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Journal of Discrete Mathematical Sciences and Cryptography cover

Journal of Discrete Mathematical Sciences and Cryptography

(Since 1998)
Hybrid ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

CiteScore 2025: 2.7 (Q1)

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Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Journal of Discrete Mathematical Sciences and Cryptography
Open Access Research Article

Enhancing cryptographic security through zero-knowledge proofs in theoretical mathematics

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pp. 913–921Vol. 29Issue 2-BFebruary 2026DOI: 10.47974/JDMSC-2542 Crossmark XML
Received:
07 May 2025
Published Online:
31 Dec 2025
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2542
Pages:
913–921

Abstract

In modern cryptography, improving the cryptographic security of Zero-Knowledge Proofs (ZKP) has become a compelling trend. Traditional models like the zk-SNARK and zk-STARK has shown strong security but are accompanied by the inherent issues of computational complexity and proof size. This work presents the Algebraic Zero-Knowledge Proof (AZKP) framework, using algebraic structures and integration of elliptic curves to optimize proof creation and verification. The suggested approach fills in key gaps found in the current methodologies, such as huge computational overhead and enormous proof sizes. Prime factorization in algebraic groups and ring homomorphisms of the AZKP framework is used to achieve small proof size without sacrificing computational efficiency. Comparing AZKP with zk-SNARK and zk-STARK models, experimental evaluation was applied to four critical performance metrics. generation time of proof, verification time, size of proof, and computational overhead. Results show that the AZKP is able to make a 48% decrease in proof generation duration and 20% increase in verification speed in comparison to zk-SNARK. Also, AZKP incurred lower computational cost than zk-STARK, with a proof size that is manageable. These results highlight the prospect of AZKP in cryptographic use where high-speed low-latency verification operations are desired. Further research will integrate AZKP in blockchain environments in order to increase real-time transaction validation. 

Keywords

Zero-knowledge proofAlgebraic cryptographyProof efficiencyComputational overheadCryptographic securityElliptic curve integration

Subject Classifications

Primary 93A30Secondary 49K15

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