Quantum algorithm for solving binary hyperelliptic curve discrete logarithm problem

Abstract It is well-established that Shor’s algorithm can solve the discrete logarithm problem (DLP) in polynomial time. The hyperelliptic curve DLP (HCDLP) of genus 2 has found widespread industrial applications and remains an active research domain. In this work, we develop a quantum algorithm for solving HCDLP over binary fields $$\mathbb {F}_{2^n}$$ F 2 n by adapting Shor’s algorithmic framework. The core innovation lies in our divisor addition implementation, which combines the geometric interpretation of divisor operations with symmetric polynomial techniques. Using representative parameters ( $$n = 163, 283, 571$$ n