Processing

Please wait...

Settings

Settings

Goto Application

1. WO2018153684 - METHOD FOR GENERATING A PRIME NUMBER FOR A CRYPTOGRAPHIC APPLICATION

Publication Number WO/2018/153684
Publication Date 30.08.2018
International Application No. PCT/EP2018/053247
International Filing Date 09.02.2018
IPC
H04L 9/00 2006.01
HELECTRICITY
04ELECTRIC COMMUNICATION TECHNIQUE
LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
9Arrangements for secret or secure communication
H04L 9/30 2006.01
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 2006.01
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 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
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 9/002
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
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]
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
Applicants
  • THALES DIS FRANCE SA [FR]/[FR]
Inventors
  • BERZATI, Alexandre
  • ROUSSELLET, Mylène
Agents
  • BRICKS, Amélie
Priority Data
17305191.321.02.2017EP
Publication Language English (EN)
Filing Language English (EN)
Designated States
Title
(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 = 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 prime candidate YP in a base B selected among said determined binary bases : YP = ∑yjBi d) computing a residue yPB from the candidate YP for said selected base such that yPB = ∑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 said cryptographic application.
(FR)
La présente invention concerne un procédé de génération d'un nombre premier et son utilisation dans une application cryptographique, comprenant les étapes consistant à : a) déterminer au moins une base binaire B avec une petite taille b = log2(B ) bits et pour chaque base déterminée B au moins un petit premier pi tel que B mod pi = 1, avec i un entier, b) sélectionner un premier candidat YP, c) décomposer le candidat principal sélectionné YP dans une base B sélectionnée parmi lesdites bases binaires déterminées : YP = ∑yjBi d) calculer un résidu yPB à partir du candidat YP pour ladite base choisie telle que yPB = ∑yj e) tester si ledit résidu calculé yPB est divisible par un petit premier pi sélectionné parmi lesdits petits nombres premiers déterminés pour ladite base B sélectionnée, f) tandis que le résidu yPB n'est pas divisible par ledit petit premier choisi, répéter de manière itérative ci-dessus l'étape e) jusqu'à ce que les tests effectués à l'étape e) prouvent que ledit calcul de résidu yPB n'est divisible par aucun des petits nombres premiers déterminés pour ladite base B choisie, g) lorsque ledit résidu calculé yPB n'est pas divisible par un quelconque desdits nombres premiers déterminés pour ladite base B sélectionnée, répéter de manière itérative des étapes c) à f) pour chaque base B parmi lesdites bases binaires déterminées, h) lorsque, pour toutes les bases B déterminées, ledit résidu yPB calculé pour une base déterminée est non divisible par un desdits petits nombres premiers déterminés pour ladite base B déterminée, exécuter un test de primalité probable rigoureux connu sur ledit candidat YP, et lorsque le test de primalité probable rigoureux connu est un succès, stocker ledit candidat principal YP et utiliser ledit candidat principal stocké YP dans ladite application cryptographique.
Latest bibliographic data on file with the International Bureau