1. US20200057611 - Method for generating a prime number by testing co-primalty between a prime candidate and a predetermined prime number in a binary base

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