More Flexible Exponentiation with Precomputation

A new precomputation method is presented for computing gR for a fixed element g and a randomly chosen exponent R in a given group. Our method is more efficient and flexible than the previously proposed methods, especially in the case where the amount of storage available is very small or quite large. It is also very efficient in computing gRyE for a small size E and variable number y, which occurs in the verification of Schnorr’s identification scheme or its variants. Finally it is shown that our method is well-suited for parallel processing as well.