U.S. patent application number 12/690278 was filed with the patent office on 2011-06-23 for computer implemented method for generating a pseudonym, computer readable storage medium and computer system.
This patent application is currently assigned to CompuGROUP Holding AG. Invention is credited to Jan Lehnhardt, Adrian Spalka.
Application Number | 20110154054 12/690278 |
Document ID | / |
Family ID | 42029946 |
Filed Date | 2011-06-23 |
United States Patent
Application |
20110154054 |
Kind Code |
A1 |
Spalka; Adrian ; et
al. |
June 23, 2011 |
COMPUTER IMPLEMENTED METHOD FOR GENERATING A PSEUDONYM, COMPUTER
READABLE STORAGE MEDIUM AND COMPUTER SYSTEM
Abstract
The invention relates to a computer implemented method for
generating a pseudonym for a user comprising entering a
user-selected secret, storing the user-selected secret in memory,
computing a private key by applying an embedding and randomizing
function onto the secret, storing the private key in the memory,
computing a public key using the private key, the public key and
the private key forming an asymmetric cryptographic key, erasing
the secret and the private key from the memory, and outputting the
public key for providing the pseudonym
Inventors: |
Spalka; Adrian; (Koblenz,
DE) ; Lehnhardt; Jan; (Koblenz, DE) |
Assignee: |
CompuGROUP Holding AG
Koblenz
DE
|
Family ID: |
42029946 |
Appl. No.: |
12/690278 |
Filed: |
January 20, 2010 |
Current U.S.
Class: |
713/189 ; 380/46;
707/736; 707/737; 707/776; 707/E17.014; 707/E17.046 |
Current CPC
Class: |
H04L 2209/08 20130101;
H04L 2209/88 20130101; H04L 9/0866 20130101; G06F 21/6245 20130101;
H04L 9/3073 20130101; H04L 2209/42 20130101 |
Class at
Publication: |
713/189 ; 380/46;
707/736; 707/776; 707/737; 707/E17.046; 707/E17.014 |
International
Class: |
G06F 12/14 20060101
G06F012/14; H04L 9/14 20060101 H04L009/14; G06F 17/30 20060101
G06F017/30 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 18, 2009 |
EP |
EP09179974 |
Claims
1. A computer implemented method for generating a pseudonym for a
user comprising: entering a user-selected secret and storing said
user-selected secret into a memory; computing a private key by
applying an embedding and randomizing function onto said
user-selected secret; storing the private key in the memory;
computing a public key using the private key, the public key and
the private key forming an asymmetric cryptographic key pair;
erasing said user-selected secret and the private key from the
memory after said public key is computed; and outputting the public
key for providing the pseudonym, wherein said pseudonym is assigned
as an identity of said user and a binding between said pseudonym
and said user's identity is not established by any third party.
2. The method of claim 1, the secret being selected from the group
consisting of a user-selected password, a secret key, biometric
data.
3. The method of claim 1, further comprising using at least one
public parameter for applying the embedding and randomization
function.
4. The method of claim 3, the public parameter being selected from
the group consisting of a username, a user email address, a user
identifier, and wherein the embedding and randomizing function is
applied on the public parameter and the secret to provide a
combination.
5. The method of claim 1, wherein the embedding and randomization
function comprises a binary Cantor pairing function for embedding
the secret.
6. The method of claim 1, the embedding and randomizing function
comprising encrypting at least the embedded secret using a
symmetric cryptographic algorithm by means of a symmetric key for
randomizing the embedded secret.
7. The method of claim 1, the embedding and randomizing function
comprising encrypting at least the secret using AES by means of a
user-specific symmetric key for embedding and randomizing the
secret.
8. The method of claim 1, wherein the embedding and randomizing
function comprises: applying a first one-way function on the secret
to provide a first value, providing a random number; embedding the
random number and the first value by combining them to provide a
combination; and applying a second one-way function on the
combination to provide a second value, wherein the second value
constitutes the private key.
9. The method of claim 8, wherein the first one-way function is a
first hash function, and the second one-way function is a second
hash function.
10. The method of claim 8, further comprising storing the random
number in a database using a public parameter assigned to the user
as a database access key.
11. The method of claim 8, wherein the computation of the public
key is performed by ECC cryptography.
12. The method of claim 11, further comprising providing a set of
domain parameters comprising a first base point for the ECC
cryptography, computing a first public key for providing a first
pseudonym by the ECC cryptography using the domain parameters and
the first base point, replacing the first base point by a second
base point in the domain parameters, and computing a second public
key by ECC cryptography using the second base point to provide a
second pseudonym.
13. The method of claim 1, further comprising using the pseudonym
as a database access key for storing a data object in a
database.
14. The method of claim 1, further comprising storing the pseudonym
in a user profile that is assigned to the user as the username.
15. A non-transitory tangible computer readable storage medium
having stored therein instructions, which when executed by a
computer system cause the computer system to generate a pseudonym
for a user upon the user's entry of a user-selected secret by
performing the steps of: receiving the user-selected secret and
storing the user-selected secret in a memory; computing a private
key by applying an embedding and randomizing function onto said
user-selected secret; storing the private key in the memory;
computing a public key using the private key, the public key and
the private key forming an asymmetric cryptographic key pair;
erasing the user-selected secret and the private key from the
memory after the public key is computed; and outputting the public
key for providing the pseudonym, wherein said pseudonym is assigned
as an identity of said user and a binding between said pseudonym
and said user's identity is not established by any third party.
16. A computer system comprising: means for entering a
user-selected secret and storing the user-selected secret and a
private key in a memory; processor means being operable to: compute
the private key by applying an embedding and randomizing function
onto the user-selected secret; compute a public key using the
private key, the public key and the private key forming an
asymmetric cryptographic key pair; erase the user-selected secret
and the private key from the memory after the public key is
computed; and output the public key for providing the pseudonym,
wherein said pseudonym is assigned as an identity of said user and
a binding between said pseudonym and said user's identity is not
established by any third party.
17. The computer system of claim 16, further comprising a database
and means for performing a database access operation using the
pseudonym for storing a pseudonymous data object in the
database.
18. The computer system of claim 17, further comprising an analytic
system for analyzing the pseudomized data objects stored in the
database, the analytic system comprising one of a data mining or a
clustering component for performing the analysis.
19. The computer system of claim 16, the means for computing a
private key by applying an embedding and randomizing function onto
the secret implementing a binary cantor pairing function for
embedding the secret.
20. The computer system of claim 16, wherein the means for
computing a private key by applying an embedding and randomizing
function onto the secret is operable to perform the steps of:
applying a first one-way function on the secret to provide a first
value; providing a random number; embedding the random number and
the first value for providing a second combination; and applying a
second one-way function on the second combination to provide a
second value, wherein the second value constitutes the private key.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the priority of European Patent
Application #EP091179974, entitled "A COMPUTER IMPLEMENTED METHOD
FOR GENERATING A PSEUDONYM, COMPUTER READABLE STORAGE MEDIUM AND
COMPUTER SYSTEM" filed on Dec. 18, 2009.
FIELD OF THE INVENTION
[0002] The present invention relates to the field of computer
implemented pseudonym generators.
BACKGROUND
[0003] Various computer implemented schemes for providing a
pseudonym for a user are as such known. A pseudonym is typically
used for protecting the informational privacy of a user such as in
a social network. Such computer implemented schemes for providing a
pseudonym typically enable the disclosure of identities of
anonymous users if an authority requests it, if certain conditions
are fulfilled. For example, Benjumea et al, Internet Research,
Volume 16, No. 2, 2006 pages 120-139 devise a cryptographic
protocol for anonymously accessing services offered on the web
whereby such anonymous accesses can be disclosed or traced under
certain conditions.
SUMMARY
[0004] The invention provides a computer implemented method for
generating a pseudonym for a user comprising: entering a
user-selected secret, storing the user-selected secret in memory,
computing a private key by applying an embedding and randomizing
function onto the secret, storing the private key in the memory,
computing a public key using the private key, the public key and
the private key forming an asymmetric cryptographic key, erasing
the secret and the private key from the memory, outputting the
public key for providing the pseudonym.
[0005] The term `user-selected secret` is understood herein as any
secret data that is selected by or related to a user, such as a
user-selected secret password or a secret key, such as a symmetric
cryptographic key. Further, the term `user-selected secret` does
also encompass a combination of biometric data obtained from the
user and a user-selected password or secret key, such as a
biometric hash value of the password or secret key.
[0006] The term `memory` as used herein encompasses any volatile or
non-volatile electronic memory component or a plurality of
electronic memory components, such as a random access memory.
[0007] The term `embedding function` or `embedding component` as
used herein encompasses any injective function that maps the
elements of an n-dimensional space onto elements of an
m-dimensional space, where n>m. For the purpose of this
invention, we focus on embedding functions where m=1. In accordance
with embodiments of this invention n is equal to 2 and m is equal
to 1 for combining two elements onto a single element. In one
embodiment, a user-selected secret and a public parameter are
mapped by the embedding function to the 1-dimensional space to
provide a combination of the user selected secret and a public
parameter, e.g. a single number that embeds the user selected
secret. This single number constitutes the embedded secret. In
another embodiment, a first hash value of the user selected secret
and a random number are mapped by the embedding function to the
1-dimensional space to provide the embedded secret.
[0008] A `randomizing function` or `randomizing component` as
understood herein encompasses any injective function that provides
an output of data values that are located within a predefined
interval and wherein the distribution of the data values within the
predefined interval is a substantially uniform distribution.
[0009] The term `embedding and randomizing function` as used herein
encompasses any function that implements both an embedding function
and a randomizing function.
[0010] Embodiments of the present invention are particularly
advantageous as an extremely high degree of protection of the
informational privacy of users is provided. This is due to the fact
that an assignment of the user's identity to the user's pseudonym
does not need to be stored and that no third party is required for
establishing a binding between the pseudonym and the user's
identity. In contrast, embodiments of the present invention enable
to generate a user's pseudonym in response to the user's entry of a
user-selected secret whereby the pseudonym is derived from the
user-selected secret. As the user-selected secret is only known by
the user and not stored on any computer system there is no way that
a third party could break the informational privacy of the user,
even if the computer system would be confiscated such as by a
government authority.
[0011] This enables to store sensitive user data, such as medical
data, in an unencrypted form in a publicly accessible database. The
user's pseudonym can be used as a database access key, e.g. a
primary key or candidate key value that uniquely identifies tuples
in a database relation, for read and write access to data objects
stored in the database.
[0012] For example, the database with pseudonymous data can be used
for a decision support system, e.g. in the medical field for
evaluating a user's individual medical data and processing the data
by rules. The result of the evaluation and processing by rules may
be hints and recommendations to the physician regarding the user's
health condition and further treatment.
[0013] In accordance with an embodiment of the invention, at least
one public parameter is used for applying the embedding and
randomization function. A public parameter may be the name of the
user, an email address of the user or another identifier of the
user that is publicly known or accessible. A combination of the
user-selected secret and the public parameter is generated by the
embedding component of the embedding and randomization function
that is applied on the user-selected secret and the public
parameter.
[0014] The combination can be generated such as by concatenating
the user-selected secret and the public parameter or by performing
a bitwise XOR operation on the user-selected secret and the public
parameter. This is particularly advantageous as two users may by
chance select the same secret and still obtain different pseudonyms
as the combinations of the user-selected secrets with the
user-specific public parameters differ.
[0015] In accordance with an embodiment of the invention, the
embedding component of the embedding and randomizing function
comprises a binary cantor pairing function. The user-selected
secret and the public parameter are embedded by applying the binary
cantor pairing function on them.
[0016] In accordance with an embodiment of the invention, the
randomizing component of the embedding and randomizing function
uses a symmetric cryptographic algorithm like the Advanced
Encryption Standard (AES) or the Data Encryption Standard (DES) by
means of a symmetric key. This can be performed by encrypting the
output of the embedding component of the embedding and randomizing
function, e.g. the binary cantor pairing function, using AES or
DES.
[0017] In accordance with an embodiment of the invention, the
symmetric key that is used for randomization by means of a
symmetric cryptographic algorithm is user-specific. If the
symmetric key is user-specific, the use of a public parameter can
be skipped, as well as embedding the user-selected secret and the
public parameter; the randomizing function can be applied then
solely on the user-selected secret. By applying a symmetric
cryptographic algorithm onto the user-selected secret using a
user-specific symmetric key both embedding and randomization of the
user-selected secret are accomplished. If the symmetric key is not
user-specific, the use of the public parameter and embedding the
user-selected secret and the public parameter are necessary.
[0018] In accordance with an embodiment of the invention, the
embedding and randomizing function is implemented by performing the
steps of applying a first one-way function on the user-selected
secret to provide a first value, providing a random number,
embedding the random number and the first value to provide a
combination, and applying a second one-way function on the
combination to provide a second value, wherein the second value
constitutes the private key. This embodiment is particularly
advantageous as it provides a computationally efficient method of
implementing an embedding and randomization function.
[0019] In accordance with an embodiment of the invention, the
computation of the public key is performed by elliptic curve
cryptography (ECC). The private key that is output by the embedding
and randomizing function is multiplied with a first base point
given by the domain parameters of the elliptic curve to provide
another point on the elliptic curve, which is the pseudonym.
[0020] In accordance with an embodiment of the invention, it is
determined whether the output of the embedding and randomizing
function fulfils a given criterion. For example, it is checked
whether the output of the embedding and randomization function is
within the interval between 2 and n-1, where n is the order of the
elliptic curve. If the output of the embedding and randomizing
function does not fulfil this criterion another random number is
generated and the embedding and randomization function is applied
again to provide another output which is again checked against this
criterion. This process is performed repeatedly until the embedding
and randomizing function provides an output that fulfils the
criterion. This output is then regarded as the private key that is
used to calculate the public key, i.e. the pseudonym, by
multiplying the private key with the first base point.
[0021] In accordance with a further embodiment of the invention the
base point is varied leaving the other domain parameters unchanged
for computation of multiple pseudonyms for a given user. This
provides a computationally efficient way to compute multiple
pseudonyms for a given user in a secure way.
[0022] In another aspect the present invention relates to a
computer readable storage medium having stored therein
instructions, which when executed by a computer system, cause the
computer system to generate a pseudonym for a user upon a user's
entry of a user-selected secret by performing the steps of storing
the user-selected secret in memory, computing a private key by
applying an embedding and randomizing function onto the secret,
storing the private key in memory, computing a public key using the
private key, the public key and the private key forming an
asymmetric cryptographic key pair, erasing the secret and the
private key from memory, outputting the public key for providing
the pseudonym.
[0023] In another aspect the present invention relates to a
computer system comprising means for entering a user-selected
secret, memory means for storing the user-selected secret and a
private key, processor means being operable to compute the private
key by applying an embedding and randomizing function onto the
secret, compute a public key using the private key, the public key
and the private key forming an asymmetric cryptographic key pair,
erase the secret and the private key as well as any intermediate
computational results from memory, and output the public key for
providing the pseudonym.
BRIEF DESCRIPTION OF THE DRAWINGS
[0024] In the following embodiments of the invention are explained
in greater detail, by way of example only, making reference to the
drawings in which:
[0025] FIG. 1 is a block diagram of a first embodiment of a
computer system of the invention.
[0026] FIG. 2 is a flowchart being illustrative of an embodiment of
a method of the invention.
[0027] FIG. 3 is a block diagram of a further embodiment of a
computer system of the invention.
[0028] FIG. 4 is a flowchart being illustrative of a further
embodiment of a method of the invention.
DETAILED DESCRIPTION
[0029] Throughout the following detailed description like elements
of the various embodiments are designated by identical reference
numerals.
[0030] FIG. 1 shows a computer system 100 that has a user interface
102 for a user's entry of a user-selected secret that is designated
as s.sub.T in the following. For example, a keyboard 104 may be
coupled to the computer system 100 for entry of s.sub.T. Instead of
a keyboard 104 a touch panel or another input device can be coupled
to the computer system 100 for entry of s.sub.T. In addition, a
sensor 106 can be coupled to the computer system 100 such as for
capturing biometric data from a biometric feature of the user. For
example, the sensor 106 may be implemented as a fingerprint sensor
in order to provide biometric fingerprint data to the computer
system 100.
[0031] A public parameter, such as the user's name or email
address, can also be entered into the computer system 100 via the
keyboard 104 or otherwise. For example, a personal set V.sub.T,i
containing at least one user-specific public parameter, such as the
user's name or email address, is entered into the computer system
100 by the user T.sub.i.
[0032] The computer system 100 has a memory 108, such as a random
access memory, and at least one processor 110. The memory 108
serves for temporary storage of the user-selected secret s.sub.T
112, a combination 114 of s.sub.T 112 and V.sub.T,i, a private key
116, a public key 118 that constitutes a pseudonym of the user
T.sub.i, and a data object 120, such as a medical data object
containing medical data related to the user T.sub.i. Further, the
memory 108 serves for loading computer program instructions 122 for
execution by the processor 110.
[0033] The computer program instructions 122 provide an embedding
and randomizing function 126, a key generator 128 and may also
provide a database access function 130 when executed by the
processor 110.
[0034] The embedding and randomizing function 126 may be provided
as a single program module or it may be implemented by a separate
embedding function 132 and a separate randomizing function 134. For
example, the embedding function 132 or an embedding component of
the embedding and randomization function 126 provides the
combination 114 by concatenating s.sub.T and the user's name or by
performing a bitwise XOR operation on s.sub.T and the user's
name.
[0035] In one implementation, the embedding and randomizing
function 126 implements symmetric encryption provided by a
symmetric cryptographic algorithm, e.g. AES, using a user-specific
symmetric key for encryption of the user-selected secret 112. This
provides both embedding and randomizing of s.sub.T 112.
[0036] In another implementation, the embedding function 132 is
implemented by a binary cantor pairing function for embedding
s.sub.T 112 and V.sub.T,i, and the randomizing function 134 is
implemented by AES encryption using a symmetric key that is the
same for the entire set of users T.
[0037] In still another embodiment the embedding and randomizing
function 126 is implemented by two different hash functions and a
random number generator (cf. the embodiment of FIGS. 3 and 4).
[0038] The key generator 128 serves to compute public key 118 using
elliptic curve cryptography (ECC). The private key 116 is
multiplied by a base point given by the domain parameters of the
elliptic curve which provides the public key 118. By varying the
base point and leaving the other domain parameters of the elliptic
curve unchanged multiple pseudonyms can be computed for the user
T.sub.i on the basis of the same secret S.sub.T.
[0039] The computer system 100 may have a network interface 136 for
coupling the computer system 100 to a database 138 via a
communication network 140, such as the Internet. The database
access function 130 enables to perform a write and a read access
for accessing the data object 120 stored in the database 138 using
the public key 118, i.e. the user's pseudonym, as a database access
key, e.g. a primary key or candidate key value that uniquely
identifies tuples in a database relation.
[0040] Further, an analytic system 140, such as a decision support
system (DSS) can be coupled to the database 138 such as via the
network 140. The analytic system 144 comprises a component 146 for
analyzing the data objects of the users T which are stored in the
database 138, such as by data mining or data clustering.
[0041] In one application the data objects stored in the database
138 contain medical data of the various users. By analyzing the
various data objects using techniques such as data mining and/or
data clustering techniques medical knowledge can be obtained. For
example, data clustering may reveal that certain user attributes
contained in the medical data increase the risk for certain
diseases.
[0042] For generating a pseudonym p.sub.T,i for a user T.sub.i
based on the secret s.sub.T 112 and domain parameters D.sub.i
containing a base point for the elliptic curve cryptography the
following steps are executed by the computer system 100 in
operation:
[0043] The user T.sub.i enters his or her user-selected secret
s.sub.T 112 such as via the keyboard 104. In addition, the user may
enter at least one public parameter V.sub.T,i such as his name or
email address via the keyboard 104 or otherwise. Such a public
parameter V.sub.T,i may also be permanently stored in the computer
system 100.
[0044] The secret s.sub.T 112 is temporarily stored in memory 108.
Upon entry of the secret s.sub.T 112 the embedding function 132 or
the embedding component of the embedding and randomizing function
126 generates the combination 114 of the secret s.sub.T 112 and the
public parameter V.sub.T,i. The resultant combination 114 is
temporarily stored in the memory 108.
[0045] Next, the randomizing function 134 or the randomizing
component of the embedding and randomizing function 126 is invoked
in order to calculate the private key 116 on the basis of the
combination 114. The resultant private key 116 is temporarily
stored in memory 108. In the next step, the key generator 128 is
started for computing the public key 118 by multiplying the private
key 116 by the base point contained in the domain parameters
D.sub.i of the elliptic curve being used.
[0046] The public key 118, i.e. the pseudonym p.sub.T,i, is stored
in memory 108. The secret s.sub.T 112, the combination 114 as well
as the private key 116 as well as any intermediate result obtained
by execution of the embedding and randomizing function 126 and the
key generator 128 are then erased from the memory 108 and/or the
processor 110. As a consequence, there is no technical means to
reconstruct the assignment of the resultant pseudonym to the user
T.sub.i as only the user knows the secret s.sub.T 112 that has led
to the generation of his or her pseudonym p.sub.T,i. A data object
120 containing sensitive data of the user T.sub.i, such as medical
data, can then be stored by execution of the database access
function 130 in the pseudomized database 138 using the pseudonym
p.sub.T,i as a database access key, e.g. a primary key or candidate
key value that uniquely identifies tuples in a database
relation.
[0047] The user-selected secret s.sub.T 112 may be obtained by
combining a user-selected password or secret key with biometric
data of the user T.sub.i that is captured by the sensor 106. For
example, a hash value of the user-selected password or secret key
is calculated by execution of respective program instructions by
the processor 110. In this instance the hash value provides the
user-selected secret s.sub.T 112 on which the following
calculations are based.
[0048] A plurality of users from the public set of enrolled
participants T may use the computer system 100 to generate
respective pseudonyms p.sub.T,i and to store data objects
containing sensitive data, such as medical information in the
database 138 as it has been described above in detail for one of
the users T.sub.i by way of example.
[0049] For reading the data object of one of the users T.sub.i from
the database 138 the user has to enter the secret s.sub.T 112.
Alternatively, the user has to enter the user-selected password or
secret key via the keyboard 104 and an acquisition of the biometric
data is performed using the sensor for computation of a hash value
that constitutes s.sub.T 112. As a further alternative, the secret
key is read by the computer system from an integrated circuit chip
card of the user. On the basis of s.sub.T 112 the pseudonym can be
computed by the computer system 100.
[0050] The pseudonym is then used for performing a database read
access on the database 138 in order to read one or more data
objects 120 that are stored in the database 138 for that user
T.sub.i. After the database access operation has been performed the
secret s.sub.T 112, the combination 114, the private key 116 and
the public key 118 are erased from the computer system 100 as well
as any intermediate computational results.
[0051] FIG. 2 shows a corresponding flowchart.
[0052] In step 200 the user T.sub.i enters his or her user-selected
secret s.sub.T and public parameter V.sub.T,i. In step 202 s.sub.T
and V.sub.T,i are combined to provide the first combination by the
embedding function (cf. embedding function 132 of FIG. 1). Next,
the randomizing function (cf. randomizing function 134 of FIG. 1).
is applied on s.sub.T and V.sub.T,i in step 204 which provides a
private key. As an alternative, an embedding and randomizing
function is applied on s.sub.T and V.sub.T,i which provides the
private key.
[0053] In step 206 a public key is computed using the private key
obtained in step 204 and the public key is used in step 208 as a
pseudonym of the user T. For example the pseudonym may be used as a
database access key, e.g. a primary key or candidate key value that
uniquely identifies tuples in a database relation for storing a
data object for the user T.sub.i in a database with pseudonymous
data (cf. database 138 of FIG. 1).
[0054] FIG. 3 shows a further embodiment of computer system 100. In
the embodiment considered here the embedding and randomizing
function 126 comprises an embedding function 132, a random number
generator 148, a first hash function 150 and a second hash function
152. In the embodiment considered here the computation of the
private key 116 based on s.sub.T 112 may be performed as
follows:
[0055] The first hash function 150 is applied on the user-selected
secret s.sub.T 112. This provides a first hash value. Next, a
random number is provided by the random number generator 148. The
random number and the first hash value are combined by the
embedding function 132 to provide the combination, i.e. the
embedded secret s.sub.T 112.
[0056] The combination of the first hash value and the random
number can be obtained by concatenating the first hash value and
the random number or by performing a bitwise XOR operation on the
first hash value and the random number by the embedding function
132. The result is a combination on which the second hash function
152 is applied to provide a second hash value. The second hash
value is the private key 116 on which the calculation of the public
key 118 is based.
[0057] Dependent on the implementation it may be necessary to
determine whether the second hash value fulfils one or more
predefined conditions. Only if such conditions are fulfilled by the
second hash value it is possible to use the second hash value as
the private key 116 for the following computations. If the second
hash value does not fulfill one or more of the predefined
conditions a new random number is provided by the random number
generator 148 on the basis of which a new second hash value is
computed which is again checked against the one or more predefined
conditions (cf. the embodiment of FIG. 4).
[0058] The random number on the basis of which the private key 116
and thereafter the public key 118 has been computed is stored in a
database 154 that is coupled to the computer system 100 via the
network 140. The random number may be stored in the database 154
using the public parameter V.sub.T,i as the database access key for
retrieving the random number for reconstructing the pseudonym at a
later point of time.
[0059] The user T.sub.i may use the pseudonym provided by the
computer system 100 for his or her registration in an anonymous
online community 156 e.g. a social network. For registration the
user T.sub.i creates his or her user profile 158 by entering the
pseudonym 118 as the username such that the various private data
entered into the user profile 158 remain private even though they
are published in the online community 156 due to the fact that the
assignment of the pseudonym to the user T.sub.i is stored nowhere
and cannot be reconstructed by technical means without knowledge of
the user-selected secret s.sub.T 112.
[0060] For reconstructing the pseudonym the user has to enter his
or her user-selected secret s.sub.T 112 into the computer system on
the basis of which the first hash value is generated by the hash
function 150 and the combination 114 is generated by the embedding
function 132 or the embedding component of the embedding and
randomizing function 126 using the first hash value and the random
number retrieved from the database 154.
[0061] Depending on the implementation, the user may also need to
enter the user's public parameter V.sub.T,i. A database access is
performed using the user's public parameter V.sub.T,i as a database
access key, e.g. a primary key or candidate key value that uniquely
identifies tuples in a database relation, in order to retrieve the
random number stored in the database 154.
[0062] In other words, the reconstruction of the private key 116 is
performed by applying the embedding function 132 on the first hash
value obtained from the user-selected secret s.sub.T 112 and the
retrieved random number which yields the combination 114. The first
hash value is combined with the random number retrieved from the
database 154 by the embedding function 132 to provide the
combination onto which the second hash function 152 is applied
which returns the private key 116, out of which the public key 118,
i.e. the pseudonym, can be computed. After the user T.sub.i has
recovered his or her pseudonym a database access for reading and/or
writing from or to the database 138 may be performed or the user
may log into the online community 156 using his or her pseudonym
for anonymous participation in the online community 156.
[0063] FIG. 4 shows a respective flowchart for generating a
pseudonym p.sub.T,i for user T.sub.i. In step 300 the user enters
the user-selected secret s.sub.T. In step 304 a first hash function
is applied on the user-selected secret s.sub.T which provides a
first hash value. In step 306 a random number is generated and in
step 308 an embedding function is applied on the first hash value
and the random number to provide a combination of the first hash
value and the random number. In other words, the first hash value
and the random number are mapped to a 1-dimensional space, e.g. a
single number, by the embedding function. The combination can be
obtained by concatenating the random number and the first hash
value or by performing a bitwise XOR operation on the first hash
value and the random number.
[0064] In step 310 a second hash function is applied on the
combination which provides a second hash value. The second hash
value is a candidate for the private key. Depending on the
implementation the second hash value may only be usable as a
private key if it fulfils one or more predefined conditions. For
example, if ECC is used, it is checked whether the second hash
value is within the interval between 2 and n-1, where n is the
order of the elliptic curve.
[0065] Fulfillment of such a predefined condition is checked in
step 312. If the condition is not fulfilled, the control returns to
step 306. If the condition is fulfilled, then the second hash value
qualifies to be used as a private key in step 314 to compute a
respective public key providing an asymmetric cryptographic
key-pair consisting of the private key and the public key. In step
316 the public key computed in step 314 is used as a pseudonym such
as for accessing a pseudomized database, participation in an
anonymous online community or other purposes.
Mathematical Appendix
1. Embedding Functions.
[0066] There exist n-ary scalar functions
d.sub.iN.times.N-N.sub.d
which are injective--and even bijective, where N is the set of
natural numbers. The function d( ) embeds uniquely an n-dimensional
space, i.e. n-tuples (k.sub.1, . . . , k.sub.n), into scalars, i.e.
natural numbers k.
2. The Binary Cantor Pairing Function
[0067] The binary cantor pairing function is an embodiment of
embedding function 132. The binary cantor pairing function is
defined as follows:
m N .times. N - N ##EQU00001## .pi. ( m , n ) = 1 2 ( m + n ) ( m +
n + 1 ) + n ##EQU00001.2##
which assigns to each fraction m/n the unique natural number
.pi.(m, n)--thus demonstrating that there are no more fractions
than integers. Hence, if we map both s.sub.T and V.sub.T,i to
natural numbers and use the fact that all identities are distinct
then .pi.(s.sub.T, V.sub.T,i) yields a unique value for each
identity, even if there are equal personal secrets. To be more
precise, since this function does not distinguish between e.g. 1/2,
2/4 etc, it assigns to each fraction an infinite number of unique
natural numbers.
3. Elliptic Curve Cryptography (ECC)
[0068] Let: [0069] p be a prime number, p>3, and |F.sub.p the
corresponding finite field a and b integers
[0070] Then the set E of points (x, y) such that
E={(x,y).epsilon.|F.sub.p.times.|F.sub.p|y.sup.2=x.sup.3+ax+b}
(F1)
defines an elliptic curve in |F.sub.p. (For reasons of simplicity,
we skip the details on E being non-singular and, as well, we do not
consider the formulae of elliptic curves over finite fields with
p=2 and p=3. The subsequent statements apply to these curves,
too.)
[0071] The number m of points on E is its order.
[0072] Let P,Q.epsilon.E be two points on E. Then the addition of
points
P+Q=R and R.epsilon.E (F2)
can be defined in such a way that E forms an Abelian group, viz, it
satisfies the rules of ordinary addition of integers. By
writing
P+P=[2]P
[0073] We define the k-times addition of P as [k]P, the point
multiplication.
[0074] Now EC-DLP, the elliptic curve discretionary logarithm
problem, states that if
Q=[k]P (F3)
then with suitably chosen a, b, p and P, which are known to public,
and the as well known to the public point Q it is computationally
infeasible to determine the integer k.
[0075] The order n of a point P is the order of the subgroup
generated by P, i.e. the number of elements in the set
{P,[2]P, . . . , [n]P} (F4)
[0076] With all this in mind we define an elliptic curve
cryptographic (ECC) system as follows. Let:
E be an elliptic curve of order m B.epsilon.Ea point of E of order
n, the base point
Then
[0077] D={a,b,p,B,n,co(B)} (F5)
with
co ( B ) = m n ##EQU00002##
defines a set of domain ECC-parameters. Let now g be an integer
and
Q=[g]B (F6)
[0078] Then (g, Q) is an ECC-key-pair with g being the private key
and Q the public key.
[0079] For we rely on findings of Technical Guideline TR-03111,
Version 1.11, issued by the Bundesamt fur Sicherheit in der
Informationstechnik (BSI), one of the best accredited source for
cryptographically strong elliptic curves, we can take that m=n,
i.e. co(B)=1, and hence reduce (F5) to
D={a,b,p,B,n} (F7)
[0080] Now we can define our one-way function. Let D be a set of
domain parameters concordant with (F7). Then
f:[2,n-1].fwdarw.E
k[k]B (F8)
i.e. the point multiplication (F6), is an injective one-way
function.
4. Implementing Key Generator Based on ECC
[0081] The key generator 128 (cf. FIGS. 1 and 3) can be implemented
using ECC.
[0082] Definitions: [0083] There are public sets of ECC-domain
parameters D.sub.1, D.sub.2, . . . concordant with (F7)
[0083] D.sub.i={a.sub.i,b.sub.i,p.sub.i,B.sub.i,n.sub.i} (F9)
[0084] There are public functions: an embedding function do, a
randomising function r( ) and our one-way function f( ) defined by
(F8). [0085] There is a public set of enrolled participants
(users)
[0085] T={T.sub.1,T.sub.2, . . . } (F10)
[0086] Note that a T.sub.i does not necessarily possess any
personally identifying details, i.e. we assume that T resembles the
list of participants in an anonymous Internet-community, in which
each participant can select his name at his discretion as long as
it is unique. [0087] Each participant T.epsilon.T chooses at his
complete discretion his personal secret s.sub.T. In particular, for
this secret is never revealed to anybody else--it is the
participant's responsibility to ensure this--it is not subject to
any mandatory conditions, such as uniqueness. [0088] Our pseudonym
derivation function is
[0088] h( )=f(r(d( )) (F11) with the following properties: [0089]
Given a T.epsilon.T with his s.sub.T, a D.sub.i and T,
D.sub.i.epsilon.V.sub.T,i
[0089] r(d(s.sub.T,V.sub.T,i))=g.sub.T,i (F12) where g.sub.T,i is a
unique and strong, i.e. sufficiently random, private ECC-key for
D.sub.i. [0090] The pseudonym p.sub.T,i corresponding to T, s.sub.T
and D.sub.i is
[0090]
p.sub.T,i=f(g.sub.T,i,D.sub.i)=[g.sub.T,i]B.sub.i=(x.sub.T,i,y.su-
b.T,i) (F13) [0091] There is a public set of pseudonyms
[0091] P={p.sub.1, p.sub.2, . . . } (F14)
such that P comprises one or more pseudonyms for each participant
in T computed according to (F11). This wording implies that here is
no recorded correspondence between a participant in T and his
pseudonyms in P, i.e. each p.sub.T,i is inserted in an anonymous
way as p.sub.k into P.
[0092] Remarks: [0093] The use of multiple domain parameters
enables us to endow a single participant with a single personal
secret with multiple pseudonyms. This in turn enables a participant
to be a member of multiple pseudonymous groups such that data of
these groups cannot--for, e.g. personal or legal reasons--be
correlated. Therefore, attempts to exploit combined pseudonymous
profiles for unintended, possibly malicious purposes, are of no
avail. [0094] The distinction between two sets of domain parameters
D.sub.i and D.sub.j can be minor. In accordance with our principle
to use only accredited domain parameters, e.g. those listed in BSI
TR-03111, we can set
[0094] D.sub.i={a,b,p,B,n} (F15) by swapping B for a statistically
independent B.sub.2, i.e. by choosing a different base point, we
can set
D.sub.j={a,b,p,B.sub.2,n} (F16) For D.sub.i and D.sub.j refer to
the same elliptic curve we can have only one function (F12) and
introduce the crucial distinction with (F13). This vastly
simplifies concrete implementations--we select a suitable curve and
vary the base points only.
[0095] Although the invention herein has been described with
reference to particular embodiments, it is to be understood that
these embodiments are merely illustrative of the principles and
applications of the present invention. It is therefore to be
understood that numerous modifications may be made to the
illustrative embodiments and that other arrangements may be devised
without departing from the spirit and scope of the present
invention as defined by the appended claims.
TABLE-US-00001 List of Reference Numerals 100 Computer system 102
User interface 104 Keyboard 106 Sensor 108 Memory 110 Processor 112
A user-selected secret 114 Combination 116 Private key 118 Public
key 120 Data object 122 Computer program instructions 124
Combination generator 126 Embedding and randomizing function 128
Key generator 130 Database access function 132 Embedding function
134 Randomizing function 136 Network interface 138 Database 140
Network 144 Analytic system 146 Component 148 Random number
generator 150 Hash function 152 Hash function 154 Database 156
Online community 158 User profile
* * * * *