Ternary public-key cryptosystem

Computer Science > Cryptography and Security [Submitted on 5 Jun 2026] Ternary public-key cryptosystem Steven Duplij, Qiang Guo, Na Fu Public-key cryptosystems eliminate the requirement for pre-shared secret keys by enabling encryption with a publicly disclosed key and decryption with a corresponding private key. In this article we generalize the public-key cryptosystems to ternary algebraic structures, with particular attention to ElGamal as a representative family. We introduce the necessary algebraic background for nonderived ternary structures, including special elements, ternary group rings, and a matrix ternarization procedure that maps binary rings and group rings to antidiagonal symbolic matrices closed under ternary multiplication. Building on these foundations, we formulate a ternary analogue of the ElGamal three-step protocol (key generation, ephemeral encryption, and decryption via querelements) and derive explicit ternary power and querelement formulas that enable correct decryption. Concrete instantiations and numerical examples over a ternary fraction field, a matrix-ternarized finite group ring, and a finite \((6,3)\)-ring (field) validate the construction and illustrate admissible word-length quantization and cycle behaviour of ternary powers. The ternary framework highlights two practical advantages: richer algebraic structure (querelements replace binary inverses) that increases algebraic complexity for attackers, and higher information density (matrix ternarization transfers paired/plaintext vectors). Formal hardness assumptions, optimized parameter choices, and comprehensive security and performance analyses remain necessary future work. Comments: 28 pages, revtex4.2 Subjects: Cryptography and Security (cs.CR) MSC classes: 16W99, 11A07, 11H71, 11R04, 17A42, 20N15, 68P25, 94A12, 94A60 ACM classes: E.3; G.2.0; G.2.1; H.1.1; C.3 Cite as: arXiv:2606.07832 [cs.CR]   (or arXiv:2606.07832v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2606.07832 Focus to learn more Submission history From: Steven Duplij [view email] [v1] Fri, 5 Jun 2026 20:45:41 UTC (25 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-06 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)