2022 KEYED HASH FUNCTION FROM LARGE GIRTH EXPANDER GRAPHS
Monika Polak, Eustrat Zhupa
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Albanian J. Math. 16(1): 25-39 (2022). DOI: 10.51286/albjm/1656414764

Abstract

In this paper we present a keyed hash function (message authentication code MAC). Our approach uses a family of expander graphs of large girth denoted as D(n,q), n2 and q is a prime power. Graphs D(n,q), n2 for arbitrary q form a family of q-regular almost Ramanujan graphs (|λ1(Gi)|2q). Expander graphs are known to have excellent mixing properties because are very dense. The girth of this family of graphs can be descibed by the formula gnlogq(q1)logq1(vn), where vn is size of graph D(n,q). All requirements for a good MAC are satisfied in our method and a discussion about collisions and preimage resistance is also part of this work. The out-puts very closely approximate the uniform distribution and the results we get appear to be indistinguishable from random sequences of bits, when tested by statistical test suite for random and pseudorandom number generators. Based on the tests, our graph based keyed hash functions shows good efficiency in comparison to other techniques. The number of operations per bit of input for DMAC-1 is given by the formula 2n+2N(1+rl(M)), where r is the length of secret key S, N is block size and l(M) is the number of blocks in a message.

Acknowledgement

The authors would like to express their gratitude to Vasyl Ustimenko for sharing his knowledge about graphs D(n,q), which made this research possible. Special thanks also to Stanislaw Radziszowski for his useful re marks.

Citation

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Monika Polak. Eustrat Zhupa. "KEYED HASH FUNCTION FROM LARGE GIRTH EXPANDER GRAPHS." Albanian J. Math. 16 (1) 25 - 39, 2022. https://doi.org/10.51286/albjm/1656414764

Information

Published: 2022
First available in Project Euclid: 11 July 2023

MathSciNet: MR4448534
zbMATH: 1497.94112
Digital Object Identifier: 10.51286/albjm/1656414764

Subjects:
Primary: 94C15
Secondary: 94A60

Keywords: Authentication , Expander graphs , Keyed hash function , large girth graphs

Rights: Copyright © 2022 Research Institute of Science and Technology (RISAT)

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