intermediate block headers from the block
containing the interaction to the latest block, which inherently
requires downloading a linear number of block headers from the
chain. However, embodiments of the invention improve upon this by
allowing for the verification of any interaction (i.e., obtain a
proof .pi..sub.rec(tx)) in the blockchain using the latest block
header of the latest block in the blockchain.
[0096] In a first solution to achieving this, a global Merkle tree
can be built on all interactions in the blockchain, i.e., every
interaction is included in the global Merkle tree. The global
Merkle tree can be updated after every new block is added to the
blockchain. However, such a solution requires miners to maintain
all interactions on the blockchain, which the miners often do not
do for performance reasons. This block verification also requires
full nodes to obtain all interactions and for the full nodes to
reconstruct the Merkle tree from scratch to keep the tree
balanced.
[0097] A Merkle tree can be a balanced binary tree where the leaves
of the tree hold some value, and each non-leaf node stores a hash
of a concatenation of the values of both children. In Bitcoin and
Ethereum, Merkle trees are used to store transaction hashes of a
particular block as the leaves, so the root of the tree is a
commitment of all interactions in that block. The root is then
stored in the header of the block. An SPV proof of an interaction
is then the Merkle proof that the hash of the interaction is a leaf
in the Merkle tree. Merkle trees and the security of a Merkle proof
is discussed as this will extend to a Merkle mountain range. An MMR
allows all previous blocks to be efficiently committed to the
latest block header in a single hash. MMR is a variant of the
original Merkle tree that allows a much more efficient update
process, thus the overhead for full nodes when processing blocks
becomes negligible. Further, introducing MMR only requires a mild
modification to the current Bitcoin and Ethereum protocol.
[0098] A Merkle tree can be defined as a balanced binary tree where
the leaves have some value, and each non-leaf node holds the value
H(left child.parallel.right child), where H is a
collision-resistant hash function. A balanced binary tree means a
tree with n leaves has a depth of O(log.sub.2 n).
[0099] Given a Merkle tree MT, with a root r, a Merkle proof that k
is a node in the Merkle tree MT can be .PI..sub.k.di-elect cons.MT.
The Merkle proof .PI..sub.k.di-elect cons.MT is a path from the
root r to the node k and the siblings of each node in the path.
Since the Merkle tree MT has a depth of O(log n), the proof has
size O(log n).
[0100] A prover verifier model, is defined below, where a verifier
knows the root of a Merkle tree and the prover wants to prove to
the verifier that a particular node exists in the tree. First, the
verifier has access to a root r of some Merkle tree MT. The prover
has access to the Merkle tree MT and can send a Merkle proof path
of some k e MT=.PI..sub.k.di-elect cons.MT to the verifier. The
verifier can check that the root r is the first value in the proof
(i.e. that the verifier was given a proof for the Merkle tree MT),
and that the hash of the two nodes at each level in the path (i.e.,
the hash of a node in the path with the node's sibling node) equals
the value of one of the nodes of the previous level. If the Merkle
proof is verified to be valid, the verifier can accept the proof,
otherwise the verifier can reject the proof.
[0101] Theorem 2. Given a Merkle tree MT, a polynomial-time
adversary cannot produce a valid Merkle proof .PI..sub.k.di-elect
cons.MT, for a node k not in the Merkle tree MT. A valid Merkle
proof means that an honest verifier will accept it. This can be
referred to as the soundness of Merkle proofs. As a proof, assume
that the adversary can produce a valid Merkle proof
.PI..sub.k.di-elect cons.MT. Let r be the root of Merkle tree MT,
the Merkle proof .PI..sub.k.di-elect cons.MT starts with the root
r, if it does not, the verifier can reject the Merkle proof. Since
kMT (i.e., the node k is not in the Merkle tree MT), the path the
adversary gives must have some initial depth i at which the path
differs from any true path in the Merkle tree MT.
[0102] Let p.sub.i' be a node in a path at level i and s.sub.i' be
its sibling, and let p.sub.i and s.sub.i be the true nodes in the
path in in the Merkle tree MT where x=p.sub.i.parallel.s.sub.i or
x=s.sub.i.parallel.p.sub.i such that H(x)=p.sub.i-1. In order for
the verifier to accept the Merkle proof .PI..sub.k.di-elect
cons.MT, x' must equal p.sub.i'.parallel.s.sub.i' or
s.sub.i'.parallel.p.sub.i' such that p.sub.i-1=H(x'). Since the
sets {p.sub.i,s.sub.i} and {p.sub.i',s.sub.i'} differ by at least
one value as stated above, x.noteq.x', therefore the adversary
found a collision of H(.perp.).
[0103] Theorem 3. Given a Merkle tree MT, and a node k.di-elect
cons.MT, a polynomial-time adversary cannot generate a Merkle proof
.PI..sub.k.di-elect cons.MT that is not a true path in the Merkle
tree MT. This is referred to as the completeness of Merkle proofs.
As a proof, similar to the proof of soundness above, if there is
some point in the path differentiates from a true path in the
Merkle tree MT, in order for it to be valid, the adversary must
have found a hash collision.
[0104] A more efficient solution leverages the recently introduced
data structure called a Merkle mountain range (MMR), see [Peter
Todd. Merkle mountain range.
https://github.com/opentimestamps/opentimestamps-server/blob/master/doc/m-
erkle-mountain-range.md], to commit to all previous block headers
in the latest block. Having this commitment allows a client device
to efficiently verify if a previous block belongs to the longest
chain based on the latest block header of the blockchain. Thus, the
full node can prove that an interaction was included in the longest
chain by providing an MMR proof (to prove that a block belongs to
the longest chain), in addition to the current Merkle proof (which
shows that the interaction is included in said block). Next, an
explanation of how MMR works and why it is better than a standard
Merkle tree will be discussed.
[0105] MMR is a variant of a Merkle tree that allows for efficient
appending of new data entries. MMR allows for the tree to be
reasonably balanced even when new data entries are appended
dynamically without rebuilding the entire tree from scratch.
Specifically, MMR appends a new data entry by modifying a few nodes
of the existing tree and still bounds the Merkle proof's length for
any data entry sitting on a leaf by log n, wherein n is the number
of leaves in the tree.
[0106] A Merkle mountain range M, can be defined as a binary hash
tree with n leaves, a root r, and the following properties: 1) M is
a hash tree; 2) M has depth [log.sub.2 n]; and 3) if n>1, let
n=2.sup.i+j for the maximum integer i such that 2.sup.i<n,
wherein r.left is an MMR with 2.sup.i leaves and wherein r.right is
an MMR with j leaves. The Merkle mountain range M is a balanced
binary hash tree, i.e., M is a Merkle tree. Therefore, for all
nodes k.di-elect cons.M,.E-backward..PI..sub.k.di-elect
cons.MT.
[0107] Appending new nodes to an MMR will now be discussed. Theorem
4. Given an MMR M, with root r and n leaves, a function
AppendLeaf(r,x) can return an MMR M', with n+1 leaves (the n leaves
of M plus a new leaf x added as the right-most leaf). An induction
proof, following, includes a base case of n=1 and an induction
step. In the base case (n=1), M is a single node r with depth 0.
r.children=0, so the function AppendLeaf can return a new node with
left=r and right=x, and value=H(x.parallel.r). This is a balanced
binary hash tree with 2 leaves and depth 1=log.sub.2 2 In the
induction step, assume the theorem holds for all M with <n
leaves. Let M be an MMR with n leaves and root r, AppendLeaf(r,x)
will return the following:
[0108] i) if n=2.sup.i for some i.di-elect cons., AppendLeaf
returns a new node r', with left=r, right=x, and
value=H(r.parallel.x). M' is the new tree with the three properties
of an MMR. The three properties being: 1) since M is a hash tree,
M' is also a hash tree; 2) Since the depth of M=log.sub.2 n, the
depth of M'=log.sub.2 n+1=[log.sub.2(n+1)]; and 3) n'=2.sup.i+1,
r'.left=M=an MMR with n'=2.sup.i leaves, and r'.right=x=an MMR with
1 leaf. The leaves of M' are the leaves of M plus x added as the
new right-most leaf.
[0109] ii) Otherwise, .E-backward.i,j.di-elect cons. such that
n=max.sub.i 2.sup.i+j, AppendLeaf returns r with r.left the same,
and r.right=AppendLeaf(r.right,x), and
value=H(r.left.parallel.r.right). M' is the new tree with the
following MMR conditions satisfied. (1 and 3) r'.left is an MMR by
definition with 2.sup.i leaves, r'.right is an MMR by the induction
hypothesis with j+1 leaves, thus M' is a hash tree. (2) M has depth
log.sub.2 2.sup.i=i.gtoreq.j, thus M' has depth
i+1=[log.sub.2(n+1)]. The leaves of M' are the leaves of
r'.left=r.left, then the leaves of r'.right which by the induction
hypothesis will be the original leaves of r.right plus x on the
right-most side.
[0110] Protocol 1, below, shows an example AppendLeaf(r,x) function
that can append a new data entry (i.e., x) to an existing MMR
(i.e., r). Protocol 1--AppendLeaf(MMR root r,new leaf node x):
TABLE-US-00001 1: if r.children = = a power of 2 then 2: root =
Node 3: return root 4: else 5: r.right = AppendLeaf(r.right,x) 6:
r.value = H(r.left.parallel.r.right) 7: r.children + + 8: return r
9: end if
[0111] FIG. 4 shows an example of updating a MMR tree when new data
entries are appended as new leaves of the tree. FIG. 4 includes a
first Merkle mountain range 402, a second Merkle mountain range
404. and a third Merkle mountain range 406. The white nodes can be
either new nodes or nodes that are changed due to a new data entry,
such as a new block header being appended as described herein. The
black nodes can be nodes that are not changed. MMR guarantees that
for every update, log n nodes are either created or modified.
[0112] The first Merkle mountain range 402 includes a first Merkle
mountain range root r0, a first block header L0, and a second block
header L1. The first block header L0 and the second block header L1
can be hashed together to determine the first Merkle mountain range
root r0.
[0113] A third block header L2, corresponding to a new, third block
that is added to the blockchain, can be appended to the Merkle
mountain range. Specifically, the third block header L2 is appended
to the first Merkle mountain range 402 resulting in the second
Merkle mountain range 404. The second Merkle mountain range 404 can
include the first block header L0, the second block header L1, and
the third block header L2. The first block header L0 and the second
block header L1 are not altered when appending the third block
header L2. Due to this, the hash of the first block header L0 and
the second block header L1 is the same in the first Merkle mountain
range 402 and the second Merkle mountain range 404. The first block
header L0 and the second block header L1 can be hashed together,
resulting in an intermediate value (that can be equivalent to the
first Merkle mountain range root r0). The intermediate value and
the third block header L2 can be hashed together, resulting in the
second Merkle mountain range root r1.
[0114] A fourth block header L3, corresponding to a new, fourth
block that is added to the blockchain, can be appended to the
Merkle mountain range. Specifically, the fourth block header L3 can
be appended to the second Merkle mountain range 404, resulting in
the third Merkle mountain range 406. The third Merkle mountain
range 406 can include the first block header L0, the second block
header L1, the third block header L2, and the fourth block header
L3. The first block header L0, the second block header L1, and the
third block header L2 are not altered when appending the fourth
block header L3. Due to this, the hash of the first block header L0
and the second block header L1 is the same in the first Merkle
mountain range 402, the second Merkle mountain range 404, and the
third Merkle mountain range 406. The first block header L0 and the
second block header L1 can be hashed together, resulting in a first
intermediate value (that can be equivalent to the first Merkle
mountain range root r0). Similarly, the third block header L2 and
the fourth block header L3 can be hashed together, resulting in a
second intermediate value. The first intermediate value and the
second intermediate value can be hashed together, resulting in the
third Merkle mountain range root r2. Any suitable number of block
headers can be appended to the Merkle mountain range in this
manner.
[0115] FIG. 4 also includes a larger Merkle mountain range 408. The
larger Merkle mountain range 408 can be created as new block
headers are appended to the third Merkle mountain range 406. The
larger Merkle mountain range 408 can be viewed as comprising three
smaller Merkle mountain ranges 408A, 408B, and 408C. As an example,
the next block header that is appended to the larger Merkle
mountain range 408 can be appended to the smaller Merkle mountain
range 408C. The three nodes in 408C can be appended similar to how
the first third block header L2 is appended to the first Merkle
mountain range 402 resulting in the second Merkle mountain range
404.
[0116] A set of MMRs can be defined as M={M.sub.1, M.sub.2, . . . ,
M.sub.n} created from some list [x.sub.1, x.sub.2, . . . ,
x.sub.n], where M, is a single node with value x.sub.1 and r.sub.i
is the root node of an i leaf MMR,
M.sub.i=AppendLeaf(r.sub.i-1,x.sub.i). A feature of the way MMRs
are constructed is that, assuming all x.sub.i's are unique, each
M.sub.i has a unique root (otherwise there would be a hash
collision), and given the Merkle proof that some x.sub.k is in
M.sub.n for k.ltoreq.n, .PI..sub.x.sub.k.sub..di-elect
cons.M.sub.n, a verifier can regenerate r.sub.k and that M.sub.k is
an ancestor of M.sub.n (i.e., M.sub.n was created from n-k appends
to M.sub.k).
[0117] This can be proved in the following theorem. Theorem 5. For
k.ltoreq.n, given an MMR proof .PI..sub.x.sub.k.sub..di-elect
cons.M.sub.n, i.e., the MMR proof that leaf x.sub.k is in M.sub.n,
a verifier can regenerate r.sub.k, the root of M.sub.k. An
induction proof, following, includes a base case of n=1 and an
induction step. In the base case (n=1), M.sub.1=Node(x.sub.1),
.PI..sub.x.sub.k.sub..di-elect cons.M.sub.n=[r.sub.1]. In the
induction step, assume the theorem holds for all M.sub.m, m<n
and k.ltoreq.m. Given M.sub.n, any k and .PI..sub.k.di-elect
cons.M.sub.n=[r.sub.n, r.sub.n.left, r.sub.n.right, . . . ], if k=n
then r.sub.k=r.sub.n. Otherwise, let i be the maximum integer such
that n=2.sup.i+j where j>0. There can be three possibilities: 1)
k=2.sup.i, r.sub.k=r.sub.n.left; 2) k<2.sup.i, thus x.sub.k is
in the left subtree of M.sub.n. Let n'=2.sup.i and
r.sub.n'=r.sub.n.left, we get that .PI..sub.x.sub.k.sub..di-elect
cons.M.sub.n'=.PI..sub.x.sub.k.sub..di-elect
cons.M.sub.n-[r.sub.n,r.sub.n.right]. Since n'<n, by the
induction hypothesis we can get r.sub.k from
.PI..sub.x.sub.k.sub..di-elect cons.M.sub.n'. 3) k>2.sup.i, thus
x.sub.k is in the right subtree of M.sub.n. Since k<n and i is
the maximum integer such that n=2.sup.i+j for some j>0, i is
also the maximum integer such that k=2.sup.i+j' for some j'>0.
Thus r.sub.k.left=r.sub.n.left. Note r.sub.n.right is the MMR
M.sub.j where k is the k'=k-2.sup.i=j'th leaf. Thus,
r.sub.k.right=M.sub.k' and .PI..sub.x.sub.k'.sub..di-elect
cons.M.sub.j=.PI..sub.x.sub.k.sub..di-elect
cons.M.sub.n-[r.sub.n,r.sub.n.left]. By the induction hypothesis
r.sub.k' can be extracted from .PI..sub.x.sub.k'.sub..di-elect
cons.M.sub.j. The verifier can hash the left and right roots to get
the value of r.sub.k.
[0118] Unlike classical Merkle trees, MMR's additionally give the
ability to prove that an MMR is the previous version of another MMR
with a short proof. That is, given the k-th MMR and the nth MMR, a
prover can give a proof of size O(log(n)) that convinces a verifier
of this fact while the verifier's state is k,n and the root of the
k-th and n-th MMRs. This property is formalized below in Lemma
1.
[0119] Lemma 1 (MMR inclusion proof). Given a list of n MMRs which
are consecutively built based on a list of n numbers, one can prove
that any k-MMR (0.ltoreq.k.ltoreq.n) is a precedent of the n-MMR
with a proof of size O(log n).
[0120] A new block header, according to embodiments of the
invention, can contain a data field for an MMR root, or the root of
the MMR tree that commits the headers of all previous blocks. A
full node, upon receiving a new block, can conduct one additional
check on the validity of the MMR root. This entails a negligible
overhead on the full node.
[0121] FIG. 5 shows a blockchain structure according to embodiments
of the invention. An MMR root M.sub.n 502 can represent the latest
MMR root that is included in the latest block header (not shown) at
the chain head 508. A Merkle mountain range 504 can comprise a
number of leaves. Each leaf of the Merkle mountain range 504 can be
a block header 506. In FIG. 5, the Merkle mountain range 504
includes three block headers, however, it is understood that the
Merkle mountain range 504 can include any suitable number of block
headers 506, such as 5 block headers, 10 block headers, 100 block
headers, 1,000 block headers, or 100,000 block headers.
[0122] The block headers 506 include a plurality of block headers
associated with a plurality of blocks. Each of the block headers
506 can comprise a MMR root 510, a Merkle root 512, a previous hash
518, a nonce 520, and a timestamp 522. The chain head 508 can be
the block header 506 that is associated with the latest block. The
block header at the chain head 508 can be the latest block header
(not shown). The nonce 520 can be used to calculate if the previous
hash 518 contains a string of leading zeros such that it is lower
than a difficulty value. The Merkle root 512, the nonce 520, the
previous hash 518, and the timestamp 522 can be inputs to a hash
function. In some embodiments, the MMR root 510 can also be an
input to the hash function. The output of the hash function is
valid if the output is less than or equal to a difficulty value. If
the resulting previous hash 518 is lower than the difficulty value,
then the block is a valid block. The timestamp 522 can be a
sequence of characters or encoded information identifying when a
certain even occurred, such as when a block is created and added to
the blockchain.
[0123] The MMR root 510 can be an MMR root of the MMR that commits
the block headers of all of the previous blocks. For example, the
MMR root at the chain head 508 (i.e., M.sub.n) can be the MMR root
of the MMR that commits the first block header, the second block
header, and the third block header. The Merkle root 512 can be a
root of a Merkle tree 514 which is a tree, as described herein, in
which every leaf node is labelled with the hash of an interaction
516. Each leaf of the Merkle tree can represent an interaction 516.
The interaction 516 can be associated with an interaction
identifier. The interaction 516 can be any suitable interaction.
For example, a suitable interaction can be a transaction, an
agreement, a communication, or any other suitable interaction as
described herein. As an example, the interaction 516 can be a
transaction that can include information such as the parties
involved, a list of transaction inputs, a list of transaction
outputs, a fee, a timestamp, a transaction identifier, and/or the
like. As another example, an interaction can be an agreement that
can include information such as the parties involved, details of
the agreement (e.g., text), a digital signature of each party
involved, a timestamp, a fee, and/or the like.
III. PROBABILISTIC VERIFICATION OF NON-MALICIOUS FULL NODE
[0124] In order to reduce the number of block headers that client
devices need to download, embodiments of the invention can employ a
probabilistic verification mechanism by which a client device can
randomly sample a logarithmic number of block headers. If these
block headers are valid, then the block B belongs to the longest
chain with high probability. The client device can determine which
block headers to sample to prevent the adversary from sampling fake
blocks. The probabilistic verification allows for the client device
to detect at least one fake block with high probability, if there
is a known fraction f.sub.b of blocks are fake, after randomly
sampling enough number of blocks.
A. Naive Approach
[0125] If the longer chain was created by a cheating prover and the
cheating prover was able to pass an initial fact check, such as
verifying a predetermined number of the most recent blocks, then
the client device can conclude that the latest possible forking
point was on or before height
L c , ##EQU00003##
wherein L is the predetermined number of the most recent blocks and
c is the malicious full node's fraction of the total mining power.
Given that f.sub.b is established, probabilistic verification can
be conducted to detect at least one fake block in an invalid chain
with high probability. Specifically, by randomly sampling K blocks
from the invalid chain, the probability that all sampled blocks are
valid blocks is (1-f.sub.b).sup.K. Hence, the probability that at
least one invalid block is sampled is:
1-(1-f.sub.b).sup.K
[0126] This probability approaches 1 quickly as K grows. Note that
a client device can check if a sampled block belongs to the
committed chain (i.e., on the same chain with the L blocks in the
initial fact check step) based on the MMR commitment in the last
block.
[0127] To evaluate the performance of the naive approach, the
client device can minimize the sum L+K, i.e., the total number of
blocks to download. O( {square root over (n)}) is the minimum value
of L+K that still gives the client device a high probability
guarantee. For example, given the Ethereum blockchain with
4,000,000 blocks, one needs to download 18,000 block headers and
their proofs to verify if they are on the correct chain. Given that
each block header is of size 500 bytes and its proof is of size
7,000 bytes (log n SHA2 hashes), the total data required to
download is still significant (i.e., 120 MB) to client devices.
B. Approach According to Embodiments of the Invention
[0128] Although the naive approach significantly reduces the number
of block headers to download, it still requires a large number of
block headers. A goal is to reduce the number of block headers
download by the client device to a much smaller value, for example
O(log n) block headers. It can now be shown that this is possible
by recursively sampling more and more block headers, by a client
device, from different intervals of the blockchain maintained by a
full node. The goal is to ensure that in each interval of the chain
a cheating prover (i.e., a malicious full node) would have to at
least create a fraction of the blocks. However, if this fraction is
larger than the fraction of the mining power the malicious full
node controls then producing these blocks will take longer than the
honest network will take to create the blocks. This ensures that
the honest network creates the blocks before the malicious full
node
[0129] If the longest chain was created by a malicious full node
and the malicious full node was able to pass the initial fact
check, then the client device can determine that the latest
possible forking point was on or before height
L c . ##EQU00004##
The malicious full node will be unable to include any honest
chain's blocks in its own blockchain (other than the genesis
block). This can be done by iteratively pushing back the latest
block the malicious full node could have forked off of.
[0130] In some embodiments, the method defines a fraction k such
that k>c. The verifier can sample random blocks out of the
first
L c ##EQU00005##
blocks to ensure that either a cheating prover will be caught or
that the cheating prover had to create at least a fraction of k
them honestly. The verifier can sample a constant number of blocks.
Concretely, to ensure that with probability 1-2.sup.-.lamda. at
least a k fraction of the blocks were created, the prover can
sample .left brkt-top.-log.sub.k(2).lamda..right brkt-bot. random
blocks. For each block, the verifier verifies that the block's MMR
is correctly included in the header's MMR and that the proof of
work meets the difficulty value, as described herein.
[0131] Assuming that the malicious node created a k fraction of the
first
L c ##EQU00006##
blocks but had a c fraction of the mining power it can be
determined that that it took the malicious full node
L k c 2 > L c ##EQU00007##
honest chain block intervals to do this. This, however, implies
that the latest possible forking point from the honest chain was at
H
H - L k c 2 . ##EQU00008##
This
[0132] process can be repeated m times to ensure that the forking
point was before
H - L c k m c ##EQU00009##
until it can be ensured that the forking point had to be before the
genesis block. This is a contradiction as the genesis block is
committed to in the header's MMR and also because the main chain
only exists from the genesis block on. Thus, it is not possible for
the malicious node to create blocks that occur before the genesis
block. Note that this will take
log k c .function. ( H c L ) = log 2 .function. ( H c L ) log 2
.function. ( k c ) = O .function. ( log .function. ( H ) )
##EQU00010##
iterations. In each iteration, a constant number of MMR proof
verifications can be performed as well as a constant number of
difficulty checks. Since the MMR proof verifications are O(log(H))
in size the asymptotic communication complexity of the protocol is
O(log(H).sup.2).
[0133] Next, the source of randomness will be discussed. Since the
probabilistic verification uses randomness for sampling, one
solution is for the client device to send the randomness to the
full node. The full node can then use the randomness to sample K
blocks and send them back to the client device. This prevents the
full node from biasing the sampled blocks and avoiding the
detection of invalid blocks. However, this mechanism requires
interaction between the client device and the full node. Further,
the client device and the full node cannot forward the proof to
other client devices as the client device and the full node cannot
prove that the randomness is actually random. The mechanism to make
embodiments of the invention non-interactive, i.e., removing the
randomness exchange step between the client device and the full
node, will be discussed in further detail below.
[0134] 1. Probabilistic Sampling
[0135] Recall that in the probabilistic sampling model the verifier
requests the MMR proof for k random block headers in the blockchain
from a full node. The full node can successively partition the
blockchain in half and queries another random k block headers from
the partition that includes the latest block header. The verifier
does this until the size of the partition is at most k (i.e.,
queries all of the last k blocks). The adversary's computing power
is less than the honest network's computing power therefore in
order to fool the verifier that the malicious full node has a
blockchain equal length to an honest full node's blockchain, the
malicious full node must insert bad blocks into their chain, i.e.,
blocks without proper proofs work.
[0136] Theorem 8. The probability the verifier fails (i.e. does not
sample any bad block) is
.ltoreq. ( 1 + c 2 ) k . ##EQU00011##
Proof. Let n be the length of the chain and c be the fraction of
computing power of the adversary relative to the honest computing
power. At any round i in the protocol, the verifier can sample
block headers from block
n 2 ##EQU00012##
to block n in the blockchain. Let h.sub.i be the number of bad
blocks the adversary has in the interval. Thus the probability the
verifier fails to sample a bad block in round i is
Pr .function. [ fail ] = P i = ( n 2 i - h i n / 2 i ) k = ( n - 2
i .times. h i n ) k . ##EQU00013##
The probability the verifier fails is then
Pr[fail]=.PI..sub.i+0.sup.log.sup.2 .sup.n P.sub.i. Since each
P.sub.i is .ltoreq.1, if one P.sub.i is small, then the probability
of failure is small.
[0137] Let a be the point at which the adversary forks from the
mainchain, there is some i such that
n 2 i .times. < .times. a < n 2 i + n 2 i + 1 .
##EQU00014##
In other words, there is some sampled interval of size
n ' = n 2 i ##EQU00015##
in the protocol where the adversary's forking point lies between
the start of the interval and the midpoint of the interval. Let l
be the length from a to n, i.e. the length of the adversary's
fork,
l > n 2 i . ##EQU00016##
The number of bad blocks in the interval,
h i = ( 1 - c ) .times. l .gtoreq. ( 1 - c ) .times. n ' 2 .
##EQU00017##
Thus, the probability that the verifier fails to catch the
adversary is at most the probability the verifier fails at step i,
i.e.,
Pr [ fail ] .ltoreq. Pr [ fail .times. .times. at .times. .times. i
] .ltoreq. ( n ' - ( 1 - c ) .times. n ' 2 n ' ) k = ( 1 + c 2 ) k
. ##EQU00018##
Note if l.ltoreq.k, the verifier will sample all the adversary's
bad blocks and Pr[fail]=0.
[0138] 2. Method
[0139] FIG. 6 shows a flowchart of a longest chain verification
method according to an embodiment of the invention. The method
illustrated in FIG. 6 will be described in the context of a client
device determining a full node, that maintains the longest
blockchain, out of a plurality of full nodes. Although the steps
are illustrated in a specific order, it is understood that
embodiments of the invention may include methods that have the
steps in different orders. In addition, steps may be omitted or
added and may still be within embodiments of the invention.
[0140] Before step S602, the client device can receive a
verification request from a prover, such as a full node or another
client device. The verification request can comprise an interaction
identifier and, in some embodiments, a Merkle proof associated with
the interaction identifier. The interaction identifier can be a
unique identifier for an interaction. The interaction identifier
(ID) can be, for example, a string of alphanumeric characters, a
randomly assigned number, a sequentially assigned number, values
corresponding to an interaction, a combination thereof, and/or the
like. The Merkle proof can include a path from a Merkle root of a
Merkle tree of interactions to a node associated with the
interaction identifier as well as siblings of each node in the
path, as described herein. In some embodiments, the verification
request can further comprise a Merkle mountain range proof
including a path from a Merkle mountain range root to a leaf node
associated with a block header containing the Merkle tree as well
as siblings of each node in the path, as described herein.
[0141] A Merkle tree 1000 is shown in FIG. 10. The Merkle tree 1000
can comprise a number of leaf nodes such as A, B, C, D, E, F, G,
and H. A Merkle proof for an interaction identifier associated with
the leaf node E can include a path from the Merkle root ABCDEFG to
the leaf node E including the nodes ABCDEFG, EFGH, EF, and E (shown
in as the bolded nodes and connection lines in FIG. 10). The Merkle
proof can also include the sibling nodes of the nodes in the path.
In this example, the sibling nodes include the nodes ABCD, GH, and
F (indicated in FIG. 10 by dashed lines).
[0142] After receiving the verification request from a prover, the
client device can determine a full node that has the longest chain
on the blockchain. To determine which full node of a plurality of
full nodes has the longest chain, the client device can perform the
following steps.
[0143] At step S602, the client device can query the plurality of
full nodes for current heights of the blockchains maintained by the
full nodes. The client device can request the current height of the
blockchain n from any suitable number of full nodes in the
verification network. The current height of the blockchain n can be
the current number of blocks in the blockchain (e.g., 100 blocks,
500 blocks, 1000 blocks, 10,000 blocks, or any other suitable
number of blocks). A height of a blockchain can also be referred to
as the length of the blockchain. In some embodiments, the client
device may query every full node in communication range of the
client device. In other embodiments, the client device can query a
predetermined number of full nodes, for example, 10 full nodes, 100
full nodes, 500 full nodes, 1000 full nodes, or any suitable number
of full nodes. The current height of the blockchain n may be
different at each full node. A malicious full node can arbitrarily
choose the current height of the blockchain n.
[0144] At step S604, after querying the plurality of full nodes for
the current height of the blockchain n, the client device can
receive a plurality of current heights of the blockchain from the
full nodes.
[0145] At step S606, the client device can determine a full node
from among the plurality of full nodes. The client device can
determine which full node reported the correct current height of
the blockchain n. In some embodiments, more than one full node may
have reported the correct current height of the blockchain n. To
determine the correct current height of the blockchain n, the
client device can determine a most frequent height of the plurality
of current heights. For example, the client device can receive 10
values for the current height of the blockchain n from ten
different full nodes, 7 of which can be equal to a height of n=100,
1 of which can be equal to a height of n=95, and 2 of which can be
equal to a height of n=101. The client device can determine the
most frequent height to be n=100. After determining the most
frequent height, the client device can select a full node of the
plurality of full nodes that reported the current height comparable
to the most frequent height, i.e., a full node with a current
height of n=100.
[0146] At step S608, after determining the full node, the client
device can query the full node for a random sampling of block
headers. The query can include a random number r.sub.j and a round
number. The random number r.sub.j can be any suitable random
number. The round number can correspond to the number of times the
client device has requested the random sampling of block headers
from the full node. The round number can be any suitable integer.
For example, the round number can be 1 for the first time that the
client device transmits a request to the full node. The full node
can determine the random sampling of block headers, as described
herein, and transmit the random sampling of block headers to the
client device. In some embodiments, after the full node receives
the query for the random sampling of block headers, the full node
can partition the blockchain maintained by the full node into an
equally sized number of partitions based on the round number. The
full node can then select the random sampling of block headers from
a most recent partition based on the random number, and then
transmit the random sampling of block headers to the client device.
The partitioning of the blockchain is described in further detail
below.
[0147] At step S610, the client device can receive the random
sampling of block headers from the full node. In some embodiments,
the client device can receive a plurality of Merkle mountain range
proofs from the full node. The random sampling of block headers can
be determined by the full node as described herein. Each MMR proof
of the plurality of MMR proofs can be include a path from a Merkle
mountain range root to a node in the MMR associated with one of the
block headers of the random sampling of block headers, as well as
include a sibling node of each node in the path.
[0148] For example, in reference to the third Merkle mountain range
406 of FIG. 4, the client device can receive a block header of a
fourth block in the blockchain (i.e., the fourth block header L3)
as a part of the random sampling of block headers. The client
device can also receive an MMR proof for the fourth block header L3
that includes a path from the MMR root r2 to the fourth block
header L3. The path can include each of the white nodes in the
third Merkle mountain range 406 of FIG. 4; this includes the MMR
root r2, I2 (i.e., the hash of the third block header L2 and the
fourth block header L3), as well as the fourth block header L3. The
MMR proof also includes the sibling node to each node in the path.
The MMR root r2 does not have a sibling node, as it is the root of
the third Merkle mountain range 406. The sibling node of I2 (i.e.,
the hash of the third block header L2 and the fourth block header
L3 is I1 (i.e., the hash of the first block header L0 and the
second block header L1. The sibling node of the fourth block header
L3 is the third block header L2. In the example of the third Merkle
mountain range 406 in FIG. 4, the client device receives each node
in the third Merkle mountain range 406 except the two nodes of the
first block header L0 and the second block header L1.
[0149] At step S612, after receiving the random sampling of block
headers from the full node, the client device can verify the block
headers. In some embodiments, the client device can verify the
block headers by verifying the validity of the previous hash value
and the nonce (e.g., the PoW solution) of each block header, as
described herein. The nonce can be used to calculate if the
previous hash contains a string of leading zeros such that it is
lower than a difficulty value. If the resulting previous hash is
lower than the difficulty value, then the client device can
determine that the block header is a valid block header. The Merkle
root, the nonce, the previous hash, and the timestamp included in
the block header can be inputs to a hash function. In some
embodiments, the MMR root can also be an input to the hash
function. The output of the hash function is valid if the output is
less than or equal to a difficulty value.
[0150] At step S614, after verifying the validity of the PoW of
each block header of the random sampling of block headers, the
client device can verify the validity of the MMR proof for each
block header. The client device can verify that each node in the
path with two child nodes is equal to the hash of that node's two
child nodes. For example, the client device can verify that the
node I2 is equal to the hash of both the third block header L2 and
the fourth block header L3. The client device can also verify that
the MMR root r2 is equal to the hash of I1 and I2. In this way, the
client device verifies that each block header of the random
sampling of block headers is in the blockchain at the full node.
The client device can also verify that the start of the path in the
MMR proof is the MMR root in the latest block header.
[0151] At step S616, the client device can determine if all of the
block headers of the plurality of random block headers and the
plurality of Merkle mountain range proofs are valid. If any one of
the block headers or the Merkle mountain range proofs is not valid,
then the client device can perform steps S606 to S616 again with a
different full node, for example, with a second full node. In some
embodiments, the client device can add the full node to a stored
list of malicious full nodes, for example by adding an IP address,
or other full node identifier, of the malicious full node to a
list. The client device can determine not to communicate with full
nodes that are in the list of malicious full nodes.
[0152] If the block headers and the Merkle mountain range proofs
are valid, then the client device can proceed to step S618. At step
S618, the client device can determine if the round number is equal
to a predetermined number of rounds. The predetermined number of
rounds can be any suitable integer. In some embodiments, the
predetermined number of rounds can be log n rounds, as described
herein, wherein n is the current height of the blockchain. If the
round number is less than the predetermined number of rounds, the
client device can proceed to step S620. If the round number is
equal to the predetermined number of rounds, the client device can
proceed to step S622.
[0153] At step S620, the client device can update the round number.
For example, If the round number is equal to 1, then the client
device can update the round number to be equal to 2. The client
device can then perform steps S608 to S618 again.
[0154] At step S622, after determining that the round number is
equal to the predetermined number of rounds, the client device can
determine that the full node has the longest chain, as the client
device has verified block headers during each round with the full
node.
[0155] FIG. 7 shows a flowchart of a longest chain verification
method performed by a full node according to an embodiment of the
invention. The method illustrated in FIG. 7 will be described in
the context of a full node receiving queries from a client device.
It is understood, however, that the invention can be applied to
other circumstances such as a full node proving that it holds the
longest blockchain. Although the steps are illustrated in a
specific order, it is understood that embodiments of the invention
may include methods that have the steps in different orders. In
addition, steps may be omitted or added and may still be within
embodiments of the invention.
[0156] At step S702, the full node can receive a query for the
current height of the blockchain n from a client device. At step
S704, after receiving the query for the current height of the
blockchain n, the full node can determine the current height of the
blockchain n. The full node can determine the current height of the
blockchain n in any suitable manner. For example, the full node can
determine the number of blocks in the blockchain. In some
embodiments, the full node can determine the number of block
headers in the blockchain.
[0157] At step S706, after determining the current height of the
blockchain n, the full node can transmit the current height of the
blockchain n to the client device. The client device, after
receiving the current height of the blockchain n, can then
determine that the current height of the blockchain reported by the
full node is comparable to the most frequent height of a plurality
of heights received by the client device from a plurality of full
nodes.
[0158] At step S708, the full node can receive a query, from the
client device, for a random sampling of block headers. The query
can include a random number. In some embodiments, the query can
include a random number and a round number (i.e., an iteration
number). At step S710, the full node can partition the blockchain
into a number of partitions based on how many queries for the
random sampling of block headers have been received. In some
embodiments, the full node can partition the blockchain into a
number of partitions based on the round number received by the
client device. Each partition of the blockchain can contain the
same number of blocks, for example, three partitions each including
10 blocks. In some embodiments, each partition of the blockchain
can contain a comparable number of blocks, for example, a first
partition including 100 blocks and a second partition including 101
blocks. If the round number is equal to 1, for example, the full
node can partition the blockchain into 1 partition, i.e., the
partition will include the full blockchain.
[0159] At step S712, after partitioning the blockchain into a
number of partitions, the full node can select a plurality of
random block headers from the last partition. The last partition
can be the partition that includes the latest block header. The
plurality of random block headers can comprise any suitable number
of random block headers. The full node can determine the number of
random block headers based on the random number received from the
client device. For example, if the random number is equal to a
value of 7, then the full node can select 7 random block headers.
In other embodiments, the full node can use the random value as an
input to a function. The full node can then select a number of
random block headers based on the output of the function.
[0160] If the round number is equal to 5 and the current height of
the blockchain is n=300, for example, then the full node can
partition the blockchain into 5 partitions, each of the 5
partitions including 60 blocks. The full node can select a
plurality of random block headers from the last partition of 60
blocks. In the next round, the round number will be equal to 6.
During this round, the full node can partition the blockchain into
6 partitions, each of the 6 partitions including 50 blocks. The
full node can then select a plurality of random block headers from
the last partition of 50 blocks. In a certain round (e.g., a final
round), the last partition of blocks will include the same number
of blocks that the full node is selecting as the random block
headers. Due to this, the full node will select the most recent
number of block headers, including the latest block header. This
method of random sampling allows the full node to select and
transmit random block headers to the client device as well as the
most recent number of block headers, including the latest block
header.
[0161] In each subsequent round (i.e., iteration), the full node
samples from a smaller and more recent partition of the blockchain.
An adversary (i.e., malicious full node) could falsify chain of
blocks by creating a fork from the longest chain. The more blocks
that the adversary includes in the falsified chain requires more
computing power. An adversary may not have large amounts of
computing power, and may only be able to falsify shorter chains.
These shorter chains will have forks closer to the latest block in
the blockchain. As such, the iterative random block header
sampling, described herein, allows the client device to verify an
increasing number of newer block headers as the partition decreases
in size over each iteration. In this way, the client device is
likely to catch a falsified shorter chain. During the last round,
the client device can receive and verify the most recent number of
block headers.
[0162] At step S714, the full node can determine a plurality of
Merkle mountain range proofs, one MMR proof for each of the random
block headers. The full node can determine each node in the MMR
that is in a path from the MMR root to the random block header. The
path can include each node that is between the MMR root and the
random block header in the MMR. The MMR proof can also include the
sibling node of each of the nodes in the path. The full node can
determine each sibling node of each node in the path in the MMR.
The full node can include the path and the sibling nodes in the MMR
proof.
[0163] At step S716, after determining the plurality of Merkle
mountain range proofs, the full node can transmit the plurality of
random block headers and the plurality of Merkle mountain range
proofs to the client device. At step S718, the full node can
determine if another query has been received. The full node can
receive another query for a random sampling of block headers. This
next query can include a round number equal to a value of 1 larger
than the previous round number. The full node can repeat steps S708
to S716 any suitable number of times, as described herein. If the
full node does not receive another query for a random sampling of
block headers, then the full node can end the process.
[0164] FIG. 8 shows a flowchart of an interaction verification
method according to an embodiment of the invention. The method
illustrated in FIG. 8 will be described in the context of a client
device receiving a verification request from a prover and
proceeding to determine that an interaction is valid. It is
understood, however, that the invention can be applied to other
circumstances (e.g., verifying that an interaction such as an
agreement, contract, transaction, or the like is valid, etc.).
Although the steps are illustrated in a specific order, it is
understood that embodiments of the invention may include methods
that have the steps in different orders. In addition, steps may be
omitted or added and may still be within embodiments of the
invention.
[0165] At step S802, the client device can receive a verification
request. The verification request can be received from a prover. In
some embodiments, the prover can a full node. In other embodiments,
the prover can be a client device. The verification request can
comprise an interaction identifier and, in some embodiments, a
Merkle proof and a Merkle mountain range proof. The interaction
identifier can be a unique identifier for an interaction. The
interaction identifier (ID) can be, for example, a string of
alphanumeric characters, a randomly assigned number, a sequentially
assigned number, values corresponding to an interaction, a
combination thereof, and/or the like. The Merkle proof can include
a path from a Merkle root to a node associated with the interaction
identifier as well as siblings of each node in the path, as
described herein. The Merkle mountain range proof can include a
path from a Merkle mountain range root to a node associated with a
block header containing the Merkle tree as well as siblings of each
node in the path, as described herein.
[0166] In some embodiments, the verification request can include a
Merkle proof comprising a first path and a first plurality of
sibling nodes. The first path can include a first plurality of
nodes in a Merkle tree from a Merkle root to a first node. The
first node can be associated with the interaction identifier. The
verification request can also include a Merkle mountain range proof
comprising a second path and a second plurality of sibling nodes.
The second path can include a second plurality of nodes in a Merkle
mountain range from a Merkle mountain range root to a second node.
The second node can be associated with a block header containing
the interaction identifier.
[0167] At step S804, after receiving the verification request, the
client device can determine a full node that has the longest chain
on the blockchain, as described herein, during which, the client
device can receive the latest block header during the last round of
querying for the sampling of random block headers.
[0168] At step S806, after determining the longest chain maintained
by an honest full node as well as receiving the latest block
header, the client device can verify the Merkle proof received in
the verification request. The client device can verify the Merkle
proof by verifying that each node in the path, included in the
Merkle proof, with two child nodes is equal to the hash of that
node's two child nodes, as described herein. The client device can
also verify that the interaction identifier is the leaf node of the
path.
[0169] The client device can verify the MMR proof received in the
verification request, as described herein. The client device can
verify the MMR proof by verifying that each node in the path,
included in the MMR proof, with two child nodes is equal to the
hash of that node's two child nodes. The client device can also
verify that the block header is the leaf node of the path, wherein
the block header contains the Merkle root of the Merkle tree.
[0170] At step S808, if either the Merkle proof or the Merkle
mountain range proof are not valid, the client device can proceed
to step S810. At step S810, the client device can determine that
the prover has provided an incorrect proof and terminate the
connection with the prover. In some embodiments, the client device
can add the IP address, or other suitable identifier, of the prover
to a list of known malicious devices.
[0171] If the Merkle proof and the Merkle mountain range proof are
valid, the client device can proceed to step S812. The client
device can determine that the interaction identifier provided by
the prover corresponds with a valid interaction. At step S812, the
client device can perform additional processing. Additional
processing can include performing an action or operation as
indicated in the interaction and/or transferring assets, physical
and digital, between the verifier and the prover as outlined in the
interaction.
[0172] FIG. 9 shows a flowchart of a longest chain verification
method according to an embodiment of the invention. The method
illustrated in FIG. 9 will be described in the context of a client
device determining a full node, that maintains the longest
blockchain, out of a plurality of full nodes, and then verifying an
interaction associated with an interaction identifier received from
a prover. Although the steps are illustrated in a specific order,
it is understood that embodiments of the invention may include
methods that have the steps in different orders. In addition, steps
may be omitted or added and may still be within embodiments of the
invention.
[0173] The method in FIG. 9 can be performed by a prover 902, a
client device 904, and a plurality of full nodes. The prover 902
can be a client device or a full node. In some embodiments, the
prover 902 can be a full node that the client device 904
communicates with during steps S918-S928.
[0174] At step S902, the prover 902 can transmit a verification
request to the client device 904. The verification request can
comprise an interaction identifier, a Merkle proof, and a Merkle
mountain range proof. The interaction identifier can be associated
with a previously performed interaction, which may, in some
embodiments, be an interaction that was performed between the
prover 902 and the client device 904. The Merkle proof can comprise
a path and sibling nodes as described herein. The Merkle proof can
be used to determine if an interaction is in a block. The Merkle
mountain range proof can comprise a path and sibling nodes as
described herein. The Merkle mountain range proof can be used to
determine if a block is in a blockchain.
[0175] At step S904-S908, after receiving the verification request,
the client device 904 can query a plurality of full nodes 906 for
current heights of blockchains maintained by the full nodes.
[0176] At step S910-S914, after the plurality of full nodes 906
receive the query for the current height of the blockchain, each of
the full nodes of the plurality of full nodes 906 can return the
height of the blockchain. The client device 904 can receive a
plurality of current heights.
[0177] At step S916, after receiving a plurality of current
heights, the client device 904 can determine a full node from among
the plurality of full nodes 906. The client device 904 can
determine that the full node returned a current height that is
consistent with a most frequently returned current height from the
plurality of full nodes 906.
[0178] At step S918, the client device 904 can query the full node
for a random sampling of block headers as well as a plurality of
MMR proofs, one MMR proof for each of the block headers of the
random sampling of block headers.
[0179] At step S920, the client device 904 can receive the random
sampling of block headers as well as a MMR proof for each of the
block headers.
[0180] At step S922, after receiving the random sampling of block
headers, the client device 904 can verify the validity of each
block header of the random sampling of block headers. The client
device 904 can verify that the proof-of-work solution of each block
header is valid. For example, the client device 904 can verify that
the nonce and the previous hash value solve a hash function such
that the solution is less than a predetermined number such as a
difficulty level.
[0181] At step S924, the client device 904 can verify the validity
of the plurality of MMR proofs received from the full node. The
client device 904 can verify the validity of the MMR proof for each
block header. The client device can verify that each node in the
path with two child nodes is equal to the hash of that node's two
child nodes, as described herein. The client device 904 can also
verify that the start of the path in the MMR proof is the MMR root
in the latest block header.
[0182] At step S926, after verifying the random block headers and
the plurality of MMR proofs, the client device 904 can repeat steps
S918-S924 any suitable number of times until a round number is
equal to a predetermined number of rounds, for example, 5 rounds,
15 rounds, 40 rounds, or any other suitable number of rounds. In
some embodiments, the client device 904 can repeat steps S918-S924
until the client device 904 receives the most recent block
header.
[0183] At step S928, after repeating steps S918-S924, the client
device 904 can determine that the full node maintains the longest
(i.e., correct) blockchain. The client device 904 can then verify
the Merkle proof and the MMR proof received from the prover 902 in
the verification request. The client device can verify the Merkle
proof and the MMR proof in any suitable method described
herein.
[0184] At step S930, after verifying the Merkle proof and the MMR
proof, the client device 904 can transmit a verification response
to the prover 902. If the Merkle proof and the MMR proof are both
valid then the client device 904 can determine that the interaction
identifier is associated with a valid interaction. The client
device can transmit a verification response indicating that the
interaction is valid to the prover 902.
[0185] After and/or concurrently with transmitting the verification
response, the client device 904 can perform additional processing
as described herein. For example, additional processing can include
performing an action or operation as indicated in the interaction
and/or transferring assets, physical and digital, between the
verifier and the prover as outlined in the interaction.
[0186] If the client device 904 determines that either the Merkle
proof or the MMR proof is invalid, then the client device 904 can
transmit a verification response indicating that the interaction is
invalid to the prover 902. In some embodiments, the client device
904 may not transmit the verification response if either the Merkle
proof or the MMR proof is invalid, in this case, the client device
904 can blacklist the prover 902 and terminate communication
therewith.
IV. NON-INTERACTIVE
[0187] Embodiments of the invention can allow for a Fiat-Shamir
protocol to remove the interaction between the client devices and
the full nodes. Specifically, a full node can figure out locally
which random blocks it should send to a client device for the
verification without any initial randomness from the client device
(e.g., in the form of a random number), yet the client device can
verify the correctness of the proof and is guaranteed that the full
node is not cheating. The Fiat-Shamir protocol will be discussed in
further detail below.
[0188] In some embodiments, all of the verifier's messages, such as
queries, are random from some known distribution. Concretely, in
some embodiments these messages are block numbers in some
predefined intervals. It is possible to turn an interactive
protocol into a non-interactive protocol whose security holds in
the random oracle model, see [Amos Fiat and Adi Shamir. How to
prove yourself: Practical solutions to identification and signature
problems. In Conference on the Theory and Application of
Cryptographic Techniques, pages 186-194. Springer, 1986.]. Every
message of the verifier can be replaced by the result of a query to
a random oracle H which in practice is replaced by a hash function
such as SHA-3. H can be queried at the current transcript and the
oracle's answer is mapped into the verifier's message space. In
other words, for some embodiments the queries are the hash of all
the previously returned block headers.
V. ANALYSIS
[0189] The overhead incurred on full nodes to i) generate new block
headers (due to generating the MMR root) and ii) verify the new
block headers (due to verification of the MMR root), can be
evaluated. We report the experimental results on Table 1,
below.
[0190] Table 1, below, shows a comparison between embodiments of
the invention and previous works. H is the size of a hash (i.e.,
256 bits for SHA256) and B is the size of a block header (i.e., 80
bytes in Bitcoin and 528 bytes in Ethereum). c and m can be
constants.
TABLE-US-00002 TABLE 1 Extra block Chain proof size Event proof
size Interactive data PoPoW mlogn mlogn loglogn Yes logn loglogn B
B + logs H NIPoPoW mlogn mlogn loglogn No logn loglogn B B + logs H
Embodiments of clognlogn B log (n s) H No 1 H the invention
[0191] As the number of block headers increases linearly with the
size of the blockchain, the resource constraints for current SPV
clients also increase. For example, the Ethereum blockchain
currently has 6 million blocks, given that each block header is of
size 528 bytes, a light client in Ethereum would have to download
and store approximately 3 GB to be able to verify all events on the
Ethereum blockchain. Such requirements are not trivial for current
client devices, such as mobile phones and tablets. Embodiments of
the invention include an efficient client device which requires
less resource constraints but still offers high security guarantee
(e.g., secure against a polynomial-time adversary).
[0192] Embodiments of the invention provide for a number of
advantages. For example, a client device can download less data
than previous light clients (e.g., a light client in Ethereum,
described above). A light client in Ethereum downloads
approximately 3 GB of data to be able to verify all events on the
Ethereum blockchain. According to embodiments of the invention, the
client device can download 12 MB, when conservative security
parameters are set. As such, compared to Ethereum, client devices
according to embodiments of the invention can receive 250 times
less data to verify an interaction on the blockchain.
[0193] As another example, a client device can download a
logarithmic number of block headers, rather than every block header
in a blockchain, in order to verify a given block and interaction
in the blockchain. This significantly reduces the amount of data
transmitted from a full node to a client device, thus not only
reducing storage and performance requirements of resource-limited
devices, but also reducing network traffic.
[0194] Another advantage is that embodiments of the invention are
not vulnerable to bribing attacks as in PoPoW. Embodiments of the
invention are not vulnerable to bribing attacks, because
embodiments do not differentiate between blocks in any way before
the blocks are mined. The set of blocks selected to serve as a
proof to the client device are determined only after those blocks
are mined via a randomness chosen by the client device during
transaction verification. Therefore, the adversary will not be able
to bribe mines in the verification network to build a blockchain of
fake, but valid, blocks.
[0195] Any of the software components or functions described in
this application may be implemented as software code to be executed
by a processor using any suitable computer language such as, for
example, Java, C, C++, C#, Objective-C, Swift, or scripting
language such as Perl or Python using, for example, conventional or
object-oriented techniques. The software code may be stored as a
series of instructions or commands on a computer readable medium
for storage and/or transmission, suitable media Include random
access memory (RAM), a read only memory (ROM), a magnetic medium
such as a hard-drive or a floppy disk, or an optical medium such as
a compact disk (CD) or DVD (digital versatile disk), flash memory,
and the like. The computer readable medium may be any combination
of such storage or transmission devices.
[0196] Such programs may also be encoded and transmitted using
carrier signals adapted for transmission via wired, optical, and/or
wireless networks conforming to a variety of protocols, including
the Internet. As such, a computer readable medium according to an
embodiment of the present invention may be created using a data
signal encoded with such programs. Computer readable media encoded
with the program code may be packaged with a compatible device or
provided separately from other devices (e.g., via Internet
download). Any such computer readable medium may reside on or
within a single computer product (e.g. a hard drive, a CD, or an
entire computer system), and may be present on or within different
computer products within a system or network. A computer system may
include a monitor, printer, or other suitable display for providing
any of the results mentioned herein to a user.
[0197] The above description is illustrative and is not
restrictive. Many variations of the invention will become apparent
to those skilled in the art upon review of the disclosure. The
scope of the invention should, therefore, be determined not with
reference to the above description, but instead should be
determined with reference to the pending claims along with their
full scope or equivalents.
[0198] One or more features from any embodiment may be combined
with one or more features of any other embodiment without departing
from the scope of the invention.
[0199] As used herein, the use of "a," "an," or "the" is intended
to mean "at least one," unless specifically indicated to the
contrary.
* * * * *
References