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<p>There have been a lot of new advances in public-key cryptography over the last few years. This paper proposes a novel Multivariate mapping, promotes the properties of Multivariate polynomials and designs an improved McEliece public-key cryptosystem by combining multivariate polynomials with Goppa polynomials. Based on error-correction algorithms, the McEliece public-key cryptosystem is designed to withstand quantum attacks. The proposed scheme that discretizes the multivariate mapping by partitioning the variable space into finite intervals over a finite field, enabling polynomial evaluations at discrete grid points. For instance, the code can be built by evaluating multivariate polynomials, which can be involved in the construction of the Goppa codes. The roots of the Goppa polynomial at a given position correspond to the proposed multivariate polynomial cryptosystem. Finally, messages encrypted with an improved McEliece cryptosystem are further authenticated using Hash-Based Message Authentication Codes (HMACs) based on the Keccak-256 hash function. This provides integrity and authentication by creating a unique hash of the encrypted data. Multivariate polynomials overcome the shortcomings such as large public key sizes, low efficiency, high complexity, and poor security in previous systems, while offering higher security and outperforming in secure communication and efficient transmission of messages for users. Overall, the proposed scheme demonstrates an overall encryption and decryption time of 2.713&#xa0;ms and 1.162&#xa0;ms, respectively, and storage efficiency of 98.12&#xa0;kb when compared to state-of-the-art schemes.</p>

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Enhancing data security using multivariate polynomial based McEliece encryption with advanced hash-based message authentication

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Talari Surendra,
  • Manteena Madhavi,
  • Chaganti Pragathi,
  • Nalluri Suryaprakash,
  • R Hari Kishore,
  • PSVS Sridhar

摘要

There have been a lot of new advances in public-key cryptography over the last few years. This paper proposes a novel Multivariate mapping, promotes the properties of Multivariate polynomials and designs an improved McEliece public-key cryptosystem by combining multivariate polynomials with Goppa polynomials. Based on error-correction algorithms, the McEliece public-key cryptosystem is designed to withstand quantum attacks. The proposed scheme that discretizes the multivariate mapping by partitioning the variable space into finite intervals over a finite field, enabling polynomial evaluations at discrete grid points. For instance, the code can be built by evaluating multivariate polynomials, which can be involved in the construction of the Goppa codes. The roots of the Goppa polynomial at a given position correspond to the proposed multivariate polynomial cryptosystem. Finally, messages encrypted with an improved McEliece cryptosystem are further authenticated using Hash-Based Message Authentication Codes (HMACs) based on the Keccak-256 hash function. This provides integrity and authentication by creating a unique hash of the encrypted data. Multivariate polynomials overcome the shortcomings such as large public key sizes, low efficiency, high complexity, and poor security in previous systems, while offering higher security and outperforming in secure communication and efficient transmission of messages for users. Overall, the proposed scheme demonstrates an overall encryption and decryption time of 2.713 ms and 1.162 ms, respectively, and storage efficiency of 98.12 kb when compared to state-of-the-art schemes.