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<p>The search for optimal cryptographic protocols and algebraic structures has been a persistent challenge in modern cryptography. Among the proposed solutions, tropical semirings have gained attention as a promising framework, with researchers developing various protocols based on matrix powers and two-sided matrix action problems. However, many of these constructions have proven vulnerable to attacks, highlighting the need for more secure and robust algebraic foundations. This work investigates the two-sided matrix action problem in tropical semirings, providing a systematic review of existing tropical cryptographic protocols. Our key contribution lies in identifying a broad class of commuting matrices over a semiring that can serve as a secure foundation for cryptographic constructions. By analyzing their structural properties and resistance to known attacks, we aim to advance the development of reliable tropical-based cryptographic schemes.</p>

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On the two-sided matrix action problem in tropical semirings

  • 期刊论文

  • 发表日期：

    2025年7月26日

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  • A. Ponmaheshkumar,
  • R. Perumal

摘要

The search for optimal cryptographic protocols and algebraic structures has been a persistent challenge in modern cryptography. Among the proposed solutions, tropical semirings have gained attention as a promising framework, with researchers developing various protocols based on matrix powers and two-sided matrix action problems. However, many of these constructions have proven vulnerable to attacks, highlighting the need for more secure and robust algebraic foundations. This work investigates the two-sided matrix action problem in tropical semirings, providing a systematic review of existing tropical cryptographic protocols. Our key contribution lies in identifying a broad class of commuting matrices over a semiring that can serve as a secure foundation for cryptographic constructions. By analyzing their structural properties and resistance to known attacks, we aim to advance the development of reliable tropical-based cryptographic schemes.