International Journal For Multidisciplinary Research

E-ISSN: 2582-2160   •   Impact Factor: 9.24

A Widely Indexed Open Access Peer Reviewed Multidisciplinary Bi-monthly Scholarly International Journal

Call for Paper Volume 8, Issue 5 (September-October 2026) Submit your research before last 3 days of October to publish your research paper in the issue of September-October.
Submit Research Paper Join as a Reviewer

Plagiarism is checked by the leading plagiarism checker TurnItIn

Call for Paper

Volume 8 Issue 5
September-October 2026

Submit your research paper

Indexing Partners
Academia Advanced Sciences Index Bielefeld Academic Search Engine CiteSeer DRJI Google Scholar Independent Search Engine & Directory Network ISI (International Scientific Indexing) Issuu Mendeley Research Networks
RefSeek ResearcherId - Thomson Reuters ResearchGate Scirus Scribd Semantic Scholar UTeM - Universiti Teknikal Malaysia Melaka Wiki for Call for Papers WorldCat Zenodo

Algebraic Construction of Post-Quantum Cryptographic Schemes over Semirings and Semimodules: Security and Computational Analysis

Author(s) Prof. Joyce. Z, Dr. R.Stella Maragatham
Country India
Abstract The advent of quantum computing necessitates the study of algebraic cryptographic schemes which would not rely explicitly on the problem of integer factorization or discrete logarithms. In this paper, we explore a framework for post-quantum cryptography with use of finite semirings, semimodules, and matrix actions with commutativity. A problem of recovering an action of a semimodule (SARP) is set up as the main computational problem, and cryptographic protocols of key exchange and hybrid public-key cryptosystems with algebraic correctness are constructed. The framework is studied in terms of its efficiency and security against attacks from the perspective of effective key spaces, collisions, orbit and stabilizer structures, algebraic recovery, exhaustive search, and generic quantum search algorithms. We derive the computational complexity of the operations in the main semiring and complement our theoretical results by an experimental implementation of those operations in Python on finite modular semiring. Our experiments of computations in semimodules of dimension n∈{16ⓜ,32ⓜ,64ⓜ,128ⓜ,256} show the expected increase of cost of action of matrices on vectors and are consistent with the theoretical complexity of quadratic growth.
Keywords Post-Quantum Cryptography, Semiring, Semimodule, Semigroup Action, SARP, Public-Key Encryption, Algebraic Cryptography.
Field Mathematics
Published In Volume 8, Issue 5, September-October 2026
Published On 2026-10-22
DOI https://doi.org/10.36948/ijfmr.2026.v08i05.90215
View / Download PDF File

Share this



E-ISSN 2582-2160
CrossRef

CrossRef DOI prefix of IJFMR is 10.36948/ijfmr

Downloads
Research Paper Format Copyright Permission Form and Undertaking Form

All research papers published on this website are licensed under Creative Commons Attribution-ShareAlike 4.0 International License, and all rights belong to their respective authors/researchers.

CC-BY-SA Open Access

About IJFMR
Fees & Payment
Current Issue
Publication Archive 		Submit Research Paper
Track Submission Status
Publication Guidelines
Publication Ethics
Peer Review & Plagiarism 		Join as a Reviewer
Editors & Reviewers
Reviewer Referral Program
Get Reviewer Membership Certi. 		Website/Journal Policies
Usage Policy
Content Policies
Privacy Policy
Contact Us +91-9687-828-838 editor@ijfmr.com
Powered by Sky Research Publication and Journals