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

Bergman's ring E _p, 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 E _p 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 E _p to the classical discrete logarithm problem in ℤ _p, the p-element field. In particular, the discrete logarithm problem in E _p can be solved, by conventional computers, in sub-exponential time.