Electron. J. Differential Equations, Vol. 2017 (2017), No. 237, pp. 1-21.

Elliptic curves differentiation with application to group signature scheme

Alin Ionut Golumbeanu, Oana Adriana Ticleanu

Starting with the presented concept by Chaum and van Heijst and its refers to digitally signing for a document by a group member, such signatures allows the signers to remains anonymous but any verifier can confirm that the signer is a group member. The signatory anonymity can be revealed only by a designated group authority that has some auxiliary information. We present a complexity efficient group signature scheme based on zero knowledge and Schnorr signature algorithm. The scheme has two phases: the first one demonstrates that the signer is a member of the group while the second generates the message signature. In the end, we modify the classic scheme using differential elliptic curve cryptography to increase the system's performance against differential attacks.

Submitted July 6, 2017. Published September 29, 2017.
Math Subject Classifications: 35H20, 35S15, 12H20, 11G07.
Key Words: Group signature; zero knowledge; discrete logarithm; Schnorr signature

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Alin Ionut Golumbeanu
University of Craiova
Department of Mathematics
Street: A. I. Cuza 13
200585 Craiova, Romania
email: alin.golumbeanu@inf.ucv.ro
Oana Adriana Ticleanu
University of Craiova
Department of Informatics
Street: A.I. Cuza 13
200585 Craiova, Romania
email: oana.ticleanu@inf.ucv.ro

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