2022
DOI: 10.1049/ise2.12092
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Recent progress in the security evaluation of multivariate public‐key cryptography

Abstract: Multivariate public-key cryptography (MPKC) is considered a leading candidate for postquantum cryptography (PQC). It is based on the hardness of the multivariate quadratic polynomial (MQ) problem, which is a problem of finding a solution to a system of quadratic equations over a finite field. In this paper, we survey some recent progress in the security analysis of MPKC. Among various existing multivariate schemes, the most important one is the Rainbow signature scheme proposed by Ding et al. in 2005, which wa… Show more

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Cited by 9 publications
(3 citation statements)
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“…Thus, a direct attack is associated with the solution of a system of 28 power equations with 34 unknowns, given in the GF(p) field of a prime 129-bit order. Considering that the computational complexity Ψ of solving a system of 26 quadratic equations with 26 unknowns in a finite field of 8-bit order has a level of 2 80 (see Table 1 in [19]) and using estimates [20] that take into account the dependence of Ψ on the value of the field order, we obtain the following preliminary estimate of the security level of the proposed algorithm to a direct attack: Ψ > 2 128 . Clarifying this assessment is an independent task.…”
Section: Discussionmentioning
confidence: 99%
“…Thus, a direct attack is associated with the solution of a system of 28 power equations with 34 unknowns, given in the GF(p) field of a prime 129-bit order. Considering that the computational complexity Ψ of solving a system of 26 quadratic equations with 26 unknowns in a finite field of 8-bit order has a level of 2 80 (see Table 1 in [19]) and using estimates [20] that take into account the dependence of Ψ on the value of the field order, we obtain the following preliminary estimate of the security level of the proposed algorithm to a direct attack: Ψ > 2 128 . Clarifying this assessment is an independent task.…”
Section: Discussionmentioning
confidence: 99%
“…Recent advancements in the security evaluation of multivariate public-key cryptography, as outlined in the referenced article, primarily revolve around the comprehensive analysis of the Rainbow signature scheme and the methodologies for assessing its security. The focus has been on refining efficient algorithms for solving the multivariate quadratic (MQ) problem and estimating their complexity within the framework of MPKC [33].…”
Section: Multivariate Cryptographymentioning
confidence: 99%
“…With the advent of the era of big data and Internet of things, the emerging services with digital information as the media make the network data grow explosively. Over the past several decades, there has been an enormous increase in demand for the secure communication [1]. Security in digital communications is largely provided through signature and verification algorithms.…”
Section: Introductionmentioning
confidence: 99%