Method for generating a prime number for a cryptographic application

Abstract

The present invention relates to a method for generating a prime number and using it in a cryptographic application, the method comprising the steps of: a) determining at least one binary base B witha small size b = log2(B) bits and for each determined base B at least one small prime pi such that B mod pi = 1, with i an integer, b) selecting a prime candidate YP, c) decomposing the selected primecandidate YP in a base B selected among said determined binary bases : YP = [sigma]yjB, d) computing a residue yPB from the candidate YP for said selected base such that yPB = [sigma]yj, e) testing if said computed residue yPB is divisible by one small prime pi selected among said determined small primes for said selected base B, f) while said computed residue yPB is not divisible by said selected small prime, iteratively repeating above step e) until tests performed at step e) prove that said computed residue yPB is not divisible by any of said determined small primes for said selected base B, g) when said computed residue yPB is not divisible by any of said determined small primes for said selected base B, iteratively repeating steps c) to f) for each base B among said determined binary bases, h) when, for all determined bases B, said residue yPB computed for a determined base is not divisible by any of said determined small primes for said determined base B, executing a known rigorous probable primality test on said candidate YP, and when the known rigorous probable primality test is a success, storing said prime candidate YP and using said stored prime candidate YP in saidcryptographic application.

Description

technical field [0001] The present invention relates to the field of prime number generation for cryptographic applications and associated cryptographic devices, and more particularly, to fast prime number generation using coprimeity tests that do not require any GCD calculations. Background technique [0002] Cryptographic applications such as encryption or cryptographic key generation often rely on prime numbers. Therefore, devices implementing such cryptographic applications, such as security devices such as smart cards, must generate prime numbers, which is one of the most resource-consuming operations embedded on such devices. The primality of the number of candidates is usually tested using a strict probable primality test such as the Miller-Rabin test. Such tests are very expensive, and candidates can be pre-excluded by testing their co-primeness with some known small primes. [0003] Such coprimeality tests are usually based on greatest common divisor (GCD) calcula...

AI Technical Summary

Problems solved by technology

However, such a GCD computation can be very expensive in itself, especially for devices with limited processing power and / or CPUs that do not include any fast dividers

GCD calculations in frames for cryptographic applications can also pose a security risk, as GCD calculation leaks can be used to retrieve secret keys such as RSA private keys

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