Individual discrete logarithm with sublattice reduction

Fusion Discrete Logarithm Problems

The Discrete Logarithm Problem is well-known among cryptographers, for its computational hardness that grants security to some of the most commonly used cryptosystems these days. Still, many of these are limited to a small number of candidate algebraic structures which permit implementing the algorithms. In order to extend the applicability of discrete-logarithm-based cryptosystems to a much ri...

Discrete logarithm in GF(2) with FFS

We give details on solving the discrete logarithm problem in the 202-bit prime order subgroup of F2809 using the Function Field Sieve algorithm (FFS). To our knowledge, this computation is the largest discrete logarithm computation so far in a binary field extension of prime degree. The Function Field Sieve is the traditional approach for solving these problems, and has been used in previous re...

The Discrete-Logarithm Problem with Preprocessing

This paper studies discrete-log algorithms that use preprocessing. In our model, an adversary may use a very large amount of precomputation to produce an “advice” string about a specific group (e.g., NIST P-256). In a subsequent online phase, the adversary’s task is to use the preprocessed advice to quickly compute discrete logarithms in the group. Motivated by surprising recent preprocessing a...

Birthday attack to discrete logarithm

The discrete logarithm in a finite group of large order has been widely applied in public key cryptosystem. In this paper, we will present a probabilistic algorithm for discrete logarithm.

Problem 3 : The Discrete Logarithm