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1. EP3364592 - METHOD FOR GENERATING A PRIME NUMBER FOR A CRYPTOGRAPHIC APPLICATION

Office
European Patent Office
Application Number 17305191
Application Date 21.02.2017
Publication Number 3364592
Publication Date 22.08.2018
Publication Kind A1
IPC
H04L 9/00
HELECTRICITY
04ELECTRIC COMMUNICATION TECHNIQUE
LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
9Arrangements for secret or secure communication
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
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
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 GEMALTO SA
ISSM SAS
Inventors BERZATI ALEXANDRE
ROUSSELLET MYLÈNE
Designated States
Priority Data 17305191 21.02.2017 EP
Title
(DE) VERFAHREN ZUR ERZEUGUNG EINER PRIMZAHL FÜR EINE KRYPTOGRAPHISCHE ANWENDUNG
(EN) METHOD FOR GENERATING A PRIME NUMBER FOR A CRYPTOGRAPHIC APPLICATION
(FR) PROCÉDÉ DE GÉNÉRATION D'UN NOMBRE PREMIER POUR UNE APPLICATION CRYPTOGRAPHIQUE
Abstract
(EN) 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 = log 2 (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 = ˆ‘ y j B i d) computing a residue y PB from the candidate Y P for said selected base such that y PB = ˆ‘ y j e) testing if said computed residue y PB is divisible by one small prime p i 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.