International Association
for Cryptologic Research

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 $\\Zp$, the $p$-element field.

In particular, the Discrete Logarithm Problem in $E_p$ can be solved, by conventional computers,

in sub-exponential time.

Along the way, we collect a number of useful basic reductions for the toolbox of discrete logarithm solvers.