A Method for the Construction of a Cryptographic Group-theoretic Language

This paper generalizes the theory of universal hashing in the construction of cryptographic protocols using group- theoretic language formalisms. This idea is due to Wegman and Carter who gave a construction in 1981 which is extremely useful when the number of authenticators is small compared to the number of possible source states (plaintext messages) in order to accommodate the situation where we would like to authenticate a sequence of messages with the same key. Unlike previous methods for doing this we do not require that each message in the sequence have a “counter” attached to it. We provide necessary definitions and theory and then give a construction which achieves our goals. Keywords: Universal hashing, projective hash family, cryptographic protocol, group-theoretic language,