分野別セミナー

The multivariate public-key cryptography (MPKC) uses evaluating multivariate non-linear polynomials over finite fields for message encryption. The security of the MPKC is based on the complexity of the problem which is finding roots of given values with multivariate non-linear polynomial systems. Such the problem is known to be NP-complete, then the MPKC is expected to be a candidate of the post-quantum cryptography, which is secure against computational performance of quantum computers. QUAD stream cipher is based on the theory of the MPKC. Stream ciphers are cryptosystems that generate pseudo-random keystream and encrypt by xor operations between keystreams and messages. Usually, stream ciphers use efficient and elaborated software algorithms or hardware circuits. Therefore, many stream ciphers can give high-speed throughputs. However, the security of such ciphers is proved by experimentations or analysis against attacks. QUAD stream cipher uses evaluating multivariate quadratic polynomials over finite fields for generating keystreams. Therefore, the security of QUAD can be proved by algebraic theory. Although, QUAD stream cipher is secure, it is slower than other stream ciphers. Hence, we should make efficient evaluation of multivariate quadratic polynomials for practical QUAD. In this work, we show how to accelerate QUAD stream ciphers on Graphics Processing Units (GPU).