Talk:Safe prime

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On the usefulness of safe primes in cryptography. The security of some public key systems depend on the use of safe primes. One known example is the secure remote password protocol. Attacks would exist if primes other than safe primes were allowed there. But not all public key systems require safe primes. For example, the primes chosen for the RSA cryptosystem need not have a special form.

Thanks for clarifying that. But I'm still wondering if the size of the safe primes matter. For instance, if I chose 23 and 47 for my N and q, could the encryption be bypassed more easily than if I chose 650183 and 1300367? PrimeFan 22:40, 12 July 2005 (UTC)

Yes the size matters in cryptographic applications. E.g., the SRP protocol requires primes that are at least 512 bits long, because that protocol would not be secure if the discrete logarithm were computable. Therefore, I also added the best known (to me) result on discrete logarithm to the article. But it seems better not to include a size requirement into the definition of the term safe prime. What size should that be? Cryptographers just have to specify in their papers things like "Let n be a sufficently large safe prime." 16 July 2005

Sounds good. PrimeFan 22:33, 21 July 2005 (UTC)

[edit] Infinitely many

Can anyone add a proof that there are infinitely many safe primes? 147.188.192.41 14:53, 4 November 2005 (UTC)

If you can prove that there are infinitely many Sophie Germain primes, then you've automatically proved that there are also infinitely many safe primes. PrimeFan 19:20, 4 November 2005 (UTC)