I read that Silver–Pohlig–Hellman algorithm solves the discrete logarithm with prime module $p$ in $O(\log^2(p))$ if $p-1$ is a smooth number. This seems pretty fatal for cryptography, since it is a ...
I need to find a prime $p$ of $1024$ bits with a $160$ bit sub group size $q$, such that $q|p-1$ , and $g$ is the generator of the sub group size $q$. I'm looking for the numeric values of $p$ , $q$ ...
Besides key and ciphertext sizes what are other advantages of elliptic curve versions of various protocols?
There are elliptic curve variants of Diffie-Hellman, ElGamal, DSA and possibly other protocols/algorithms. I know that these elliptic curve variants have smaller key and ciphertext sizes which will ...