Graphics Processing Unitを用いた非線形連立多元方程式解決法の高速化

抄録

Multivariate Public Key Cryptography (MPKC) is expected a candidate of post-quantum cryptography, which resists against attacks using quantum computers. The security of MPKC depends on complexity of solving multivariate non-linear equations (MP). MP is known an NP-complete problem. The eXtended linearizations (XL) algorithm is a solving method for MP. It is based on linearization method. In this work, we show an implementation of XL algorithm on graphics processing units (GPU). Our XL solves 16-unknown 40-equation quadratic systems over GF(2) in 12 seconds on GPU.