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On ideal lattices, Grobner bases and generalized hash functions

Francis, Maria and Dukkipati, Ambedkar (2018) On ideal lattices, Grobner bases and generalized hash functions. In: JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 17 (6).

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Official URL: https://dx.doi.org/10.1142/S0219498818501128

Abstract

In this paper, we draw connections between ideal lattices and multivariate polynomial rings over integers using Grobner bases. Univariate ideal lattices are ideals in the residue class ring, Zx]/< f > (here f is a monic polynomial) and cryptographic primitives have been built based on these objects. Ideal lattices in the univariate case are generalizations of cyclic lattices. We introduce the notion of multivariate cyclic lattices and show that ideal lattices are a generalization of them in the multivariate case too. Based on multivariate ideal lattices, we construct hash functions using Grobner basis techniques. We define a worst case problem, shortest substitution problem with respect to an ideal in Zx(1), . . .,x(n)] and use its computational hardness to establish the collision resistance of the hash functions.

Item Type: Journal Article
Additional Information: Copy right of this article belong to WORLD SCIENTIFIC PUBL CO PTE LTD, 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 12 Jun 2018 16:01
Last Modified: 12 Jun 2018 16:01
URI: http://eprints.iisc.ac.in/id/eprint/59994

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