A Secured Digital Signature Using Conjugacy and DLP on Non-commutative Group over Finite Field
In the present paper, we propose a secured scheme of digital signature connecting both conjugacy problem and discrete logarithm problem based on non-commutative group generated over a finite field. For this, we define a non-commutative group over matrices
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Abstract In the present paper, we propose a secured scheme of digital signature connecting both conjugacy problem and discrete logarithm problem based on non-commutative group generated over a finite field. For this, we define a non-commutative group over matrices with the elements of finite field such that conjugacy and discrete logarithm problems can be executed together proficiently. By doing so, we can formulate the signature structures using conjugacy and discrete logarithm through non commutative group. In some domains, the above combination reduces to completely in discrete logarithm problem. This digital signature scheme more elemental over F*q(x) = G Ln (Fq). Here the security of the signature protocol depending on complexity of the problems associated with conjugacy and discrete logarithm. The security analysis and intermission of proposed protocol of digital signature is presented with the aid of order of complexity, existential forgery and signature repudiation. Keywords Digital signature Discrete logarithm problem
⋅ Public key cryptography ⋅ Conjugacy problem ⋅ ⋅ Quasideterminant and non commutative ring
1 Introduction A digital signature scheme is a scientific approach for demonstrating the legitimacy of an advanced message or record. A substantial digital signature delivers for a beneficiary reason to have confidence that those message might have been made by an known sender, such and such the sender cannot rebuff hosting sent those message (authentication and non-repudiation). Also note that those messages might have been not modified, when the message being transmitted(integrity). In the L. Narendra Mohan ⋅ G.S.G.N. Anjaneyulu (✉) Department of Mathematics, SAS, VIT University, Vellore 632014, Tamil Nadu, India e-mail: [email protected] L. Narendra Mohan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2017 S.C. Satapathy et al. (eds.), Proceedings of the 5th International Conference on Frontiers in Intelligent Computing: Theory and Applications, Advances in Intelligent Systems and Computing 516, DOI 10.1007/978-981-10-3156-4_47
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present scenario, Digital signatures are essential and regularly utilized to programming distribution, economic transactions, what’s more to other situations the place, where it is imperative should recognize falsification or damaging. Diffie and Hellman principally presented the basic notion about advanced signature scheme along with the first introduced the concept of Digital signature scheme using cryptography. This piece of information of a “digital signature” at first disclosed in Diffie and Hellman’s inspiring paper, “New Directions in Cryptography” [1]. They suggested that each client must distribute an “open key”(used for validating/Confirming signatures), and at the same time keeping mystery “secret key” (used for producing signatures). At the inception, in their protocol, Entity A’s signature for a message M is a worth which relies on upon M and on A’s private key, so that any individual may be
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