Semigroup action based on skew polynomial evaluation with applications to Cryptography

2025/12/02 by Daniel Camazón-Portela, Camazón-Portela, Daniel, Juan Antonio López Ramos +1
Computer Science · #16S36 #20M30 #94A60 #Advanced Authentication Protocols Security #Cryptography and Data Security #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Information Theory (cs.IT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2512.02603

openalex publication_date 2025/12/02 · openalex created_date 2025/12/04 · openalex updated_date 2026/07/28

Abstract

Through this work we introduce an action of the skew polynomial ring \mathbbF_q[X; σ, δ] over \mathbbF_q based on its polynomial valuation and the concept of left skew product of functions. This lead us to explore the construction of a certain subset T(X)⊂\mathbbF_q[X; σ, δ] that allow us to control the non-commutativity of this ring, and exploit this fact in order to build a public key exchange protocol that is secure in Canetti and Krawczyk model.

Citations

• Skew-convex function rings and evaluation of skew rational functions
• Cryptographic Group and Semigroup Actions
• Public key cryptography based on twisted dihedral group algebras
• Matroidal Root Structure of Skew Polynomials over Finite Fields
• Group key management based on semigroup actions
• Public Key Cryptography based on Semigroup Actions
• Theory of Non-Commutative Polynomials

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