(EN) 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.
(ZH) 本发明涉及一种用于生成素数并在密码应用中使用所述素数的方法，所述方法包括以下步骤：a）确定具有小的大小b=log2（B）比特的至少一个二进制基数B，并且对于每个确定的基数B，确定至少一个小素数pi，使得B mod pi=1，其中i是整数，b）选择素数候选者YP，c）在所述确定的二进制基数中选择的基数B中分解选择的素数候选者YP：，d）计算来自针对所述选择的基数的候选者YP的残差yPB，使得，e）测试所述计算的残差yPB是否可被在针对所述选择的基数B的所述确定的小素数中选择的一个小素数pi整除，f）当所述计算的残差yPB不能被所述选择的小素数整除时，迭代地重复上述步骤e），直到在步骤e）处执行的测试证明所述计算的残差yPB不能被针对所述选择的基数B的所述确定的小素数中的任何确定的小素数整除为止，g）当所述计算的残差yPB不能被针对所述选择的基数B的所述确定的小素数中的任何确定的小素数整除时，针对所述确定的二进制基数中的每个基数B迭代地重复步骤c）至f），h）当对于所有确定的基数B，针对确定的基数计算的所述残差yPB不能被针对所述确定的基数B的所述确定的小素数中的任何确定的小素数整除时，对所述候选者YP执行已知的严格可能素性测试，并且当已知的严格可能素性测试是成功时，存储所述素数候选者YP，并在所述密码应用中使用所述存储的素数候选者YP。
