US20220318403A1 - Cryptographic Pseudonym Mapping Method, Computer System, Computer Program And Computer-Readable Medium - Google Patents

Cryptographic Pseudonym Mapping Method, Computer System, Computer Program And Computer-Readable Medium Download PDF

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US20220318403A1
US20220318403A1 US17/627,762 US202017627762A US2022318403A1 US 20220318403 A1 US20220318403 A1 US 20220318403A1 US 202017627762 A US202017627762 A US 202017627762A US 2022318403 A1 US2022318403 A1 US 2022318403A1
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data
data source
mapping
mapper
key
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Ferenc Vágujhelyi
Gergely Vágujhelyi
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Xtendr Zrt
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/50—Monitoring users, programs or devices to maintain the integrity of platforms, e.g. of processors, firmware or operating systems
    • G06F21/55—Detecting local intrusion or implementing counter-measures
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0866—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving user or device identifiers, e.g. serial number, physical or biometrical information, DNA, hand-signature or measurable physical characteristics
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/21—Design, administration or maintenance of databases
    • G06F16/211—Schema design and management
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/30—Information retrieval; Database structures therefor; File system structures therefor of unstructured textual data
    • G06F16/31—Indexing; Data structures therefor; Storage structures
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/60—Protecting data
    • G06F21/602—Providing cryptographic facilities or services
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0819—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s)
    • H04L9/0825—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s) using asymmetric-key encryption or public key infrastructure [PKI], e.g. key signature or public key certificates
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0894—Escrow, recovery or storing of secret information, e.g. secret key escrow or cryptographic key storage
    • H04L9/0897—Escrow, recovery or storing of secret information, e.g. secret key escrow or cryptographic key storage involving additional devices, e.g. trusted platform module [TPM], smartcard or USB
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3006—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters
    • H04L9/302—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters involving the integer factorization problem, e.g. RSA or quadratic sieve [QS] schemes
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3066—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/42—Anonymization, e.g. involving pseudonyms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/76—Proxy, i.e. using intermediary entity to perform cryptographic operations

Definitions

  • the invention relates to a cryptographic method and computer system for pseudonym mapping, a computer program and a computer-readable medium, preferably for implementing a system for data sharing wherein the data can be analysed in an anonymous manner.
  • the invention provides a secure pseudonymisation solution that complies with the regulations of GDPR.
  • the present invention provides a solution for the problem of providing the option, exclusively for a competent authority, to assign data that have been pseudonymised for analytic purposes, anonymised by other appropriate means, and are not utilised for official purposes, to unencrypted data utilising a specially handled cryptographic key that was generated for this purpose.
  • WO 2017/141065 A1 entitled “Data management method and registration method for an anonymous data sharing system, as well as data manager and anonymous data sharing system” discloses a solution for analysing data residing with multiple mutually independent entities—hereinafter, data sources—in a way that the data are loaded in a single unified database in which the identifiers of the entities (for example, persons, companies) are stored applying pseudonyms adapted for protecting anonymity, ensuring that the original data cannot be restored from the pseudonyms.
  • the present invention complements the solution disclosed in WO 2017/141065 A1 with a pseudonym mapping method that is secure from a number-theoretical aspect.
  • the analysis of these data allows for making valuable inferences.
  • the data are stored at a plurality of entities that are usually not in a dependent relationship with one another.
  • the data are often characteristic of entities (for example, persons, companies, institutions, properties, apparatuses, financial assets, etc.) or describe the behaviour thereof.
  • the entities are referred to applying widely known entity identifiers (for example, social security number, tax number, land registry number).
  • entity identifiers for example, social security number, tax number, land registry number.
  • the analysable data that are characteristic of the entities according to the entity identifiers are called attributes.
  • the aim of the analysis is not understanding the properties, behaviour or contact network of a particular person or thing, but recognising patterns of behaviour that can be expected from (anonymous) individuals in a larger population, analysing the structure of contact networks, and making inferences related to the future course of events.
  • mapping between the unencrypted, open entity identifier and the anonymous identifier (hereinafter: pseudonym) stored in the common database are defined by the method disclosed in WO 2017/141065 A1.
  • This mapping can be practically implemented only by utilizing a special information-technology device, namely, a cryptoprocessor (a dedicated computer unit that performs cryptographic operations under physically protection). In open multi-user systems this poses problems for the applicability of the system.
  • the known technical solution usually provides protection against “brute force”-type attacks (by possessing information on the operation of the encryption system, the applied key is determined by trying each possible key), but malicious cooperation between a data source and the entity performing the mapping can be prevented only by applying a complementary method, for example by encrypting the mapped values by an additional entity.
  • the pseudonym can be applied for the purposes of the above described analysis if a given open entity identifier is entered into the common database under the same pseudonym, irrespective of which data source sent it, i.e. the mapping between the unencrypted identifiers and the pseudonyms has to be a one-to-one mapping, where the inverse of the mapping cannot be computed, i.e. the unencrypted entity identifier cannot be generated from the pseudonym, by any entity. If the mapping is carried out by the data sources, then they also have to apply the same mapping.
  • a cryptographic hash function is usually applied, with the unencrypted data being the input of the function, and the output value being in the case the pseudonym.
  • the multiplicity of the entity identifiers is usually low, on the order of between a hundred million and a few tens of billions.
  • a rainbow table (a pre-computed table for inverting cryptographic hash functions) can be generated in a very short time. Therefore, in the course of computing the hash value, the input data are complemented with “salt” (randomly chosen data applied as additional input data of hash functions).
  • Another possibility is to entrust the generation of the relation between the unencrypted data or the data encrypted by the data sources applying the same encryption and the pseudonym to a trusted cooperator.
  • the trusted cooperator is able to compile the rainbow table—trivially in the first case, and in the second case, by gaining access to only a single data source's system. Therefore, the solution according to WO 2017/141065 A1 came to the conclusion that the data sources have to apply an encryption method based on a unique, for example, an own, cryptographic key.
  • the same entity identifier is sent by the data sources as different ciphers (encrypted data), while pseudonym mapping has to be performed such that the different ciphers have to be assigned to the same pseudonym if the particular ciphers were computed from the same unencrypted identifier.
  • RSA keys are applied, wherein the decryption key is stored in a Trusted Platform Module (TPM, see for example ISO/IEC 11889), the decryption process and the mapping of the unencrypted data into the pseudonym is carried out utilizing a secure cryptoprocessor.
  • TPM Trusted Platform Module
  • EP 3 188 070 A1 discloses a double encryption method, while proxy cryptography is disclosed in Giuseppe Ateniese et al, “Improved Proxy Re-Encryption Schemes with Applications to Secure Distributed Storage”, IACR, International Association For Cryptologic Research, Vol. 20060111:153421, 11 Jan. 2006 (2006-01-11), page 1-25, and in Ivan A. et al, “Proxy Cryptography Revisited”, Proceedings of the Symposium on Network and Distributed System Security, XX, XX, 1 Feb. 2003 (2003-02-01), page 1-19.
  • the object of the invention is to eliminate, or to reduce the impact of, the drawbacks of prior art technical solutions, especially the prior art solution presented above.
  • the primary object of the invention is to provide a cryptographic pseudonym mapping solution that does not require—for performing decryption and for mapping the unencrypted data to the pseudonym—the use of secure hardware, for example a cryptoprocessor.
  • the cryptographic pseudonym mapping method is adapted for generating a pseudonymised database from entity data, wherein the data are identified at the data sources utilizing the entity identifiers of the respective entities, and wherein the data are identified in the pseudonymised database utilizing pseudonyms assigned to the respective entity identifiers applying a one-to-one mapping.
  • the present invention is a solution that utilizes the properties of modular exponentiation performed on residue classes, and the properties of operations based on specially selected discrete points of elliptic curves, and implements the required abstract mapping, while not containing the above-mentioned limitations related to the prior art.
  • the invention does not require any special hardware for storing the cryptographic keys or for performing calculations, but instead solves the problem by purely cryptographic means.
  • Information technology devices apply a binary representation of data, so data can be interpreted as positive integers that can be utilized for performing calculations. In the following, it is assumed of the domain of the mappings that it is capable of providing a unique representation of the entity identifiers and the computed ciphers.
  • the modulus is chosen to be large enough that a sufficient number of residue classes are available. Due to the key sizes applied in practical implementations, this does not pose a problem.
  • the exponent can be represented applying much more bits compared to practically occurring entity identifiers. In such cases, the so-called “padding” of the values can be considered, such that the exponentiation performed with a low base cannot be inverted by ordinary root computation. This occurs in case modular arithmetic is not required during the process of computing the result. Due to the requirement of applying a one-to-one mapping only deterministic padding methods can be applied.
  • each data source comprising a database containing entity identifiers and attributes.
  • the data have to be collected in a common database such that the entity identifiers are included therein applying pseudonyms according to the following:
  • Conditions (1) and (2) together imply that the mapping has to be a one-to-one mapping.
  • Cryptographic mappings meet this requirement, provided we remain inside the domain (in cryptography, the message domain) thereof.
  • To fulfil condition (4) such a method is required that is adapted to generate unencrypted data from the ciphers mapped applying cryptographic keys utilised by the other entities, while the other entities are not able to compute this decryption key from their respective own cryptographic keys. Because the relationship between the pseudonym and the unencrypted data is to be protected by all means, it is the cipher computed by the data sources that has to be applied for fulfilling this condition.
  • the data source It must not be possible for the data source to track the first and second step of the mapping, because otherwise it can trivially obtain the pseudonym as the result of the second computation step.
  • the entity carrying out the second mapping can trivially access the pseudonym, so it must not access the unencrypted entity identifier. This can be provided if the entity identifiers are sent by the data sources to the mapper entity applying their own unique encryption, i.e. utilizing their own cryptographic key, but the data sources either cannot “see” the pseudonym mapping computation or they cannot relate the result thereof to the data provided by themselves.
  • pseudonym mapping has to be performed applying the cipher by breaking down the mapping into steps wherein a given step can be performed only by a single participating entity adapted to perform the mapping:
  • D is the entity identifier
  • P is the pseudonym
  • i is the numeric identifier of the data source
  • C i is the cipher computed applying its own key.
  • the different mappings in an encryption system usually execute the same algorithm applying different keys. Therefore, the mapping g performed applying the key b can be replaced by f b .
  • the mapper is adapted for decrypting the cipher, following by mapping the unencrypted data to the pseudonym P applying the pseudonym mapping key b.
  • the cryptographic key of the i-th data source is (e i , N), where e is the encryption exponent and N is the modulus.
  • the cipher is obtained by the calculation
  • this calculation is performed for example applying a secure cryptoprocessor such that the mapper cannot access the unencrypted data but can use the results for computing the pseudonym.
  • the pseudonym is obtained from the unencrypted data utilizing the cryptographic key (b, N) of the mapping g ⁇ f b (here, unlike elsewhere in this description, the E sign denotes identity rather than congruence):
  • An object is to present a computation method for performing the latter two mappings in the course of which the entity performing the computation
  • condition (i.) that the entity performing the computation must also not be able to access d i because otherwise it could decrypt the cipher.
  • Condition (ii.) is required in order to prevent a successful trial-and-error or rainbow-table based attack by the mapper.
  • data are represented applying residue classes defined by a positive integer modulus (N).
  • decryption applying an inverse key and pseudonym mapping can be performed in an arbitrary number of steps such that unencrypted data (an entity identifier) is not generated in the course of the computations, no entity is able to obtain the decryption key key i ⁇ 1 , and also no entity is able to obtain the pseudonym mapping key b, i.e. no entity is able to generate a pseudonym from unencrypted data in secret, i.e. to compile a rainbow table.
  • information technology methods based on known number theoretical bases are applied.
  • FIG. 1 is the schematic diagram illustrating a solution according to the invention that is implemented applying a single key manager and comprises a specially authorised entity that is adapted for deciphering the encrypted data (cipher) of the data source.
  • the entity identifiers and corresponding data are stored in databases at mutually independent data sources, and, after pseudonymisation according to the invention, the data, together with the pseudonyms generated from the entity identifiers, are stored, assigned to each other, in a central pseudonymised database.
  • the relationship between unencrypted data and the pseudonym cannot be affected by the origin of the data (i.e. what data source it came from).
  • the process of mappings i.e. the operations performed at the particular stages, are unique for each data source, that is, different cryptographic keys (for example, modular exponents) have to be used for performing the same mapping.
  • the implementation of a data gathering system necessarily begins with selecting an appropriate modulus. This is carried out in practice by the provider of the data gathering service, or the data gathering community first deciding upon the bit length of the applicable keys. Then, two such prime numbers are selected of which the product (applied as the modulus) can be represented using the given number of bits.
  • the entity generating the keys (hereinafter: the key manager) has to know the modulus N and also the value ⁇ (N) given by the Euler function, or in other words, its totient value.
  • the value N of the modulus has to be known by all participating entities performing mappings. If the representation size of the entity identifiers to be mapped is significantly smaller than the key size, some kind of padding method is preferably applied. This method has to be deterministic in the sense that every data source has to receive the same value such that the pseudonym is also deterministic, irrespective of the data source.
  • the basic data of the mapping are therefore N and ⁇ (N).
  • random selection it is meant that the implementation of the method is not dependent on which particular elements of the given set are chosen. Accordingly, random selection is meant to include also quasi-random or pseudo-random selection, as well as all such selection methods (even according to rules unknown to an observer) wherein the selection appears to be random to the outside observer. If the set constitutes an algebraic structure, then, if it has a null element and/or a unit element, then it/they are not regarded as randomly selected. Also, in the case of residue classes, the selection of non-relatively prime values is avoided. However, for cryptography considerations it is worth selecting such values for which the bit length of their representation fills up all the available space.
  • entity identifiers D and attributes (the latter are not shown in the diagram) describing the entities or their behaviour are stored by data sources DS i in their respective own databases.
  • the relationship between a particular entity and the other entities can be regarded as a characteristics of the given entity.
  • the entity identifiers of the other entities are regarded as attributes (for example, B is a client of A, in which case B is an attribute and an entity identifier at the same time).
  • B is a client of A, in which case B is an attribute and an entity identifier at the same time.
  • the attributes related to the entity identifiers D are preferably passed on by the data sources DS; as unencrypted data, while the entity identifiers D are encrypted by the data sources DS i utilizing their own cryptographic keys.
  • the resulting cipher is sent to the entity adapted to perform the mapping to the pseudonym P, i.e. to the mapper M.
  • an assignment between the unencrypted data and the cipher, i.e. the encrypted entity identifier is maintained, because the database required for data analysis can only be loaded with useful information in such a manner.
  • the inventive technical solution applying a single mapper M common for all data sources DS is implemented as follows. In a first step, encryption is performed by the data source DS i , followed by the pseudonym P being computed by the mapper M in a second step. If these two entities cooperate, then they are able to connect the unencrypted data with the pseudonym P, so they can even generate a rainbow table.
  • the solution can be applied therefore in case supervision of the mapper M is complemented by further informational technology means.
  • the i-th data source DS i uses its own secret cryptographic key that is referred to as (e i , N) using the references applied above.
  • Each data source may utilize an arbitrary number of keys, so more than one key identifier index i can correspond to it. Therefore, the entity identifier D is sent to the mapper as the cipher
  • the pseudonym is generated by the mapper performing the operation
  • the entity identifier D i.e. the unencrypted data appears somewhere in the course of the above calculation. If the modular exponentiation above was performed as a sequence of multiplications, then after performing d i multiplications the unencrypted identifier D would be obtained, which would make the method useless because the entity performing the computation can easily check if the obtained partial result is of the form expected from the entity identifier, especially if it also contains a CDV (check digit value). However, due to the minimally applicable key size of 2048 bits, the decimal form of the exponent has 616 digits, i.e. as many as 10 616 modular multiplications would have to be carried out. In practice, this is not feasible.
  • the exponentiation x y is performed applying a binary exponentiation method (see for example: modular exponentiation, right-to-left binary method).
  • the numbers are represented in binary form, as a sum of powers of two. For example, for y:
  • y i is the i-th bit of the binary representation of the number, i.e. it is either zero or one, contributing either zero or 2 i to the sum.
  • x y ⁇ x y 0 ⁇ 2 0 +y 1 ⁇ 2 1 +y 2 ⁇ 2 2 +y 3 ⁇ 2 + x y 0 ⁇ 2 ⁇ x y 1 ⁇ 2 1 ⁇ x y 2 ⁇ 2 2 ⁇ x y 3 ⁇ 2 3 ⁇ . . . ⁇ x y n ⁇ 1 ⁇ 2 n ⁇ 1
  • the intermediate result is multiplied by one, while if the i-th bit is one, then it is multiplied by x 2 i , i.e. by x 1 , x 2 , x 4 , x 8 , . . . , x 2n ⁇ 1 .
  • exponentiation applying powers of two can be carried out as a bitwise shift operation. Thereby, practical computability has been achieved.
  • the intermediate result is the product of the powers computed applying exponents of (the corresponding) powers of two of the non-zero digits of the binary representation of the cipher C i .
  • the common identifiers of the data gathering network are characterised by the following.
  • the only requirement for the exponent b utilized for mapping the unencrypted data into the pseudonym is that it is relatively prime to ⁇ (N).
  • the modular multiplicative inverse of b for ⁇ (N) (the multiplicative inverse of a is a ⁇ 1 modulo m if a ⁇ 1 a ⁇ 1 mod m) is not computed because it is not used for any calculations.
  • the process of generating a pair of mapping keys is the following: After carrying out the above calculations, an exponent d i that is relatively prime to ⁇ (N) is chosen randomly. Then the extended Euclidean algorithm is applied for computing e i , for which the formula e i d i ⁇ 1 mod ⁇ (N) will hold true. After that, h i ⁇ d i ⁇ b mod ⁇ (N) is computed.
  • a key manager KM is required that is adapted for generating the keys and making them accessible to the entities performing the computations.
  • the values of p, q and b are thus generated by the key manager and are kept secret.
  • the value ⁇ (N) is accessible also only to the key manager, i.e. it is the only entity that is capable of generating keys (e i , d i and h i ), i.e. the above described pair of mapping keys is generated by the key manager KM.
  • ciphers originating directly from the data sources DS i are preferably applied for this purpose.
  • the key manager KM pass on the key d i to this entity over an encrypted data channel. Then, provided that it has the required legal authorisation or the permission of the data gathering community, it may request the required cipher data from the mapper M.
  • the keys d i and the data are obtained by the authority A for example from the key manager KM and from the entity responsible for managing the pseudonymised database DB, respectively. Thereby, only those ciphers and exclusively those cryptographic keys are passed on to it that correspond to the data included in its authorisation.
  • An exemplary solution that can be seen in FIG. 1 comprises the following steps:
  • the data are encrypted by the data sources DS i applying respective own secret cryptographic keys e i identified by the index i, where a data source DS i can have an arbitrary number of keys.
  • prime numbers are known (it is (p ⁇ 1) ⁇ (q ⁇ 1)).
  • pseudonym mapping can also be performed applying points of elliptic curves (see for example the Wikipedia article “Elliptic curve”) defined over the number field of residue classes modulo p (where p is a prime).
  • the unencrypted entity identifier m has to be assigned to a point of the curve. Let us choose a point G of the curve having an order q that is sufficiently great that the points of the message space can be assigned to the points generated by G applying a one-to-one mapping.
  • this point is projected by the i-th data source DS i to another point C i of the curves applying its own cryptographic key, followed by it being projected by the mappers to the point P utilized as a pseudonym such that the different ciphers C i are assigned to the same point P if and only if the point M was identical.
  • Applying the formula h i a i +b, it generates the mapping key corresponding to the data source DS i .
  • the key is then passed on to the mapper M in encrypted form.
  • the above process carried out on residue classes is modified only in that the below described operation is performed on the points of the curve.
  • the operation ⁇ utilizing such values are hereinafter denoted with the operator ⁇ .
  • the pseudonym P is obtained through the combination of the two mappings:
  • the same entity identifier D is sent by each data source as a different cipher, but finally it is assigned to the same pseudonym P.
  • the x coordinate of the point P can also be applied as the pseudonym.
  • the authority A may request the required cipher data from the mapper M.
  • the following data conversion is performed by the pseudonym mapping system according to the invention:
  • the computer system for cryptographic pseudonymisation comprises
  • the key manager KM is preferably an apparatus comprising a processor adapted for executing a program and memory adapted for providing data writing, storage, and read-out functions.
  • the program run on the apparatus is adapted to generate the data required for executing the mappings, for example the modular exponent adapted for generating a pseudonym from unencrypted data and the totient value of the modulus.
  • the apparatus is adapted for storing these values such that they cannot be accessed by anybody else, but it can still be capable of performing computations utilizing them.
  • TPM Trusted Platform Module
  • the mapper M j is preferably an apparatus that is adapted for reading any input parameters of modular exponentiation (base, exponent, modulus), as well as executing the operation and making the result available for readout.
  • a module can for example be implemented as a general-purpose computer or microcontroller.
  • TPM circuits also fulfil all the above listed requirements.
  • Another aspect of the invention is a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the method according to the invention.
  • the invention further relates to a computer-readable medium adapted for storing the above-mentioned computer program.
  • the invention can be applied for various purposes; one of these being the analysis of loyalty card purchase databases involving multiple stores. Let us assume that a company engaged in business analysis and market research activities prepares an analysis of typical customer behaviour in retail stores, which is then purchased by its clients. The analysis is aimed at defining customer groups based on characteristics like the products purchased, the frequency of purchases, the relationship between type and location of stores, the season of year, and the products purchased, etc.
  • the idea may arise that a mapping implemented utilizing a so-called “salted” cryptographic hash function can be applied to the personal data (such as name, sex, birth date, and postcode), but certain lawyers representing the stores may reject this option because the resulting hash data can be connected, by the entity performing the data analysis, to the personal data simply by registering itself as a store and compiling a rainbow table for example from the electoral register.
  • the invention provides a solution to this problem.
  • the implementation of the solution according to the invention can comprise a server software component that allows that the data sources DS i receive the cryptographic key generated by the key manager KM over an encrypted data channel after authentication at a web page.
  • a computer implementation of the computations performed by the mapper M can be provided.
  • the key generation and mapping service can be activated a cloud service provider such that its operation cannot be affected (except for starting and stopping it) by any of the entities; this setup can preferably also be audited.
  • the mapping factors corresponding to the cryptographic keys of the stores are passed on by the key manager KM to the mapper M over an encrypted data channel, the mapper M then applying them for computing the pseudonym P.
  • the analyses can be applied for picking out customers who typically make their purchases in a given store but usually buy a particular product somewhere else, or on certain days do their shopping at a different location shortly after store closure. These are valuable pieces of information that can support business decisions. For example, it is preferable to stock another brand of a particular product, or to close an hour later on Fridays.
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