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1. CN110495133 - METHOD FOR GENERATING A PRIME NUMBER FOR A CRYPTOGRAPHIC APPLICATION

Office
China
Application Number 201880012780.8
Application Date 09.02.2018
Publication Number 110495133
Publication Date 22.11.2019
Publication Kind A
IPC
H04L 9/00
HELECTRICITY
04ELECTRIC COMMUNICATION TECHNIQUE
LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
9Arrangements for secret or secure communication
H04L 9/30
HELECTRICITY
04ELECTRIC COMMUNICATION TECHNIQUE
LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
9Arrangements for secret or secure communication
28using particular encryption algorithm
30Public key, i.e. encryption algorithm being computationally infeasible to invert and users' encryption keys not requiring secrecy
G06F 7/72
GPHYSICS
06COMPUTING; CALCULATING OR COUNTING
FELECTRIC DIGITAL DATA PROCESSING
7Methods or arrangements for processing data by operating upon the order or content of the data handled
60Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations
72using residue arithmetic
CPC
G06F 7/72
GPHYSICS
06COMPUTING; CALCULATING; COUNTING
FELECTRIC DIGITAL DATA PROCESSING
7Methods or arrangements for processing data by operating upon the order or content of the data handled
60Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations ; , e.g. using difunction pulse trains, STEELE computers, phase computers
72using residue arithmetic
H04L 9/003
HELECTRICITY
04ELECTRIC COMMUNICATION TECHNIQUE
LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
9Cryptographic mechanisms or cryptographic; arrangements for secret or secure communication
002Countermeasures against attacks on cryptographic mechanisms
003for power analysis, e.g. differential power analysis [DPA] or simple power analysis [SPA]
G06F 2207/7204
GPHYSICS
06COMPUTING; CALCULATING; COUNTING
FELECTRIC DIGITAL DATA PROCESSING
2207Indexing scheme relating to methods or arrangements for processing data by operating upon the order or content of the data handled
72Indexing scheme relating to groups G06F7/72 - G06F7/729
7204Prime number generation or prime number testing
H04L 9/3033
HELECTRICITY
04ELECTRIC COMMUNICATION TECHNIQUE
LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
9Cryptographic mechanisms or cryptographic; arrangements for secret or secure communication
30Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
3006underlying computational problems or public-key parameters
3033details relating to pseudo-prime or prime number generation, e.g. primality test
H04L 9/002
HELECTRICITY
04ELECTRIC COMMUNICATION TECHNIQUE
LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
9Cryptographic mechanisms or cryptographic; arrangements for secret or secure communication
002Countermeasures against attacks on cryptographic mechanisms
Applicants THALES DIS FRANCE SA
泰雷兹数字安全法国股份有限公司
Inventors BERZATI ALEXANDRE
A.贝尔扎蒂
ROUSSELLET MYLENE
M.鲁塞莱
Agents 中国专利代理(香港)有限公司 72001
中国专利代理(香港)有限公司 72001
Priority Data 17305191 21.02.2017 EP
Title
(EN) METHOD FOR GENERATING A PRIME NUMBER FOR A CRYPTOGRAPHIC APPLICATION
(ZH) 用于生成用于密码应用的素数的方法
Abstract
(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。