Efficient Generation of Prime Numbers

12 years 1 months ago
Efficient Generation of Prime Numbers
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 impleme...
Marc Joye, Pascal Paillier, Serge Vaudenay
Added 24 Aug 2010
Updated 24 Aug 2010
Type Conference
Year 2000
Where CHES
Authors Marc Joye, Pascal Paillier, Serge Vaudenay
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