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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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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