Almost all primes can be quickly certified
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Strong primes are easy to find
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Distributed primality proving and the primality of (23539+1)/3
EUROCRYPT '90 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
On Generation of Probable Primes By Incremental Search
CRYPTO '92 Proceedings of the 12th 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
Algorithms in number theory
Information Processing Letters
Information Processing Letters
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Many cryptographic algorithms use number theory. They share the problem of generating large primes with a given (fixed) number n of bits. In a series of articles, Brandt, Damgard, Landrock and Pomerance address the problem of optimal use of probabilistic primality proofs for generation of cryptographic primes. Maurer proposed using the Pocklington lemma for generating provable primes. His approach loses efficiency due to involved mechanisms for generating close to uniform distribution of primes. We propose an algorithm which generates provable primes and can be shown to be the most efficient prime generation algorithm up to date. This is possible at the cost of a slight reduction of the set of primes which may be produced by the algorithm. However, the entropy of the primes produced by this algorithm is assymptotically equal to the entropy of primes with random uniform distribution. Primes are sought in arithmetic progressions and proved by recursion. Search in arithmetic progressions allows the use of Eratosthenes sieves, which leads finaly to saving 1/3 of the psuedo prime tests compared to random search.