Research on Attacking a Special Elliptic Curve Discrete Logarithm Problem

Abstract

Cheon first proposed a novel algorithm for solving discrete logarithm problem with auxiliary inputs. Given some points , , 2 , . . . , ∈ G, an attacker can solve the secret key efficiently. In this paper, we propose a new algorithm to solve another form of elliptic curve discrete logarithm problem with auxiliary inputs. We show that if some points , , , 2 , 3 , . . . , ( )−1 ∈ G and a multiplicative cyclic group = ⟨ ⟩ are given, where is a prime, ( ) is the order of . The secret key ∈ F * can be solved in O(√( − 1)/ + ) group operations by using O(√( − 1)/ ) storage.