Constantin POPESCU
Department of Mathematics and Computer Science, University of Oradea
Oradea 410087, Romania

Abstract: A blind signature is a form of digital signature in which the content of a message is blinded before it is signed. The first blind digital signature scheme was proposed by Chaum in 1982. Chaum constructed the blind signatures as a key tool for developing anonymous electronic cash system. In this paper we propose two blind signature schemes and an elliptic curve version of Shao’s signature scheme. Our schemes are based on the difficulty of solving the elliptic curve discrete logarithm problem.

Keywords: Blind signatures, elliptic curve cryptography, digital signatures, cryptosystems.

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CITE THIS PAPER AS:
Constantin POPESCU, Blind Signature Schemes Based on the Elliptic Curve Discrete Logarithm Problem, Studies in Informatics and Control, ISSN 1220-1766, vol. 19 (4), pp. 397-402, 2010.

1. Introduction

Diffie and Hellman proposed in 1976 the public key cryptography [3]. They have invented the concept of the encryption scheme and the digital signature scheme based on the public key. Since then, several digital signature schemes have been constructed. The most popular signature schemes are the RSA signature scheme [18] and the ElGamal signature scheme [4]. The RSA signature scheme is based on the difficulty of factoring a large composite number and the ElGamal signature scheme is based on the difficulty of solving discrete logarithms. Schnorr proposed in 1991 a variant [19] of the ElGamal signature scheme. Also, NIST proposed the DSA signature scheme [12]. The Schnorr’s signature and the DSA signature were shortened to 320 bits.

David Chaum proposed first in 1982 blind signatures [1] in order to construct an electronic version of money (electronic cash system). Blind signatures allow a user to obtain signatures from a signer on any document, in such a way that the signer learns nothing about the message that is being signed. Blind signature schemes have been widely used to protect customers’ right to privacy in the untraceable electronic cash (e-cash) systems [2]. However, it is easy to make multiple copies of the electronic coin, which is in the form of number strings. Therefore, blind signature schemes are used in order to eliminate the possible abuse of unlinkability. A number of blind signature schemes have been proposed to date [5], [10], [11], [14], [22]. The blind signature schemes are useful in some applications [21] where the anonymity is a big issue. Examples include the online voting systems and the electronic cash systems [13], [15], [16], [17].

In this paper we propose two blind signature schemes and an elliptic curve version of Shao’s signature scheme.

The rest of this paper is organized as follows. In the next section we review the model of a blind signature scheme, the elliptic curves cryptography and the Shao’s signature scheme. Then we present our signature schemes in the section 3. Furthermore, we discuss some aspects of security in the section 4. The section 5 concludes the work of our paper.