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Certain sequence of arithmetic progressions and a new key sharing method

Srikanth, C (2020) Certain sequence of arithmetic progressions and a new key sharing method. In: Cryptography and Communications .

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Official URL: https://dx.doi.org/10.1007/s12095-019-00416-z

Abstract

We consider a special type of sequence of arithmetic progressions, in which consecutive progressions are related by the property: ithterms ofjth, (j + 1)thprogressions of the sequence are multiplicative inverses of each other modulo(i + 1)thterm ofjthprogression. Such a sequence is uniquely defined for any pair of co-prime numbers. A computational problem, defined in the context of such a sequence and its generalization, is shown to be equivalent to the integer factoring problem. The proof is probabilistic. As an application of the equivalence result, we propose a method for how users securely agree upon secret keys, which are ensured to be random. We compare our method with factoring based public key cryptographic systems: RSA (Rivest et al., ACM 21, 120�126, 1978) and Rabin systems (Rabin 1978). We discuss the advantages of the method, and its potential use-case in the post quantum scenario.

Item Type: Journal Article
Publication: Cryptography and Communications
Publisher: Springer
Additional Information: Copyright of this article belongs to Springer
Keywords: Arithmetic progressions; GCD algorithm; Integer factoring; Key sharing; Quadratic residuosity; RSA systems
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 26 Feb 2020 05:42
Last Modified: 26 Feb 2020 05:42
URI: http://eprints.iisc.ac.in/id/eprint/64592

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