QUAD stream cipher uses multivariate polynomial systems. It has provable
security based on the computational hardness assumption. More specifically,
the security of QUAD depends on hardness of solving non-linear multivariate
systems over a finite field, and it is known as an NP-complete problem.
However, QUAD is slower than other stream ciphers, and an efficient
implementation, which has a reduced computational cost, is required. In this
paper, we propose an efficient implementation of computing multivariate
polynomial systems for multivariate cryptography on GPU and evaluate
efficiency of the proposal. GPU is considered to be a commodity parallel
arithmetic unit. Moreover, we give an evaluation of our proposal. Our
proposal parallelizes an algorithm of multivariate cryptography, and makes it
efficient by optimizing the algorithm with GPU.