Tropical matrix-based cryptosystems: a post-quantum approach to public key security

Articles in Press

Document Type : Research Paper

Authors

1 Department of Pure Mathematics, Faculty of mathematical sciences, University of Guilan, Rasht, Iran

2 Department of Computer Engineering, University of Guilan, Rasht, Iran

Abstract

In recent years, cryptographic constructions based on alternative algebraic structures have been explored as candidates for post-quantum security. Tropical algebra, with its unique min-plus operations and NP-hard associated computational problems, provides a promising foundation for such schemes. In this work, we introduce a new public key cryptosystem built upon tropical block matrices. Specifically, we design (i) a key exchange protocol and (ii) an encryption scheme analogous to the ElGamal cryptosystem. The security of our protocols relies on the hardness of solving nonlinear systems over tropical semirings. We analyze the resistance of the proposed constructions against brute force and algebraic attacks and discuss their computational efficiency. Our results suggest that tropical block matrix–based schemes offer a novel direction for post-quantum cryptography and extend the scope of tropical algebra applications in secure communication.

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Journal of Algebra and Related Topics

Articles in Press, Accepted Manuscript
Available Online from 01 June 2026

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