  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.

Cryptography and Security;Group Theory