Inferring Bivariate Polynomials for Homomorphic Encryption Application
Inspired by the advancements in (fully) homomorphic encryption in recent decades and its practical applications, we conducted a preliminary study on the underlying mathematical structure of the corresponding schemes. Hence, this paper focuses on investigating the challenge of deducing bivariate poly...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Cryptography |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2410-387X/7/2/31 |
| _version_ | 1797595390208376832 |
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| author | Diana Maimuţ George Teşeleanu |
| author_facet | Diana Maimuţ George Teşeleanu |
| author_sort | Diana Maimuţ |
| collection | DOAJ |
| description | Inspired by the advancements in (fully) homomorphic encryption in recent decades and its practical applications, we conducted a preliminary study on the underlying mathematical structure of the corresponding schemes. Hence, this paper focuses on investigating the challenge of deducing bivariate polynomials constructed using homomorphic operations, namely repetitive additions and multiplications. To begin with, we introduce an approach for solving the previously mentioned problem using Lagrange interpolation for the evaluation of univariate polynomials. This method is well-established for determining univariate polynomials that satisfy a specific set of points. Moreover, we propose a second approach based on modular knapsack resolution algorithms. These algorithms are designed to address optimization problems in which a set of objects with specific weights and values is involved. Finally, we provide recommendations on how to run our algorithms in order to obtain better results in terms of precision. |
| first_indexed | 2024-03-11T02:35:45Z |
| format | Article |
| id | doaj.art-5b158318b51c4c79b4e603fa446ce53a |
| institution | Directory Open Access Journal |
| issn | 2410-387X |
| language | English |
| last_indexed | 2024-03-11T02:35:45Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Cryptography |
| spelling | doaj.art-5b158318b51c4c79b4e603fa446ce53a2023-11-18T09:55:41ZengMDPI AGCryptography2410-387X2023-06-01723110.3390/cryptography7020031Inferring Bivariate Polynomials for Homomorphic Encryption ApplicationDiana Maimuţ0George Teşeleanu1Advanced Technologies Institute, 10 Dinu Vintilă, 021102 Bucharest, RomaniaAdvanced Technologies Institute, 10 Dinu Vintilă, 021102 Bucharest, RomaniaInspired by the advancements in (fully) homomorphic encryption in recent decades and its practical applications, we conducted a preliminary study on the underlying mathematical structure of the corresponding schemes. Hence, this paper focuses on investigating the challenge of deducing bivariate polynomials constructed using homomorphic operations, namely repetitive additions and multiplications. To begin with, we introduce an approach for solving the previously mentioned problem using Lagrange interpolation for the evaluation of univariate polynomials. This method is well-established for determining univariate polynomials that satisfy a specific set of points. Moreover, we propose a second approach based on modular knapsack resolution algorithms. These algorithms are designed to address optimization problems in which a set of objects with specific weights and values is involved. Finally, we provide recommendations on how to run our algorithms in order to obtain better results in terms of precision.https://www.mdpi.com/2410-387X/7/2/31bivariate polynomialLagrange interpolationmodular knapsack problemlattice reduction |
| spellingShingle | Diana Maimuţ George Teşeleanu Inferring Bivariate Polynomials for Homomorphic Encryption Application Cryptography bivariate polynomial Lagrange interpolation modular knapsack problem lattice reduction |
| title | Inferring Bivariate Polynomials for Homomorphic Encryption Application |
| title_full | Inferring Bivariate Polynomials for Homomorphic Encryption Application |
| title_fullStr | Inferring Bivariate Polynomials for Homomorphic Encryption Application |
| title_full_unstemmed | Inferring Bivariate Polynomials for Homomorphic Encryption Application |
| title_short | Inferring Bivariate Polynomials for Homomorphic Encryption Application |
| title_sort | inferring bivariate polynomials for homomorphic encryption application |
| topic | bivariate polynomial Lagrange interpolation modular knapsack problem lattice reduction |
| url | https://www.mdpi.com/2410-387X/7/2/31 |
| work_keys_str_mv | AT dianamaimut inferringbivariatepolynomialsforhomomorphicencryptionapplication AT georgeteseleanu inferringbivariatepolynomialsforhomomorphicencryptionapplication |