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A bivariate polynomial-based cryptographic hard problem and its applications

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Abstract

The problem of factoring a composite integer into the product of two distinct primes (the factoring problem) is one of the famous hard problems on which the security of many cryptographic primitives relies. In this paper, we introduce a new cryptographic hard problem (RSA-polynomial problem) and prove that solving the RSA-polynomial problem is at least as hard as solving the factoring problem. As applications of the RSA-polynomial problem, we propose a commitment scheme. The proposed scheme is free of any group-exponentiation and outperforms the previous commitment schemes. Also, using the lattice basis reduction techniques and the RSA-polynomial problem, we propose a method to factor composite integers that are the product of two distinct primes.

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Acknowledgements

The author would like to thank the anonymous reviewers and the editor whose valuable suggestions increased the readability and quality of the paper.

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Authors and Affiliations

  1. Faculty of Applied Sciences, Research Center of Science and Technology of Applied Mathematics and Cryptography, Malek Ashtar University of Technology, Isfahan, Iran

    Bagher Bagherpour

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  1. Bagher Bagherpour
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Correspondence to Bagher Bagherpour.

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Communicated by C. Blundo.

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Bagherpour, B. A bivariate polynomial-based cryptographic hard problem and its applications. Des. Codes Cryptogr. 91, 2723–2735 (2023). https://doi.org/10.1007/s10623-023-01229-1

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