Generation of cryptographic keys

A method for cryptographically processing a message in a cryptographic system using encryption and/or digital signature mechanisms, the method comprising the following steps performed by an electronic cryptographic device comprising a processor of a cryptographic device in the cryptographic system:

• generating, by a processor of an electronic cryptographic device in the cryptographic system, a public cryptographic key e and a private cryptographic key d in the additive group of integers modulo n, such that:
• n=p·q, where p and q are prime numbers,
• 1<e<Φ(n), where e and Φ(n) are prime numbers among themselves and Φ(n)=(p-1)·(q-1), and
• d·e=1 mod λ(n), λ(n) being the least common multiple between p-1 and q-1,
• testing the security of the electronic cryptographic device against an attack, and
• encrypting and/or digitally signing the message using the generated cryptographic keys,
• wherein testing the security of the electronic cryptographic device against an attack includes a step of disrupting the calculation, by the processor of the electronic cryptographic device, of the value λ(n), in such a way as to obtain, instead and in place of the value λ(n), a value λ′(n)=λ(n)/α, where α divides λ(n), said disruption resulting in the calculation of a private key d′, instead and in place of the private key d such that d′·e=1 mod λ(n)/α.

A non-transitory storage medium containing a computer program comprising instructions that when loaded in and executed by a processor of an electronic cryptography device in a cryptographic system, causes the electronic cryptography device in the cryptographic system to carry out a method for cryptographically processing a message in the cryptographic system using encryption and/or digital signature mechanisms, the method comprising the following steps performed by the cryptographic device:

• 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, and
• encrypting and/or digitally signing the message using the generated cryptographic keys, wherein generating the pair of public and private cryptographic keys comprises the following steps, performed by a processor of a cryptographic device in the cryptographic system:
• calculating (209) a public exponent e for said public key, and
• calculating (210) a private exponent d for said private key from said public exponent and said public modulus, where d·e=1 mod λ(n), λ(n) the least common multiple between p-1 and q-1,
• checking (207) that λ(n)=0 mod (p-1) and λ(n)=0 mod (q-1), before generating, in case of positive check, the public and private cryptographic keys from the calculated public and private exponents.

An electronic cryptographic device comprising a processor of a cryptographic device in a cryptographic system configured to carry out a method for cryptographically processing a message in the cryptographic system using encryption and/or digital signature mechanisms, the method comprising the following steps performed by the electronic cryptographic device in the cryptographic system:

• 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, and
• encrypting and/or digitally signing the message using the generated cryptographic keys, wherein generating the pair of public and private cryptographic keys comprises the following steps, performed by a processor of a cryptographic device in the cryptographic system:
• calculating (209) a public exponent e for said public key, and
• calculating (210) a private exponent d for said private key from said public exponent and said public modulus, where d·e=1 mod λ(n), λ(n) the least common multiple between p-1 and q-1,
• checking (207) that λ(n)=0 mod (p-1) and λ(n)=0 mod (q-1), before generating, in case of positive check, the public and private cryptographic keys from the calculated public and private exponents.

A non-transitory storage medium containing a computer program comprising instructions that when loaded in and executed by a processor of an electronic cryptography device in a cryptographic system, causes the electronic cryptography device in the cryptographic system to carry out a method for cryptographically processing a message in the cryptographic system using encryption and/or digital signature mechanisms, the method comprising the following steps performed by the cryptographic device:

• generating, by a processor of an electronic cryptographic device in the cryptographic system, a public cryptographic key e and a private cryptographic key d in the additive group of integers modulo n, such that:
• n=p·q, where p and q are prime numbers,
• 1<e<Φ(n), where e and Φ(n) are prime numbers among themselves and Φ(n)=(p-1)·(q-1), and
• d·e=1 mod λ(n), λ(n) being the least common multiple between p-1 and q-1,
• testing the security of the electronic cryptographic device against an attack, and
• encrypting and/or digitally signing the message using the generated cryptographic keys,
• wherein testing the security of the electronic cryptographic device against an attack includes a step of disrupting the calculation, by the processor of the electronic cryptographic device, of the value λ(n), in such a way as to obtain, instead and in place of the value λ(n), a value λ′(n)=λ(n)/α, where α divides λ(n), said disruption resulting in the calculation of a private key d′, instead and in place of the private key d such that d′·e=1 mod λ(n)/α.

An electronic cryptographic device comprising a processor of a cryptographic device in a cryptographic system configured to carry out a method for cryptographically processing a message in the cryptographic system using encryption and/or digital signature mechanisms, the method comprising the following steps performed by the electronic cryptographic device in the cryptographic system:

• generating, by a processor of an electronic cryptographic device in the cryptographic system, a public cryptographic key e and a private cryptographic key d in the additive group of integers modulo n, such that:
• n=p·q, where p and q are prime numbers,
• 1<e<Φ(n), where e and Φ(n) are prime numbers among themselves and Φ(n)=(p-1)·(q-1), and
• d·e=1 mod λ(n), λ(n) being the least common multiple between p-1 and q-1,
• testing the security of the electronic cryptographic device against an attack, and
• encrypting and/or digitally signing the message using the generated cryptographic keys,
• wherein testing the security of the electronic cryptographic device against an attack includes a step of disrupting the calculation, by the processor of the electronic cryptographic device, of the value λ(n), in such a way as to obtain, instead and in place of the value λ(n), a value λ′(n)=λ(n)/α, where α divides λ(n), said disruption resulting in the calculation of a private key d′, instead and in place of the private key d such that d′·e=1 mod λ(n)/α.