## Cryptology ePrint Archive: Report 2008/064

Remarks on the NFS complexity

Pavol Zajac

Abstract: In this contribution we investigate practical issues with implementing the NFS algorithm to solve the DLP arising in XTR-based cryptosystems. We can transform original XTR-DLP to a DLP instance in $\mathbb{F}_{p^6},$ where $p$ is a medium sized prime. Unfortunately, for practical ranges of $p,$ the optimal degree of NFS polynomial is less than the required degree 6. This leads to a problem to find enough smooth equations during the sieve stage of the NFS algorithm. We discuss several techniques that can increase the NFS output, i.e. the number of equations produced during the sieve, without increasing the smoothness bound.

Category / Keywords: public-key cryptography / cryptanalysis, discrete logarithm problem, number field sieve

Publication Info: Submitted to: TATRA MOUNTAINS Mathematical Publications