Abstract
D. Chaum and H. van Antwerpen first introduced the concept of an undeniable signature scheme where the verification step is verified with the signer’s co-operation. In this paper, first we discuss a combination of Discrete Logarithm Problem (DLP) and Conjugacy Search Problem (CSP) analysing its security. Then we propose an undeniable signature scheme in a non-abelian group over group ring whose security relies on difficulty of the combination of the DLP and the CSP. The complexity and security of our proposed scheme has also been discussed.
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Notes
We can choose the set of positive integers of cardinality p (where p may or may not be prime) in place of finite cyclic group. \({\mathbb {Z}}^{*}_{p}\) is used only for exploring the DLCSP in an undeniable signature scheme.
The choice of \(a\in {\mathbb {Z}}^{*}_{p}~\text {and}~z\in H\) should be such that \(z^{a}\ne 1.\)
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Acknowledgments
The authors would like to express their sincere thanks to the reviewers of the manuscript for their valuable comments and suggestions which were very useful to improve the manuscript. The authors are grateful to the editorial board of the journal for their support and co-operation. The authors are also thankful to the Director SAG for allowing us to pursue this work.
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Goel, N., Gupta, I., Dubey, M.K. et al. Undeniable signature scheme based over group ring. AAECC 27, 523–535 (2016). https://doi.org/10.1007/s00200-016-0293-8
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DOI: https://doi.org/10.1007/s00200-016-0293-8