Multivariate Polynomial Inference in a Cryptographic Setting

Corbeanu, Ramona; Maimuţ, Diana; Teşeleanu, George

doi:10.3390/math14111903

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Open AccessArticle

Multivariate Polynomial Inference in a Cryptographic Setting

by

Ramona Corbeanu

¹

,

Diana Maimuţ

^2,*

and

George Teşeleanu

^3,*

¹

Department of Mathematics, Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania

²

Advanced Technologies Institute, 021101 Bucharest, Romania

³

Simion Stoilow Institute of Mathematics of the Romanian Academy, 010702 Bucharest, Romania

^*

Authors to whom correspondence should be addressed.

Mathematics 2026, 14(11), 1903; https://doi.org/10.3390/math14111903

Submission received: 27 March 2026 / Revised: 12 May 2026 / Accepted: 22 May 2026 / Published: 29 May 2026

(This article belongs to the Special Issue Computational Methods for Cryptography and Security)

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Abstract

In this paper, we generalize to the multivariate setting the current state-of-the-art methods in the literature for the inference of bivariate polynomials constructed recursively, by means of repeated additions and multiplications. We present two main approaches: the first one based on polynomial interpolation and the second one relying on lattice-based techniques for solving modular knapsack-type problems. Both the directions yield natural and practical generalizations, supported by detailed analyses of the underlying mathematical structures. Our methods can be useful for analyzing the security of cryptographic algorithms, given their connection to basic operations serving as building blocks, for example in fully homomorphic encryption schemes.

Keywords: multivariate polynomial; Lagrange interpolation; modular knapsack problem; lattice reduction

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MDPI and ACS Style

Corbeanu, R.; Maimuţ, D.; Teşeleanu, G. Multivariate Polynomial Inference in a Cryptographic Setting. Mathematics 2026, 14, 1903. https://doi.org/10.3390/math14111903

AMA Style

Corbeanu R, Maimuţ D, Teşeleanu G. Multivariate Polynomial Inference in a Cryptographic Setting. Mathematics. 2026; 14(11):1903. https://doi.org/10.3390/math14111903

Chicago/Turabian Style

Corbeanu, Ramona, Diana Maimuţ, and George Teşeleanu. 2026. "Multivariate Polynomial Inference in a Cryptographic Setting" Mathematics 14, no. 11: 1903. https://doi.org/10.3390/math14111903

APA Style

Corbeanu, R., Maimuţ, D., & Teşeleanu, G. (2026). Multivariate Polynomial Inference in a Cryptographic Setting. Mathematics, 14(11), 1903. https://doi.org/10.3390/math14111903

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