分野別セミナー

Solving the elliptic curve discrete logarithm problem (ECDLP) by using Grobner basis has recently appeared as a new threat to the security of elliptic curve cryptography and pairing-based cryptosystems. At Eurocrypt 2012, Faugere, Perret, Petit and Renault proposed a new method using a multivariable polynomial system to solve ECDLP over finite fields of characteristic 2. At Asiacrypt 2012, Petit and Quisquater showed that this method may beat generic algorithms for extension degrees larger than about 2000. In this talk, we describe a variant of FPPR attack that practically reduces the computation time and memory required. Our variant is based on the idea of symmetrization. This idea already provided practical improvements in several previous works for composite-degree extension fields, but its application to prime-degree extension fields has been more challenging. To exploit symmetries in an efficient way in that case, we specialize the definition of factor basis used in FPPR attack to replace the original polynomial system by a new and simpler one. We provide theoretical and experimental evidence that our method is faster and requires less memory than FPPR method when the extension degree is large enough. The talk is based on joint work with Christophe Petit, Naoyuki Shinohara and Tsuyoshi Takagi.