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In 2009, Xu et al. found that Lee et al.'s [3] scheme is vulnerable to offline password guessing attack. Xu et al. also demonstrated that Lee and Chiu's [4] scheme is vulnerable to forgery attack. Furthermore, Lee and Chiu's scheme does not achieve mutual authentication and thus can not resist malicious server attack. Therefore, Xu et al. proposed an improved scheme that inherits the merits of Lee et al.'s and Lee and Chiu's schemes and resists different possible attacks. However, we found that Xu et al.'s scheme is vulnerable to forgery attack. This paper presents an improved scheme to resolve the aforementioned problem, while keeping the merits of Xu et al.'s scheme.

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The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of the Digital Signature Algorithm (DSA). It was accepted in 1999 as an ANSI standard, and was accepted in 2000 as IEEE and NIST standards. It was also accepted in 1998 as an ISO standard, and is under consideration for inclusion in some other ISO standards. Unlike the ordinary discrete logarithm problem and the integer factorization problem, no sub exponential-time algorithm is known for the elliptic curve discrete logarithm problem. For this reason, the strength-per-keybit is substantially greater in an algorithm that uses elliptic curves. This paper describes the implementation of ANSI X9.62 ECDSA over elliptic curve P-192, and discusses related security issues.