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Mathematical Problems in Engineering
Volume 2016, Article ID 5361695, 8 pages
Research Article

Research on Attacking a Special Elliptic Curve Discrete Logarithm Problem

1State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China
2Air Force Engineering University, Xi’an 710038, China
3Basic Department, Army Aviation Institution, Beijing 101123, China

Received 17 December 2015; Revised 15 May 2016; Accepted 31 May 2016

Academic Editor: Nazrul Islam

Copyright © 2016 Jiang Weng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Cheon first proposed a novel algorithm for solving discrete logarithm problem with auxiliary inputs. Given some points , 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 and a multiplicative cyclic group are given, where is a prime, is the order of . The secret key can be solved in group operations by using storage.