Wikipedia:Reference desk/Archives/Mathematics/2014 October 10

= October 10 =

non-Gaussian primes
I don't know much about cryptography. Is a secret prime number "weaker" if it is not a Gaussian prime? —Tamfang (talk) 09:20, 10 October 2014 (UTC)


 * The positive integer Gaussian primes are the prime numbers congruent to 3 modulo 4, so this is a simple property. For certain applications, primes might be "weaker" or "stronger" against specific attacks; for example, the prime factors of the modulus in RSA are sometimes required to be strong primes to prevent certain factoring attacks, although even this condition is often dropped. I don't see that this relates to Gaussian primes, though. Factoring in the containing integral domain of Gaussian integers seems like an interesting line of enquiry, though. —Quondum 13:09, 10 October 2014 (UTC)


 * From a cryptography standpoint, there is no such thing as strong/weak primes. The current algorithms based on ECM or sieves don't behave differently based on the strength of the primes. 209.149.115.99 (talk) 19:09, 10 October 2014 (UTC)


 * It is not entirely true that there is no such thing. Firstly, the concept is defined.  And while in most cases, due to the effectiveness of modern general factoring algorithms, it does not particularly make sense to choose strong primes, there are contexts (especially where one does no have full control of the key generation process and non-repudiation is important) where one might still consider constraints. —Quondum 19:59, 10 October 2014 (UTC)