Blind digital signature calculation algorithms based on the Ukrainian national digital signature standard DSTU 4145-2002
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and Systems Analysis, Vol. 48, No. 4, July, 2012
BLIND DIGITAL SIGNATURE CALCULATION ALGORITHMS BASED ON THE UKRAINIAN NATIONAL DIGITAL SIGNATURE STANDARD DSTU 4145-2002 AND RUSSIAN DIGITAL SIGNATURE STANDARD GOST R 34.10-20011 A. I. Kochubinskya† and O. M. Fal’a‡
UDC 681.3
Abstract. Algorithms of blind digital signature calculation based on the national digital signature standards (Ukrainian DSTU 4145-2002 and Russian GOST R 34.10-2001) are proposed. An example of the algorithm implementation based on the Ukrainian standard is provided. The application of blind digital signature is discussed.
Keywords: blind digital signature, standard, cryptographic transformation, discrete logarithm, algorithms of signature evaluation and verification.
The concept of blind digital signature was proposed by D. Chaum [1]. Such a signature is calculated during the interaction of two participants, a client and a server. As the result, the client obtains a signed message, while the server has no access to the client’s document for which the digital signature is evaluated, and cannot authenticate the client who has requested for service of evaluating the blind digital signature. As a result of evaluations, a standard digital signature is formed. In other words, use is made of an ordinary digital signature verification algorithm that employs the cryptographic transformation chosen to create the blind digital signature. This algorithm can be applied in payment systems, in elections, and in any other fields where client’s anonymity is crucially important. D. Chaum used the RSA algorithm as a cryptographic transformation. Blind digital signature algorithms based on other cryptographic algorithms were described later. For example, [2] describes a rather general method to develop blind digital signature algorithms based on cryptographic transformations whose security is based on taking discrete logarithms. Based on the approach described in [2], we formulate algorithms to calculate a blind digital signature proceeding from the cryptographic transformations defined in the national standard of Ukraine DSTU 4145-2002 [3] and standard of the Russian Federation GOST R 34.10-2001 in the edition presented in the International Standard ISO/IEC 14888-3:2006/Amd 1:2010 [4]. As a result, the functional capabilities of blind digital signature appear as a part of the public key infrastructure that exists in Ukraine, in particular, public key certification centers. In the paper, we will use the terminology and notation adopted in these standards. Let E ( Fq ) be an elliptic curve over a finite field Fq , q = 2m , m be the degree of extension of finite field from those allowed by the DSTU 4145-2002, and P be a reference point of the elliptic curve of order n. The elliptic curve, finite field, reference point, and its order satisfy the requirements of the DSTU 4145-2002. Let also d be a private key of the digital signature DSTU 4145-2002, Q = -dP be a public key of the digital signature corresponding to this private key, and H (× ) be a hash function.
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