The cubic sieve is an algorithm for computing discrete logarithms mostly in prime fields. It’s performance is less than the number field sieve but it’s faster than the linear sieve. See the paper here.
- How to compute the factor base ? How to do it in the case of finite fields having dimension>1 ?
- How many relations should I collect for a 255 bits safeprime ?
- What’s the complexity of each phases in O(n) notation ?
- The algorithm can be adapted to finite field having dimensions>1, but in such case what does it means to select $\alpha$ below the factor base in finite fields of large dimensions during the sieving phase ? Does it means the finite field element of $\alpha$ must start by
{1: 1: 1: 1: 1:…}in order to be considered below the factor base ?
