Efficient Computing over GF(2^16) Using Graphics Processing Unit

Evaluating non-linear multivariate polynomial systems over finite fields is an important subroutine, e.g., for encryption and signature verification in multivariate cryptography. The security of multivariate cryptography definitely becomes lower if a larger field is used instead of GF(2) given the same number of bits in the key. However, we still would like to use larger fields because multivariate cryptography tends to run faster at the same level of security if a larger field is used. In this paper, we compare the efficiency of several techniques for evaluating multivariate polynomial systems over GF(2¹⁶) vi their implementations on graphics processing units.