Generating cryptographic checksums

A computer program product comprising a non-transitory computer readable medium storing a computer program comprising:

• instructions for pseudo-randomly selecting, based on a first cryptographic key, a generator polynomial p(x) from the set of polynomials of degree n over a Galois Field, wherein the generator polynomial p(x) is a reducible polynomial;
• and
• instructions for generating a cryptographic checksum for a message M(x), wherein
• the instructions for generating the cryptographic checksum for message M(x) comprises instructions for calculating:
• g(ƒ(M(x))mod p(x)), wherein g is a first function, and ƒ is a second function.

An apparatus, the apparatus being configured to:

• pseudo-randomly select, based on a first cryptographic key, a generator polynomial p(x) from the set of polynomials of degree n over a Galois Field, wherein the generator polynomial p(x) is a reducible polynomial;
• and
• generate a cryptographic checksum for a message M(x) by performing a process comprising calculating:
• g(ƒ(M(x))mod p(x)), wherein
• g a first function, and
• ƒ is a second function.