Concrete Quantum Cryptanalysis of Binary Elliptic Curves via Addition Chain

ePrint Report: Concrete Quantum Cryptanalysis of Binary Elliptic Curves via Addition Chain

Ren Taguchi, Atsushi Takayasu

Thus far, several papers reported concrete resource estimates of Shor's quantum algorithm for solving the elliptic curve discrete logarithm problem (ECDLP). In this paper, we study quantum FLT-based inversion algorithms over binary elliptic curves. There are two major algorithms proposed by Banegas et al. and Putranto et al., where the former and latter algorithms achieve fewer numbers of qubits and smaller depths of circuits, …

addition algorithm algorithms binary cryptanalysis elliptic eprint report major numbers papers problem quantum qubits report shor study