Year: 2025
Type: article
Abstract: : Algebraic geometry offers a powerful and elegant mathematical framework for the design and analysis of modern cryptographic protocols. This research paper investigates the application of algebraic geometry methods—such as elliptic curves, abelian varieties, and projective algebraic structures—in enhancing the security, efficiency, and scalability of cryptographic systems. By bridging advanced algebraic structures with cryptographic primitives, the study demonstrates how algebraic geometry enables the construction of secure public key protocols, zero-knowledge proofs, and post-quantum resilient schemes. Through theoretical modeling, performance benchmarking, and comparative analysis with classical cryptographic approaches, the paper illustrates the advantages of algebraic geometry in terms of computational hardness assumptions, structural integrity, and potential for innovation in secure communications. The findings contribute to the evolving landscape of cryptography by positioning algebraic geometry as a foundational tool in next-generation cryptographic protocol design. Keywords: algebraic geometry, cryptographic protocols, elliptic curves, public key cryptography, post-quantum cryptography, projective varieties, zero-knowledge proofs, secure communication, mathematical cryptography, abelian varieties
DOI: 10.62311/nesx/rp2525
Author: Murali Krishna Pasupuleti
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4409647635