Using Cyclotomic Polynomials to Construct Efficient Discrete Logarithm Cryptosystems Over Finite Fields

We show how to use cyclotomic polynomials to construct subgroups of multiplicative groups of finite fields that allow very efficient implementation of discrete logarithm based public key cryptosystems. Depending on the type of application and implementation, the resulting schemes may be up to three times faster than the fastest known schemes of comparable security that use more conventional choices of subgroups or finite fields.