On ElGamal signature modification for application in one class of e-voting systems using the blind signature mechanism

Abstract

—In this paper we consider the scenario of the signature scheme application in one class of e-voting systems using the blind signature mechanism. The specificities of this class of systems are the signature generation on the voter’s mobile device and the inclusion of the signature value in the ballot. In this case the classical signature scheme may be required to provide a short signature length and remain secure even in case of using unreliable sources of randomness. Standard ElGamal signature schemes do not meet these requirements. The repeating of the random value used in the signature generation process leads to recovering the secret signing key. This paper shows that ElGamal signature schemes can be modified in order to ensure these properties. The proposed modification is described on the example of the standardized signature scheme, defined in the document GOST R 34.10- 2012. It allows to reduce the length of the signature by a quarter and additionally uses the HMAC function. We obtain the security bound of the proposed scheme in the SUF-CMRA model, which allows the adversary to control random values, as well as timestamps used in the signature generation process.