Abstract: A cryptographic processing method comprises the following steps: obtaining a second number determined by adding to a first number the order of a finite group or a multiple of this order; determining a quotient and a remainder by dividing the second number by a random number; obtaining a third element equal to the combination of elements equal to a first element of the finite group and in number equal to the product of the quotient and the random number; obtaining a fourth element equal to the combination of elements equal to the first element and in number equal to the remainder; determining a second element by combining the third element and the fourth element.

Abstract: A cryptographic processing method comprises the following steps: obtaining a second number determined by adding to a first number the order of a finite group or a multiple of this order; determining a quotient and a remainder by dividing the second number by a random number; obtaining a third element equal to the combination of elements equal to a first element of the finite group and in number equal to the product of the quotient and the random number; obtaining a fourth element equal to the combination of elements equal to the first element and in number equal to the remainder; determining a second element by combining the third element and the fourth element.

Abstract: A cryptographic processing method transforming an input byte into an output byte comprises the following steps: converting a plurality of words, each comprising at least one bit of the input byte, into input cryptograms by application, to each of said words, of a homomorphic encryption function from a first group to a second group provided with an operation; obtaining output cryptograms as a function of the input cryptograms, this obtaining step including at least one processing during which said operation is applied to two intermediate cryptograms, this processing producing a cryptogram that is an image by the homomorphic encryption function of a word including a Boolean logic combination of two bits comprised respectively in two words that are arguments, for the homomorphic encryption function, of said two intermediate cryptograms; determining bits of the output byte by applying respectively to the output cryptograms, an inverse function of the homomorphic encryption function.

Abstract: The present invention relates to a method for implementing a cryptographic algorithm having a given secret key comprising the execution by data processing means (11a) of an equipment (10a) of a code implementing said cryptographic algorithm stored on data storage means (12a) of the equipment (10a), the method being characterized in that at least one so-called obfuscated part of said code parameterized with said secret key uses only one so-called cmov instruction, which is a conditional move instruction in a first operand of the instruction of a second operand of the instruction, with at least one occurrence of said cmov instruction in said obfuscated part of the code being dummy.

Abstract: Generation of a message m of order ?(n) for a test of the integrity of the generation of a pair of cryptographic keys within the multiplicative group of integers modulo n=p·q, including: —key pair generation including, to generate p and q: a random selection of candidate integers; and a primality test; —a first search of the multiplicative group of integers modulo p for a generator a; —a second search of the multiplicative group of integers modulo q for a generator b; —a third search for a number y, as message m, verifying: 1???n?1, where ?=a mod p and ?=b mod q, the first or second search being performed during the primality test.

Abstract: Method for generating a pair of public and private cryptographic keys in the additive group of integers modulo n, where n is the product of two prime numbers p and q, the method including the following steps: calculating a public exponent e for said public key, and calculating a private exponent d for said private key from said public exponent and said public modulus, where d·e=1 mod ?(n), ?(n) being the least common multiple between p-1 and q-1, characterized in that the method furthermore comprises a step: of checking to check that ?(n)=0 mod (p-1) and ?(n)=0 mod (q-1).

Abstract: Method of integrity verification of cryptographic key pairs, the method including an integrity test with: at least one first step implementing one of the private and public keys and an initial test datum, the first step making it possible to generate a first result, at least one second step implementing at least the first result and the key not used during the at least one first step, the second step making it possible to generate a second result, and a comparison of the second result and of the initial test datum, characterized in that the test is re-executed upon each positive comparison, and in that the test is executed at least 2 times.

Abstract: Method of integrity verification of public and private cryptographic key pairs in the additive group of integers modulo n, with n being the product of two prime numbers p and q, the method including the following steps: of computation (201), on the basis of the number n, of a public exponent e of the public key, and of a private exponent d of the private key, of two candidate factors p? and q? corresponding respectively to the numbers p and q, of verification (206) so as to verify the consistency of the private exponent with respect to the public exponent and to the number n, the verification step involving the candidate factors.

Abstract: Generation of a message m of order ?(n) for a test of the integrity of the generation of a pair of cryptographic keys within the multiplicative group of integers modulo n=p·q, including: —key pair generation including, to generate p and q: a random selection of candidate integers; and a primality test; —a first search of the multiplicative group of integers modulo p for a generator a; —a second search of the multiplicative group of integers modulo q for a generator b; —a third search for a number y, as message m, verifying: 1???n?1, where ?=a mod p and ?=b mod q, the first or second search being performed during the primality test.

Abstract: Method for generating a pair of public and private cryptographic keys in the additive group of integers modulo n, where n is the product of two prime numbers p and q, the method including the following steps: calculating a public exponent e for the public key, and calculating a private exponent d for the private key from the public exponent and the public modulus, where d·e=1 mod ?(n), ?(n) being the least common multiple between p-1 and q-1, characterized in that the method furthermore includes a step: of checking to check that ?(n)=0 mod (p-1) and ?(n)=0 mod (q-1).

Abstract: Method of integrity verification of cryptographic key pairs, the method including an integrity test with: at least one first step implementing one of the private and public keys and an initial test datum, the first step making it possible to generate a first result, at least one second step implementing at least the first result and the key not used during the at least one first step, the second step making it possible to generate a second result, and a comparison of the second result and of the initial test datum, characterized in that the test is re-executed upon each positive comparison, and in that the test is executed at least 2 times.

Abstract: Method of integrity verification of public and private cryptographic key pairs in the additive group of integers modulo n, with n being the product of two prime numbers p and q, the method including the following steps: of computation (201), on the basis of the number n, of a public exponent e of the public key, and of a private exponent d of the private key, of two candidate factors p? and q? corresponding respectively to the numbers p and q, of verification (206) so as to verify the consistency of the private exponent with respect to the public exponent and to the number n, the verification step involving the candidate factors.