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BY-NC-ND 3.0 license Open Access Published by De Gruyter November 14, 2013

Generating safe primes

  • Joachim von zur Gathen EMAIL logo and Igor E. Shparlinski

Abstract.

Safe primes and safe RSA moduli are used in several cryptographic schemes. The most common notion is that of a prime p, where is also prime. The latter is then a Sophie Germain prime. Under appropriate heuristics, they exist in abundance and can be generated efficiently. But the modern methods of analytic number theory have – so far – not even allowed to prove that there are infinitely many of them. Thus for this notion of safe primes, there is no algorithm in the literature that is unconditionally proven to terminate, let alone to be efficient. This paper considers a different notion of safe primes and moduli. They can be generated in polynomial time, without any unproven assumptions, and are good enough for the cryptographic applications that we are aware of.

Received: 2013-03-08
Accepted: 2013-08-05
Published Online: 2013-11-14
Published in Print: 2013-12-01

© 2013 by Walter de Gruyter Berlin Boston

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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