Prime numbers and computer methods for factorization
Prime numbers and computer methods for factorization
Faster primality testing (extended abstract)
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Handbook of Applied Cryptography
Handbook of Applied Cryptography
On Generation of Probable Primes By Incremental Search
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Efficient Generation of Shared RSA Keys (Extended Abstract)
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Speeding up Prime Number Generation
ASIACRYPT '91 Proceedings of the International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
On the Implementation of a Fast Prime Generation Algorithm
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
Parallelization of prime number generation using message passing interface
CIMMACS'07 Proceedings of the 6th WSEAS international conference on Computational intelligence, man-machine systems and cybernetics
Fast generation of prime numbers on portable devices: an update
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
A practical and tightly secure signature scheme without hash function
CT-RSA'07 Proceedings of the 7th Cryptographers' track at the RSA conference on Topics in Cryptology
RSA key generation: new attacks
COSADE'12 Proceedings of the Third international conference on Constructive Side-Channel Analysis and Secure Design
Generating provable primes efficiently on embedded devices
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
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The generation of prime numbers underlies the use of most public-key schemes, essentially as a major primitive needed for the creation of key pairs or as a computation stage appearing during various cryptographic setups. Surprisingly, despite decades of intense mathematical studies on primality testing and an observed progressive intensification of cryptographic usages, prime number generation algorithms remain scarcely investigated and most real-life implementations are of rather poor performance. Common generators typically output a n-bit prime in heuristic average complexity O(n4) or O(n4/ log n) and these figures, according to experience, seem impossible to improve significantly: this paper rather shows a simple way to substantially reduce the value of hidden constants to provide much more efficient prime generation algorithms. We apply our techniques to various contexts (DSA primes, safe primes, ANSI X9.31-compliant primes, strong primes, etc.) and show how to build fast implementations on appropriately equipped smart-cards, thus allowing on-board key generation.