  Galois field (GF) arithmetic is used to implement critical arithmetic
components in communication and security-related hardware, and verification of
such components is of prime importance. Current techniques for formally
verifying such components are based on computer algebra methods that proved
successful in verification of integer arithmetic circuits. However, these
methods are sequential in nature and do not offer any parallelism. This paper
presents an algebraic functional verification technique of gate-level GF (2m )
multipliers, in which verification is performed in bit-parallel fashion. The
method is based on extracting a unique polynomial in Galois field of each
output bit independently. We demonstrate that this method is able to verify an
n-bit GF multiplier in n threads. Experiments performed on pre- and
post-synthesized Mastrovito and Montgomery multipliers show high efficiency up
to 571 bits.

Symbolic Computation;Cryptography and Security;Logic in Computer Science