The discrete logarithm problem in Bergman's non-representable ring

Abstract

Bergman's ring , parameterized by a prime number p, is a ring with p5 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 using simple modular arithmetic, and suggested that this ring may be a useful source for intractable cryptographic problems. We present a deterministic polynomial time reduction of the discrete logarithm problem in to the classical discrete logarithm problem in , the p-element field. In particular, the discrete logarithm problem in can be solved, by conventional computers, in sub-exponential time.

Keywords

• cryptanalysis
• discrete logarithm problem
• bergman endomorphism ring
• representation attacks