Patent Publication Number: US-9418242-B2

Title: Computer implemented method for analyzing data of a user with the data being stored pseudonymously in a database

Description:
RELATED APPLICATIONS 
     The present application is a divisional of co-pending U.S. patent application Ser. No. 12/968,520, entitled “COMPUTER IMPLEMENTED METHOD FOR ANALYZING DATA OF A USER WITH THE DATA BEING STORED PSEUDONYMOUSLY IN A DATABASE,” filed on Dec. 15, 2010, the entirety of which is herein incorporated by reference. 
     U.S. application Ser. No. 12/968,520 claims the priority of:
     1. European Application Number: EP10 194 677.0, filed Dec. 13, 2010;   2. European Application Number: EP10 173 198.2, filed Aug. 18, 2010;   3. European Application Number: EP10 173 175.0, filed Aug. 18, 2010;   4. European Application Number: EP10 173 163.6, filed Aug. 18, 2010;   5. European Application Number: EP10 167 641.9, filed Jun. 29, 2010;   6. European Application Number: EP10 156 171.0, filed Mar. 11, 2010; and   7. European Application Number: EPOS 179 974.2, filed Dec. 18, 2009   

    
    
     FIELD OF THE INVENTION 
     The present invention relates to the field of computer implemented identifier generators. 
     BACKGROUND AND RELATED ART 
     With the continuously increasing amount of personal data stored in databases with respect to individual persons, the possibility arises that by means of specialized data analysis, systems information about the individual person can be gathered and analyzed with respect to certain data contents. For example, the personal data may comprise medical data of a person, wherein the analysis system may be used to determine if based on the medical data the person may be assigned to a certain disease management program. 
     Further, various computer implemented schemes for providing an identifier for a database exist. The identifier could for instance be a pseudonym. A pseudonym is typically used for protecting the informational privacy of a user. 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. 
     Even in case absolute anonymity is guaranteed using a certain pseudonym with increasing amount of data the risk increases that by means of data correlation techniques of the data stored with respect to said pseudonym, conclusions can be drawn from said data about the owner of the pseudonym. Further, a large number of different features stored with respect to a person increases the probability that the person&#39;s identity can be revealed, for example by means of the combination of the ZIP code, age, profession, marital status and height. Thus, with an increasing amount of data stored with respect to a pseudonym, the risk of breaking the user&#39;s anonymity is also increasing. 
     SUMMARY 
     The invention provides a computer implemented method, a computer program product and a computing device in the independent claims. Embodiments are given in the dependent claims. 
     The invention provides a computer implemented method for analyzing data of a first user, wherein an asymmetric cryptographic key pair is associated with the first user, said asymmetric cryptographic key pair comprising a public key and a private key, the data being stored pseudonymously in a database with the data being assigned to an identifier, wherein the identifier comprises the public key, the method comprising receiving a set of rules, the set of rules describing data processing steps, receiving the identifier, retrieving the data assigned to the identifier from the database, analyzing the retrieved data by applying the set of rules and providing a result of the analysis. 
     The term ‘identifier’ as used herein may be a reference used for identifying or locating data in the database. For example, in some embodiments an identifier may be a pseudonym. The pseudonym allows identification of the ownership of various records. In other embodiments the identifier may identify a record or records within the database. Records may be individual data files or they may be a collection of data files or tuples in a database relation. An identifier may be an access key like a primary key for a relation in a database. An identifier may also be a unique key for a relation in a relational database. 
     Embodiments of the invention have the advantage that even though personal data of a user is stored in a database in an unencrypted manner, analyzing the data of the user only provides a result of the analysis which does not permit to draw any conclusions about the user&#39;s identity. The only identifier which assigns the data to the user comprises a public key of the user, which appears as a random value and thus does not allow to draw any conclusions about the user&#39;s identity. 
     Preferably, the first user has a private key, from which a whole set of public keys is calculated, wherein the private key and each public key of the set of public keys form an asymmetric cryptographic key pair. Then, the user&#39;s data is stored pseudonymously in the database with the data being assigned to an identifier, wherein the identifier comprises one of the public keys. With an increasing number of public keys generated from a single private key and the data being stored pseudonymously in the database with the data being assigned to identifier, each identifier comprising a different one of said user&#39;s public keys, personal anonymity is further enhanced. Thus, a user may be associated with ‘multiple identities’ using a single credential, namely the private key. 
     In an embodiment, the public keys may be used as identifiers in a database such that the identifiers are database identifiers. In this case, the method preferably comprises depositing data into the database using the identifiers. For example, the data may comprise medical datasets of a patient, the patient being the owner of the private key, wherein the medical datasets may be stored in the database sorted by medical topics. In this case, an individual public key of the set of public keys of the patient may be associated with a certain medical topic. Thus, the medical datasets are not stored in the database using one common identifier for all medical topics, but the datasets are stored in a distributed manner in the database using a set of identifiers with a different identifier for each medical topic. Nevertheless, by means of his one private key the patient is able to individually generate the set of public keys for identification of the datasets stored in the database. 
     Consequently, correlation attacks fail since correlations can only be detected for one given identifier. 
     The term ‘database’ as used herein is a collection of logically-related data or files containing data that provide data for at least one use or function. Databases are essentially organized data that may be provided or used by an application. Examples of a database include, but are not limited to: a relational database, a file containing data, a folder containing individual data files, and a collection of computer files containing data. 
     In accordance with an embodiment of the invention, the identifier corresponds to the public key of the first user. 
     In accordance with an embodiment of the invention, the identifier is a pseudonym of the first user and/or wherein the identifier is an access key to the data in the database. 
     In accordance with an embodiment of the invention, analyzing the retrieved data is performed by an inference engine. Herein, the term ‘inference engine’ is understood as any device or computer program that derives answers from the database. Inference engines are considered to be a special case of reasoning engines, which can use more general methods of reasoning. In an embodiment, analyzing the data can be performed by a decision support system, e.g. in the medical field for evaluating a user&#39;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&#39;s health condition and further treatment. 
     In accordance with an embodiment of the invention, the method further comprises retrieving a digital signature of the data stored in the database with the data and verifying the digital signature using the public key of the first user. Thus, the public key of the first user has two purposes. First, it is used as an identifier for the user&#39;s data in the database. Second, it is used in order to verify for example the integrity of the user&#39;s data by applying the user&#39;s public key to the digital signature of the data. This significantly simplifies the data analysis process since no further actions have to be taken in order to ensure the data integrity. Only the first user is able to sign his data using his private key—which is only known to the first user. Consequently, counterfeiting of the user&#39;s data is not possible and also errors which occurred during data storage in the database can easily be detected. 
     In accordance with an embodiment of the invention, providing the result of the analysis comprises sending the result to said first user with the recipient address to which the result is sent comprising the public key. 
     This has the advantage, that a ‘blind messaging’ can be performed. Thus, the recipient&#39;s identity is not revealed when sending the result to the first user with the recipient address to which the message is sent comprising the first user&#39;s public key. Further, even though the data is stored in the database associated with the public key of the first user, it will not be possible to identify the respective ‘real person’ that is associated with said public key of the first user even when having full access to said database. 
     Since with the continuously increasing amount of personal data stored in databases with respect to individual persons, the people consciousness regarding data privacy protection increases. This results in the problem that on the one hand personal data has to remain available for data analysis systems like inference engines, wherein the data analysis system must be able to provide an analysis result to the owner of the data. On the other hand, data privacy protection has to be ensured. By providing the result of the analysis to the first user by sending the result to said first user with the recipient address to which the result is sent comprising the public key, this conflict is solved in an elegant but safe manner. 
     It has to be noted here, that generally the ‘result of the analysis’ is understood as either the direct outcome of the analysis performed on the first user&#39;s data, or as an indirect outcome of the analysis performed on the first user&#39;s data. In a practical embodiment, in case the analysis is performed with respect to a determination if based on the user&#39;s data the user qualifies for participation in a certain disease management program (DMP), the result of the analysis may either be ‘qualified for DMP xyz’ which is considered as a direct outcome of the analysis, or the result of the analysis may just be ‘please consult a medical doctor’. 
     Similarly, in case the data is medical data, the result of the analysis may comprise a laboratory value like ‘liver function test results a value of 1234’ or it may comprise an advice ‘stop drinking alcohol’. However, the invention is not limited to medical data but may comprise any kind of user data like personal qualifications, personal documents, information about a user&#39;s daily requirements regarding purchased convenience goods, information about water and electricity consumption etc. 
     In accordance with an embodiment of the invention, the recipient address corresponds to the public key of the first user. However, the invention is not limited to this specification. For example, it may be possible to add a domain name to the public key of the first user such to make such kind of messaging compatible to already existing internet messaging systems: the invention thus either permits to direct a message directly to the address ‘public_recipient_key’ or to direct the message to for example the address ‘public_recipient_key@securedomain.com’. 
     In case of SMS messaging in mobile telecommunication networks, for example the message may be directed to a central provider telephone number, wherein the body of the SMS message may contain the public key of the first user and the message ‘message’ like for example ‘public_recipient_key∥message’. 
     The skilled person will understand that there are further possibilities to realize the basic idea according to the invention in various messaging environments. 
     In accordance with an embodiment of the invention, said message is sent encrypted with the public key to the first user. Thus, again the public key of the first user has a double purpose: the first purpose is the usage as anonymous recipient address and the second purpose is the usage as encryption key. Since only the recipient possesses the private key, only he will be able to decrypt the message. Thus, in a highly convenient manner, secure messaging can be performed in an anonymous manner, wherein only one type of information is required to be known by the sender: the public key. 
     In accordance with an embodiment of the invention, said message is sent from a second user, wherein a sender asymmetric cryptographic key pair is associated with the second user, said key pair comprising a public sender key and a private sender key, the method further comprising generating a signature of the message using the private sender key and sending the signature to said first user. This further enables the first user to verify the authenticity of the message in a very convenient manner. Preferably, the public sender key is available in a respective database such that it is possible to also verify that the sender of the message is an ordinary member of the group of participants which is allowed to send messages to the recipient. 
     Referring back to the above mentioned example of providing advices to the first user based on the outcome of the analysis of his data, this ensures that the first user is protected from fake information or fake advices of third parties which would confuse or even misguide the first user. 
     In accordance with an embodiment of the invention, the message is a synchronous or asynchronous conferencing message. For example, synchronous conferencing may comprise any kind of data conferencing, instant messaging, Internet Relay Chat (IRC), videoconferencing, voice chat, or VoIP (voice over IP). Asynchronous conferencing may comprise email, Usenet, SMS or MMS. 
     In accordance with an embodiment of the invention, the message is an email message with the message being sent to the first user by email, wherein the email address comprises the public key of the first user. For example, in this case the public key of the first user is comprised in the header of the email as the recipient address to which the message is sent, wherein the message is comprised in the body of the email. Variations like having the public key of the first user being comprised in the body with the message being sent to a central email service with central email address are also possible. 
     In another aspect, the invention relates to a computer implemented method for receiving a result from a second user by a first user, wherein an asymmetric cryptographic key pair is associated with the first user, said key pair comprising a public key and a private key, the method comprising receiving the result by said first user with the recipient address at which the result is received comprising the public key. 
     In another aspect, the invention relates to a computer implemented method for storing data of a first user in a database, the first user having a private key, the method comprising calculating a set of public keys, wherein the private key and each public key of the set of public keys form an asymmetric cryptographic key pair and storing the data pseudonymously in the database with the data being assigned to an identifier, wherein the identifier comprises one of the public keys. 
     In accordance with a further embodiment of the invention, the method further comprises generating a digital signature for data using the private key, wherein the digital signature is stored in the database along with the data. This embodiment is particularly advantageous because the digital signature for the data allows authentication of the data. In this way the authorship of the data can be verified. 
     In accordance with a further embodiment of the invention, the method further comprises directly receiving the private key or generating the private key, wherein generating the private key comprises receiving an input value and applying a cryptographic one-way function to the input value for generation of the private key, wherein the cryptographic one-way function is an injective function. 
     In accordance with an embodiment of the invention, the method further comprises the step of depositing data into a database using the identifier. This embodiment is advantageous because the identifier may be used to control access to the database. Alternatively the identifier could be used as a pseudonym for which data deposited into the database is referenced against. This provides anonymity for a user. 
     Thus, some 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 because an assignment of the user&#39;s identity to the user&#39;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&#39;s identity. Some embodiments of the present invention enable to generate a user&#39;s pseudonym in response to the user&#39;s entry of a user-selected secret whereby the pseudonym is derived from the user-selected secret. As the user-selected secret is known only by the user and not stored on any computer system there is no feasible 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. 
     This enables to store sensitive user data, such as medical data, in an unencrypted form in a publicly accessible database. The user&#39;s pseudonym can be used as a database identifier, 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. 
     In accordance with a further embodiment of the invention, the public key of the first user or the set of public keys is calculated from the private key using elliptic curve cryptography, wherein said calculation is performed by a variation of the domain parameters used for performing the elliptic curve cryptography. For the case of simplicity, only one parameter of the domain parameters, for example the base point, is varied here accordingly. For example, in a first step of calculating a first public key the private key and a first base point and a set of further domain parameters may be used. The first public key is calculated using asymmetric cryptography which is implemented using elliptical curve cryptography. Then, the first base point is replaced by a second base point that is not inferable from the first base point in an easy way in the domain parameters, wherein the other domain parameters are kept unmodified. Finally, a second public key is calculated by elliptic curve cryptography using the private key, the second base point and the set of unmodified further domain parameters. 
     However, the invention is not limited to a variation of base points for calculating the set of public keys—any of the domain parameters may be varied for this purpose. Nevertheless, a base point variation is preferred since this provides a computationally efficient way to compute multiple identifiers for a given user in a secure way. Furthermore, it is by far more complicated to vary one or more of the other domain parameters because doing this would result in a different elliptic curve that would have to fulfill many conditions in order to be considered valid. 
     This embodiment is advantageous because a single private key has been used to generate a set of public keys to be used as identifiers. This is particularly advantageous because the public keys cannot be inferred from each other supposed their respective base points cannot be either, yet only a single input value is needed for all of them. In other words, in case of a base point variation knowledge of one of the public keys does not allow an attacker to determine any other public key. The used public keys are therefore not correlatable. However, all of the public keys are determined by a single input value or private key. It has to be noted that preferably the base points are meant to be public. Nevertheless, an embodiment of the invention where the base points are at the user&#39;s discretion may also be possible. 
     In accordance with a further embodiment of the invention, the method further comprises either directly receiving the private key or generating the private key, wherein generating the private key comprises receiving an input value and applying a cryptographic one-way function to the input value for generation of the private key, wherein the cryptographic one-way function is an injective function. 
     This embodiment has the advantage that a user may either directly use a private key for the generation of the identifiers, or alternatively he may use a certain input value from which the private key may be calculated. The input value may be a user-selected secret. 
     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. 
     In accordance with a further embodiment of the invention, the method further comprises receiving the user-selected secret as the input value, storing the user-selected secret in a memory, computing the private key by applying an embedding and/or randomizing function onto the secret, storing the private key in the memory, computing the set of public keys using the private key and erasing the secret and the private key from the memory. 
     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. Examples of computer memory include, but are not limited to: RAM memory, registers, and register files of a processor. 
     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&gt;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 to 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 the public parameter, e.g. a single number that embeds the user selected secret and the public parameter. 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. 
     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. 
     The term ‘embedding and randomizing function’ as used herein encompasses any function that implements both an embedding function and a randomizing function. 
     Even though, any known method for generation of asymmetric cryptographic keys may be employed in order to carry out the invention, the embodiment employing the user-selected secret for generating the public key and the private key(s) is particularly advantageous as an extremely high degree of protection of the informational privacy of users is provided. This is because an assignment of the user&#39;s identity to the user&#39;s public keys does not need to be stored and that no third party is required for establishing a binding between the public keys and the user&#39;s identity. In contrast, embodiments of the present invention enable to generate a set of user public keys in response to the user&#39;s entry of a user-selected secret whereby the public keys are 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. 
     This enables to store sensitive user data, such as medical data, even in an unencrypted form in a publicly accessible database. A user&#39;s public key can be used as the database identifier, e.g. a primary key or candidate key value that uniquely identifies tuples in a database relation, for access to data objects stored in the database. 
     The usage of an embedding and/or randomizing function is advantageous because the input value may be clear text or an easily guessed value. By using an embedding and/or randomizing function a pseudonym which is more difficult to decrypt may be constructed. 
     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. 
     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. The use of a public parameter is particularly advantageous as two users may by chance select the same secret and still obtain different identifiers as the combinations of the user-selected secrets with the user-specific public parameters differ. 
     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. 
     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. 
     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 embedding can be skipped and randomization of the user-selected secret is 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. 
     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. 
     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 fulfill 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, by multiplying the private key with the first base point. 
     In another aspect, the invention relates to a computer program product comprising computer executable instructions to perform any of the method steps described above. 
     In another aspect, the invention relates to a computer system for analyzing data of a first user, wherein an asymmetric cryptographic key pair is associated with the first user, said asymmetric cryptographic key pair comprising a public key and a private key, the data being stored pseudonymously in a database with the data being assigned to an identifier, wherein the identifier comprises the public key, the system comprising:
         a first interface for receiving a set of rules, the set of rules describing data processing steps,   a second interface for receiving the identifier,   a third interface for retrieving the data assigned to the identifier from the database,   an analyzing component for analyzing the retrieved data by applying the set of rules,   an output component for providing a result of the analysis.       

     In another aspect, the invention relates to a computer system for receiving a result from a second user by a first user, wherein an asymmetric cryptographic key pair is associated with the first user, said key pair comprising a public key and a private key, the system comprising means for receiving the result by said first user with the recipient address at which the result is received comprising the public key. 
     In another aspect, the invention relates to a computer system for storing data of a first user in a database, the first user having a private key, the system comprising:
         processor means for calculating a set of public keys, wherein the private key and each public key of the set of public keys form an asymmetric cryptographic key pair,   means for storing the data pseudonymously in the database with the data being assigned to an identifier, wherein the identifier comprises one of the public keys.       

     The term ‘computer system’ as used herein encompasses any device comprising a processor. The term ‘processor’ as used herein encompasses any electronic component which is able to execute a program or machine executable instructions. References to the computing device comprising “a processor” or a “microcontroller” should be interpreted as possibly containing more than one processor. The term ‘computer system’ should also be interpreted to possibly refer to a collection or network of computing devices each comprising a processor. Many programs have their instructions performed by multiple processors that may be within the same computing device or which may be even distributed across multiple computing devices. 
     In accordance with an embodiment of the invention, the system either comprises means for directly receiving the private key or means for receiving an input value, wherein the processor means are further operable for generating the private key, wherein generating the private key comprises applying a cryptographic one-way function to the input value for generation of the private key, wherein the cryptographic one-way function is an injective function. 
     In accordance with an embodiment of the invention, the input value is a user-selected secret, the system further comprising a memory for storing the user-selected secret and a private key and a processor operable for executing instructions stored in the memory, wherein the memory contains instructions for performing the steps of:
         storing the user-selected secret in a memory;   computing the private key by applying an embedding and/or randomizing function onto the secret;   storing the private key in the memory;   computing the set of public keys using the private key; and   erasing the secret and the private key from the memory.       

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the following embodiments of the invention are explained in greater detail, by way of example only, making reference to the drawings in which: 
         FIG. 1  is a block diagram of a first embodiment of a computer system of the invention, 
         FIG. 2  is a flowchart being illustrative of an embodiment of a method of the invention, 
         FIG. 3  is a block diagram of a further embodiment of a computer system of the invention, 
         FIG. 4  is a flowchart being illustrative of a further embodiment of a method of the invention, 
         FIG. 5  is a flowchart being illustrative of a further embodiment of a method of the invention, 
         FIG. 6  is a flowchart being illustrative of a further embodiment of a method of the invention, 
         FIG. 7  shows an embodiment of a data analysis system. 
     
    
    
     DETAILED DESCRIPTION 
     Throughout the following detailed description like elements of the various embodiments are designated by identical reference numerals. 
       FIG. 1  shows a computer system  100  that has a user interface  102  for a user&#39;s entry of a user-selected secret  112  that is designated as s T  in the following. For example, a keyboard  104  may be coupled to the computer system  100  for entry of s 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 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 . 
     A public parameter, such as the user&#39;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 T,i  containing at least one user-specific public parameter, such as the user&#39;s name or email address, is entered into the computer system  100  by the user T i . 
     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 T    112 , a combination  114  of s T    112  and V T,i , a private key  116 , a public key  118  that constitutes an identifier for a database and/or a pseudonym of the user T i , and a data object  120 , such as a medical data object containing medical data related to the user T i . Further, the memory  108  serves for computer program instructions  122  to be loaded for execution by the processor  110 . 
     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 . 
     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 T  and the user&#39;s name or by performing a bitwise XOR operation on s T  and the user&#39;s name. 
     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 randomizing of s T    112 , while embedding can be skipped. 
     In another implementation, the embedding function  132  is implemented by a binary cantor pairing function for embedding s T    112  and V 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. 
     In still another embodiment the embedding and randomizing function  126  is implemented by an embedding function, two different hash functions and a random number generator (cf. the embodiment of  FIGS. 3 and 4 ). 
     The key generator  128  serves to compute public key  118  using elliptic curve cryptography (ECC). The base point given by the domain parameters of the elliptic curve is multiplied by the private key  116  which provides the public key  118 . By varying the base point and leaving the other domain parameters of the elliptic curve unchanged multiple identifiers and/or pseudonyms comprising respective public keys can be computed for the user T i  on the basis of the same secret s T . Thus, this results in a set of public keys. 
     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&#39;s pseudonym, as a database access key, e.g. a primary key, candidate or foreign key value that uniquely identifies tuples in a database relation. 
     As mentioned above, it is preferred not to store all data objects  120  in the database  138  using only one identifier, since data correlation analysis performed on said data objects  120  may yield information which may enable to identify the user, i.e. owner of said data objects. Instead, the data objects are stored in the database  138  in a distributed manner with different data objects  120  being accessible with different public keys  118 , wherein the private key  116  and each public key of the set of public keys form an asymmetric cryptographic key pair. 
     Further, an analytic system  144 , such as a decision support system (DSS) or generally an inference engine 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. 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. 
     The outcome of the analysis may then be provided by the analytic system  144  to the users T, i.e. the owners of the records stored in the database. Sending the result of the individual analysis of the records of each user to the respective user may be performed by any kind of messaging, as described above. Preferably, the recipient address to which a respective analysis result is sent comprises the public key. Reception of the result may be performed either using the system  100  via its interface  136  and a dedicated reception component implemented by hardware or software. 
     Further, an external provider may be used for managing the reception of the results provided by the system  144 : for example, in case the result is sent by email with an address comprising the public key of the recipient user, a respective email management may be performed by an email provider  156 . For registration the user T i  creates his or her user account  158  by entering the public key  118  as the email address such that the email messages or data entered into the account  158  remain private even though they may be accessed by other persons, like for example governmental authorities. Privacy is retained due to the fact that the assignment of the public key to the user T i  is stored nowhere and cannot be reconstructed by technical means without knowledge of the user-selected secret s T    112 . 
     Instead of providing a result of the analysis to the individual users T, it is also possible to generally provide all the results of all users to an external service provider which may use the results anonymously for example for statistic purposes. 
     For generating a pseudonym p T,i  for a user T i  based on the secret s T    112  and domain parameters D i  containing a base point for the elliptic curve cryptography the following steps are executed by the computer system  100  in operation: 
     The user T i  enters his or her user-selected secret s T    112  such as via the keyboard  104 . In addition, the user may enter at least one public parameter V T,i  such as his name or email address via the keyboard  104  or otherwise. Such a public parameter V T,i  may also be permanently stored in the computer system  100 . 
     The secret s T    112  is temporarily stored in the memory  108 . Upon entry of the secret s T    112  and possibly the public parameter V T,i , the embedding function  132  or the embedding component of the embedding and randomizing function  126  generates the combination  114  of the secret s T    112  and the public parameter V T,i . The resultant combination  114  is temporarily stored in the memory  108 . 
     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 base point contained in the domain parameters D i  of the elliptic curve being used by the private key  116 . 
     The public key  118  which is the identifier, i.e. in the present embodiment the pseudonym p T,i , is stored in memory  108 . The secret s 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 i  as only the user knows the secret s T    112  that has led to the generation of his or her pseudonym p T,i . A data object  120  containing sensitive data of the user T i , such as medical data, can then be stored by execution of the database access function  130  in the pseudonymous database  138  using the pseudonym p T,i    118  as a database access key, e.g. a primary key or candidate key value that uniquely identifies tuples in a database relation. 
     The user-selected secret s T    112  may be obtained by combining a user-selected password or secret key with biometric data of the user T 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 T    112  on which the following calculations are based. 
     A plurality of users from the public set of enrolled participants T may use the computer system  100  to generate respective pseudonyms p 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 i  by way of example. 
     For reading the data object of one of the users T i  from the database  138  the user has to enter the secret s 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 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 T    112  the pseudonym can be computed by the computer system  100 . 
     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 i . After the database access operation has been performed, the secret s 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. 
     The above mentioned steps may be repeated several times for the generation of the set of identifiers from a single secret s T    112  or a single private key  116 , wherein preferably only the base point is varied. 
       FIG. 2  shows a corresponding flowchart. 
     In step  200  the user T i  enters his or her user-selected secret s T  and public parameter V T,i . In step  202  s T  and V T,i  are combined to provide the combination  114  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 T  and V T,i  in step  204  which provides a private key. As an alternative, an embedding and randomizing function  126  is applied on s T  and V T,i  which provides the private key. 
     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 i . For example the pseudonym may be used as a database identifier, 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 i  in a database with pseudonymous data (cf. database  138  of  FIG. 1 ). 
     When carrying out step  206 , the public key is calculated from the private key using elliptic curve cryptography, wherein said calculation is performed by a variation of the domain parameters used for performing the elliptic curve cryptography. For example, a base point variation may be performed for this purpose. 
     Even though the above description always speaks about using the public key as a pseudonym and using the pseudonym as a database access key, the invention is not limited to this embodiment. For example, the public keys generated using the steps above may only be a part of respective database access keys or pseudonyms, i.e. they may be comprised in the access keys or the pseudonyms. An example may be that the public key is given by ‘FF06763D11A64’, wherein the identifier used for accessing data in a database named ‘xyz’ may be given by ‘xyz-FF06763D11A64’. 
       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 T    112  may be performed as follows: 
     The first hash function  150  is applied on the user-selected secret s 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  114 , i.e. the embedded secret s T    112 . 
     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. 
     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 ). 
     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 T,i  as the database identifier for retrieving the random number for reconstructing the pseudonym at a later point of time. 
     By means of the system  100 , a set of identifiers comprising different public keys  118  is generated using the single secret  112  or directly the single private key  116 , wherein for example in case of elliptic curve cryptography only a base point of a set of domain parameters is varied for this purpose. Individual base points  190  used for generation of the individual public keys  118  may also be stored in the memory  108  of the computing system  100 . Alternatively, the base points may be stored in the database  154  or any other database external to the system  100 . 
     Generated identifiers may be used for accessing the database  138  using the module  130 , which was described with respect to  FIG. 1 . 
     The user T i  may use the public key provided by the computer system  100  for sending a message comprising data to an address comprising the public key or to an address which consists of the public key. The message management may be performed by a message provider  156 . For registration the user T i  creates his or her user account  158  by for example entering the public key  118  as the message address such that the messages or data entered into the account  158  remain private even though they may be accessed by other persons, like for example governmental authorities. Privacy is retained due to the fact that the assignment of the public key to the user T i  is stored nowhere and cannot be reconstructed by technical means without knowledge of the user-selected secret s T    112 . 
     It has to be noted that knowledge of the user&#39;s public key permits the user T i  to send information to his messaging account, as well as any other institution or device or person who knows the user&#39;s public key  118  to send information to the user T. As discussed with respect to  FIG. 1 , the analytic system  144  may analyze content of the database  138 , wherein data of a certain user T i  is stored assigned to an identifier, wherein the identifier comprises the public key of this user. Analysis of the content of the database  138  may result in the public key of the certain user T i , as well in an analysis result. Thereupon, the analytic system  144  may send this result as a message or in a message using a recipient address comprising the determined public key of the certain user T i . The message will then be received either directly by the user via the computing system  100 , or via the message provider  156 . 
     In the general case, when a user T 1  wants to send a message to user T 2 , this requires that user T 1  is able to obtain the messaging address of T 2  For this purpose, he may access a PKI (public key infrastructure) from which the address may be obtained. 
     According to an embodiment, access to the PKI may be performed by the user T 1  by using a pseudonym of the user T 2 . It has to be noted, that this pseudonym is not to be confused with the pseudonym comprising the public user key. Here, the pseudonym may be any identifier which is associated in a database of the PKI with the user&#39;s messaging address. Thus, the user T 2  may provide his pseudonym to user T 1  which may then access the PKI for retrieval of the respective messaging address of user T 2 . 
     Generally, for reconstructing the public key, the user has to enter his or her user-selected secret s 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 . 
     Depending on the implementation, the user may also need to enter the user&#39;s public parameter V T,i . A database access is performed using the user&#39;s public parameter V T,i  as a database identifier, 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 . 
     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 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 identifier, can be computed. After the user T i  has recovered his or her identifier 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 banking system  156  for performing online banking transactions using his identifier as a TAN. 
       FIG. 4  shows a respective flowchart for generating a pseudonym p T,i  for user T i . In step  300  the user enters the user-selected secret s T . In step  304  a first hash function is applied on the user-selected secret s 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. 
     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. 
     Fulfillment of such predefined conditions 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 an identifier such as for accessing a pseudonymous database or other purposes. 
     In case elliptic curve cryptography is used in step  314  for generating the public key, in step  318  a single domain parameter is varied, preferable a base point, wherein all other domain parameters are left unmodified. However, also more than one domain parameter may be modified in step  318 . Afterwards, using the modified domain parameter (s), steps  314  and  316  are repeated which results in a further public key which can be used as an identifier. 
     The method with steps  318 ,  314  and  316  may be repeated as often as necessary in order to generate a desired set of identifiers. 
       FIG. 5  shows a block diagram which illustrates an embodiment of the method according to the invention. In step  500  an input value is accessed. The input value may be stored in a computer memory or computer storage device or the input value may be generated. For example, the input value could be generated from a user-selected secret. In step  502  an asymmetric cryptographic key pair is calculated. The input value could be used to generate both the public and private key, or the input value could also possibly be the private key. In step  504  the public key of the cryptographic key pair is outputted as the identifier. 
     In step  506 , a domain parameter or a set of domain parameters are varied in accordance to a predefined scheme. Then, steps  502  to  504  are repeated using the same input value which results in a further identifier. Again, this is followed by step  506  and the cyclic performance of steps  502  to  504 . 
       FIG. 6  shows a further embodiment of the method according to the invention as a block diagram. In step  600  an input value is accessed. In step  602  an asymmetric cryptographic key pair is calculated. In step  604  the public key of the cryptographic key pair is outputted as the identifier. In step  606  a digital signature for data which is to be deposited into a database is generated using the private key of the cryptographic key pair. In step  608  data is deposited along with the digital signature and possibly the information which of the (variations of the) domain parameter sets has been used to create the digital signature into a database using the identifier. The identifier may be used to grant access to the database or as a permission to write data into the database or it may also serve as a database access key for the data being deposited into the database. In step  610  the authenticity of the data is verified using the identifier, even though this step may alternatively performed at a later point in time. The identifier is the complementary public key to the private key considering the (variation of the) domain parameter set used to create the digital signature. The private key was used to generate the digital signature for the data and the public key can be used to verify the digital signature. 
     Again, steps  602  to  608  and optionally step  610  may be repeated for generation of different identifiers using a single private key, i.e. a single input value. Different datasets may be signed using the single private key, wherein the different datasets and digital signatures are then deposited into the database possibly along with the information which of the (variations of the) domain parameter sets has been used to create the digital signature using the respective identifiers. I.e., the datasets are deposited in a distributed manner in the database. 
       FIG. 7  shows an embodiment of a data analysis system  144  which was discussed with respect to  FIGS. 1 and 3  in more detail. The data analysis system is for example a computer system for analyzing data of users, wherein the data is stored in the database  138  in a pseudonymous manner. As discussed above, data objects may be stored in the database  138  assigned with pseudonyms, wherein each pseudonym corresponds to a public key of a user. 
     In order to analyze the data, the system  144  uses a first interface  700  to access a set of rules in a rule database  708  describing data processing steps to be performed on the data comprised in the database  138 . Rules may for example comprise any kinds of logical operations and decisions to be performed on the data. The rule database  708  may be comprised in the system  144  or be external to the system  144 . 
     An interface  702  receives an identifier, for example a public key, wherein a further interface  704  is used to access the database  138  and to retrieve data assigned with said identifier. The analyzing component  146  will then analyze the retrieved data by applying the set of rules, wherein a result of the analysis will be provided via an output system  706  implemented in the system  144 . The output system may for example be any kind of messaging system, like an email messaging system. However, in the simplest case the output system may only be a database in which the result is saved assigned with its respective public key or identifier. 
     MATHEMATICAL APPENDIX 
     1. Embedding Functions. 
     There exist n-ary scalar functions
 
 d   1   N× . . . ×N→N  
 
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 1 , . . . , k n ), into scalars, i.e. natural numbers k.
 
2. The Binary Cantor Pairing Function
 
     The binary cantor pairing function π is an embodiment of embedding function  132 . The binary cantor pairing function is defined as follows: 
               π   ⁢     :     ⁢           ⁢   N   ×   N     -&gt;   N                 π   ⁡     (     m   ,   n     )       =         1   2     ⁢     (     m   +   n     )     ⁢     (     m   +   n   +   1     )       +   n           
which assigns to each fraction
 
             m   n         
the unique natural number π(m, n)—thus demonstrating that there are no more fractions than integers. Hence, if we map both s T  and V T,i  to natural numbers and use the fact that all identities are distinct, then π(s T , V T,i ) yields a unique value for each identity, even if there are equal personal secrets. To be more precise, since this function does 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)
 
     Let:
         p be a prime number, p&gt;3, and |F p  the corresponding finite field   a and b integers       

     Then the set E of points (x, y) such that
 
 E ={( x,y )ε| F   p   ×|F   p   |y   2   =x   3   +ax+b}   (F1)
 
defines an elliptic curve in |F 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.) The number m of points on E is its order.
 
     Let P,QεE be two points on E. Then the addition of points
 
 P+Q=R  and  RεE   (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  
 
     We define the k-times addition of P as [k]P, the point multiplication. 
     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 the public, and the as well known to the public point Q it is computationally infeasible to determine the integer k.
 
     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)
 
     With all this in mind we define an elliptic curve cryptographic (ECC) system as follows. Let:
         E be an elliptic curve of order m   BεE a point of E of order n, the base point       

     Then
 
 D={a,b,p,B,n,co ( B )}  (F5)
 
with
 
               co   ⁡     (   B   )       =     m   n           
defines a set of domain ECC-parameters. Let now g be an integer and
 
 Q=[g]B   (F6)
 
     Then (g, Q) is an ECC-key-pair with g being the private key and Q the public key. 
     For we rely on findings of Technical Guideline TR-03111, Version 1.11, issued by the Bundesamt für Sicherheit in der Informationstechnik (BSI), one of the best accredited sources 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)
 
     Now we can define our one-way function. Let D be a set of domain parameters concordant with (F7). Then
 
 f:[ 2 ,n− 1 ]→E  
 
 k     [k]B   (F8)
 
i.e. the point multiplication (F6), is an injective one-way function.
 
4. Implementing Key Generator Based on ECC
 
     The key generator  128  (cf.  FIGS. 1 and 3 ) can be implemented using ECC. 
     Definitions: 
     
         
         
           
             There are public sets of ECC-domain parameters D 1 , D 2 , . . . concordant with (F7)
 
 D   i   ={a   i   ,b   i   ,p   i   ,B   i   ,n   i }  (F9)
 
             There are public functions: an embedding function d( ), a randomizing function r( ) and our one-way function f( ) defined by (F8). 
             There is a public set of enrolled participants (users)
 
 T={T   1   ,T   2 , . . . }  (F10)
 
             Note that a T 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. 
             Each participant TεT chooses at his complete discretion his personal secret s T . In particular, for this secret is never revealed to anybody else—it is the participant&#39;s responsibility to ensure this—it is not subject to any mandatory conditions, such as uniqueness. 
             Our pseudonym derivation function is
 
 h ( )= f ( r ( d ( )))  (F11)
 
             with the following properties: 
             Given a TεT with his s T , a D i  and T, D i εV T,i  
 
 r ( d ( s   T   ,V   T,i ))= g   T,i   (F12)
 
             where g T,i  is a unique and strong, i.e. sufficiently random, private ECC-key for D i . 
             The pseudonym p T,i  corresponding to T, s T  and D i  is
 
 p   T,i   =f ( g   T,i   ,D   i )=[ g   T,i   ]B   i =( x   T,i   ,y   T,i )  (F13)
 
             There is a public set of pseudonyms
 
 P={p   1   ,p   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 T,i  is inserted in an anonymous way as p k  into P.
 
Remarks:
 
             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. 
             The distinction between two sets of domain parameters D i  and D 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
 
 D   i   ={a,b,p,B,n}   (F15)
 
             by swapping B for a statistically independent B 2 , i.e. by choosing a different base point, we can set
 
 D   j   ={a,b,p,B   2   ,n}   (F16)
 
             For D i  and D 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. 
           
         
       
    
     While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary and not restrictive; the invention is not limited to the disclosed embodiments. 
     Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. A computer program may be stored/distributed on a suitable medium, such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems. Any reference signs in the claims should not be construed as limiting the scope. 
     LIST OF REFERENCE NUMERALS 
     
         
         
           
               100  Computer system 
               102  User interface 
               104  Keyboard 
               106  Sensor 
               108  Memory 
               110  Processor 
               112  User-selected secret 
               114  Combination 
               116  Private Key 
               118  Public Key 
               120  Data Object 
               122  Computer program instructions 
               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  Data Analysis Component 
               148  Random number generator 
               150  Hash function 
               152  Hash function 
               154  Database 
               156  Computer system 
               158  User account 
               190  Set of base points