A method for verification at a computing device of a signed message received from a first party over a public communications channel, the method including extracting a message digest “a” belonging to a semigroup from the signed message; obtaining a public key [c,e] for the first party, including a fixed value checker “c” and an endpoint “e”, checker “c” and endpoint “e” belonging to the semigroup and the endpoint comprising a multiplication of a private key “b” for the first party and the checker “c”, multiplying the message digest “a” and the endpoint “e” to create an endmatter “ae”; extracting a signature “d” from the signed message, the signature “d” belonging to the semigroup and being a multiplication of message digest “a” and private key “b”; multiplying the signature “d” and the checker “c” to create a signcheck “dc”; and verifying that the endmatter “ae” matches the signcheck “dc”.