Discrete Logarithm in Galois Rings

The Discrete Logarithm Problem in non-representable rings

Bergman’s Ring Ep, parameterized by a prime number p, is a ring with p 5 elements that cannot be embedded in a ring of matrices over any commutative ring. This ring was discovered in 1974. In 2011, Climent, Navarro and Tortosa described an efficient implementation of Ep using simple modular arithmetic, and suggested that this ring may be a useful source for intractable cryptographic problems. W...

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...

Quantum algorithm for the discrete logarithm problem for matrices over finite group rings

We propose a polynomial time quantum algorithm for solving the discrete logarithm problem in matrices over finite group rings. The hardness of this problem was recently employed in the design of a key-exchange protocol proposed by D. Kahrobaei, C. Koupparis, and V. Shpilrain [4]. Our result implies that the Kahrobaei et al. protocol does not belong to the realm of post-quantum cryptography.

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