Informatica

In this paper, we propose a new ID-based threshold signature scheme from the bilinear pairings, which is provably secure in the random oracle model under the bilinear Diffie–Hellman assumption. Our scheme adopts the approach that the private key associated with an identity rather than the master key of PKG is shared. Comparing to the-state-of-art work by Baek and Zheng, our scheme has the following advantages. (1) The round-complexity of the threshold signing protocol is optimal. Namely, during the signing procedure, each party broadcasts only one message. (2) The communication channel is optimal. Namely, during the threshold signing procedure, the broadcast channel among signers is enough. No private channel between any two signing parties is needed. (3) Our scheme is much more efficient than the Baek and Zheng scheme in term of computation, since we try our best to avoid using bilinear pairings. Indeed, the private key of an identity is indirectly distributed by sharing a number xID∈ $\mathbb{Z}^{*}_{q}$, which is much more efficient than directly sharing the element in the bilinear group. And the major computationally expensive operation called distributed key generation protocol based on the bilinear map is avoided. (4) At last, the proactive security can be easily added to our scheme.

In 2001, Hsu et al. proposed a non‐repudiable threshold proxy signature with known signers. In their scheme, the proxy group cannot deny having signed the proxy signature if they did. However, Hsu et al.'s scheme is vulnerable to some attacks. A malicious original signer or malicious proxy signer can impersonate some other proxy signers to generate proxy signatures. In this article, we shall present our cryptanalysis of the Hsu et al.'s scheme. After that, we shall propose a new threshold proxy signature that can overcome the weaknesses.

Smart card has been adopted to various applications. In 2000, Hwang and Li proposed a remote user authentication scheme, which is also using smart card. Nine months later, Chan and Cheng pointed out that there is a weakness in the remote authentication scheme proposed by Hwang and Li. In this paper, we show that Chan and Cheng's attack does not work well because they did not consider the format of user's identity. In addition, we propose several ways to solve the problem of Chan and Cheng's attack.

Sun's nonrepudiation threshold proxy signature scheme is not secure against the collusion attack. In order to guard against the attack, Hwang et al. proposed another threshold proxy signature scheme. However, a new attack is proposed to work on both Hwang et al.'s and Sun's schemes. By executing this attack, one proxy signer and the original signer can forge any valid proxy signature. Therefore, both Hwang et al.'s scheme and Sun's scheme were insecure.

In the papers (Kaminskas, 1973; Kaminskas and Nemura, 1975) the stopping rule of recursive least squares (RLS) is worked out using the length of the confidence interval for the respective current meaning of the true output signal of a linear dynamic system. The aim of the given paper is the development of techniques for calculating threshold intervals of respective criteria, used in such a stopping rule. In this connection adaptive threshold intervals based on the Cramer-Rao lower bound according to Pupeikis (1995) are proposed here, too. The results of numerical simulation by IBM PC/AT are given.