Parallelization of QUAD Stream Cipher Using Linear Recurring Sequences on Graphics Processing Units

Proposed by Berbain, Gilbert, and Patarin in Euro crypt 2006, QUAD is a provably secure stream cipher. The speed of QUAD depends on the computational cost of evaluating quadratic polynomials over finite fields. For QUAD with m quadratic polynomials in n unknowns over GF(q), this requires O (mn²) GF(q) additions and multiplications. Petzoldt is able to reduce the evaluation cost to O(mn) GF(q) additions and multiplications by using linear recurring sequences to generate the coefficients. In this work, we parallelize and optimize his algorithm for running on Graphics Processing Unit (GPU). The result shows that our GPU implementation of the parallelized algorithm has achieved the best performance in the literature.