Classifications

• • 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
  • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
  • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
  • H04L9/3249—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using RSA or related signature schemes, e.g. Rabin scheme

Definitions

• the invention relates to an encryption method, and an associated cryptographic system, with application in particular in the field of public key cryptography.
• the invention can be implemented in electronic devices such as smart cards.
• a complete public key cryptographic system generally includes an encryption algorithm and a signature algorithm.
• Such a cryptographic system can be implemented for example in a smart card comprising in particular, in an integrated circuit, calculation means programmed to implement the algorithms, and storage means, for storing public keys and / or secret keys necessary for the implementation of the algorithms.
• a known algorithm used in public key cryptographic systems is the RSA algorithm (from Rivest, Shamir and Adleman). It can be used to perform encryption operations and signature operations.
• the RSA algorithm consists in carrying out an exponentiation operation, using a public or private key, of a clear message formatted by an encryption function or a signature function, as the case may be.
• the encrypted message c can then be decrypted in again using the RSA algorithm, with the inverse function f _1 (x, N, d), (N, d) being a private key associated with the public key (N, e).
• the signature can then be verified using the RSA algorithm again, with the inverse function f (x, N ', e'), (N 1 , e ') being a public key associated with the private key (N 1 , of).
• N p * q, N ' ⁇ p' * q '.
• the numbers d, of integers depend on the numbers N, N 'and are also large.
• the numbers e, e 'integers are however often small. For security reasons, the keys ((N, e);
• a signature function ⁇ ' is said to be safe if it is not possible to create a signature s of a message m without knowing the private key, even if signatures if, s2 of messages ml, m2 are known.
• the functions ⁇ 'used in cryptographic systems are constructed to verify this condition.
• PSS Probabilistic Signature Scheme, in French probabilistic signature function
• the PSS function is parameterized by integers k, ko, kl and uses two hash functions: H: ⁇ 0, l ⁇ k "kl ⁇ ⁇ 0, l ⁇ l G: ⁇ 0, l ⁇ kl ⁇ ⁇ 0, l ⁇ "kl
• PSS (m, r) ⁇
• s with r a random parameter associated with the PSS function,
• the concatenation function, ⁇ H (m
• r), s G ( ⁇ ) ⁇ (m
• an encryption function ⁇ is said to be secure if it is not possible to distinguish two encrypted messages cl, c2 obtained from the function ⁇ and two clear messages ml, m2, even if one of the clear messages associated ml or m2 is known.
• the ⁇ functions used in cryptographic systems are constructed to verify this security condition.
• the signature functions ⁇ ′ and the encryption functions ⁇ are not the same.
• the same formatting function is used, both as an encryption function and as a signature function. More precisely, according to the invention, to implement an encryption method, use is made of the PSS function, known elsewhere for implementing a signature method.
• the formatting function is the PSS function.
• the PSS function is a secure function for encryption operations. Indeed, it is shown that the PSS function is safe for encryption operations, in the random oracle model, as defined in D2: M. Bellare and P. Rogaway, Random oracles are practical: a paradigm for designing efficient protocols. Proceedings of the First Annual Conference on Computer Communication Security, ACM, 1993. In addition, currently in the field of cryptography, the concept of security in the random oracle model and the concept of strongest security for real applications.
• the invention also relates to a cryptography system comprising an encryption method and a signature method, both using the PSS function as a formatting function.
• the cryptographic system includes:
• a step of exponentiation of the result of the formatting step using a second key (N 1 , d 1 ) according to the relation s ⁇ (m) of mod N ', s being a signed message, ⁇ (m) being the result of the formatting step, and d 'and N' of the elements of the second key.
• Such a cryptographic system is advantageous compared to known cryptographic systems, insofar as it requires approximately half the resources
• the first key and the second key are respectively a public key of a first pair of keys and a private key of a second pair of keys.
• the first pair of keys and the second pair of keys are identical.
• the same set of keys is used, both to implement the encryption method and the signature method. It is shown in fact that decrypting a message, encrypted according to an encryption method using the PSS function and a given set of keys, does not allow obtaining sufficient information to sign a message (possibly the decrypted message) according to a signature method. using the PSS function and the same set of keys.
• the invention is particularly applicable to the RSA cryptography algorithm, which is the most widely used algorithm to date in the field of cryptography.
• the invention also relates to an electronic component comprising means programmed for the implementation of an encryption method as described above, using the PSS function as a formatting function.
• the programmed means notably comprise a central unit and a program memory.
• the invention also relates to an electronic component comprising means programmed for the implementation of a cryptographic system as described above, comprising an encryption operation or a signature operation, executed alternately.
• the programmed means notably comprise a central unit and a program memory.
• the invention is particularly advantageous for smart card type applications, in which the components used must be as small as possible, and the implementation of the methods is as rapid as possible.

Landscapes

• Engineering & Computer Science (AREA)
• Computer Security & Cryptography (AREA)
• Computer Networks & Wireless Communication (AREA)
• Signal Processing (AREA)
• Computing Systems (AREA)
• Theoretical Computer Science (AREA)
• Storage Device Security (AREA)

Applications Claiming Priority (3)

Publications (1)

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Family Applications (1)

Country Status (6)

Families Citing this family (1)

• 2002
  • 2002-07-26 FR FR0209475A patent/FR2842967B1/fr not_active Expired - Fee Related
• 2003
  • 2003-07-25 AU AU2003269063A patent/AU2003269063A1/en not_active Abandoned
  • 2003-07-25 WO PCT/FR2003/002364 patent/WO2004012372A2/fr not_active Ceased
  • 2003-07-25 US US10/522,420 patent/US20060147039A1/en not_active Abandoned
  • 2003-07-25 EP EP03750849A patent/EP1535424A2/de not_active Withdrawn
  • 2003-07-25 JP JP2004523891A patent/JP2005534068A/ja active Pending

Non-Patent Citations (2)

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