A family of binary group operations for block cipher applications

A family of multiplication-like group operations over m-bit words is investigated. The operations are defined by a homomorphic mapping of binary words into the elements of a multiplicative group modulo 2/sup k/F/sub n/, where k is an integer >or=1, and F/sub n/ is the n-th Fermat prime (n=0,1,2,3,4). The order of the multiplicative group is 2/sup N+k-1/, where N=2/sup n/. The operations are usable for any given value of m if k and n are chosen such that m=2/sup n/+k-1. Expressions are presented for the mapping function for each value of n, and their inverses. Application of the results in block cipher design is discussed.<
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