A Block Encryption Construction Based on Bi-Periodic Pell Matrices and Elliptic Curve Group Operations
Year: 2026
Type: article
Abstract: This paper presents a theoretical algebraic block transformation based on bi-periodic Pell matrices and elliptic-curve point-valued blocks. The construction uses block-dependent scalar key matrices Ki=P~m+i−1(a,b)∈GL2(Fq) to transform plaintext blocks whose entries lie in a selected elliptic-curve subgroup G=⟨G0⟩⊆E(Fp) of prime order q. The encryption operation is defined by the elliptic-curve scalar matrix action Mi=Bi⋆Ki, where the entries of Ki act as scalar coefficients modulo q, and point additions are performed in G. The main purpose of the construction is to formalize the interaction between recursive Pell-type matrix sequences over Fq and elliptic-curve point-valued block transformations. The algebraic correctness follows from the invertibility of Ki over Fq and the compatibility of the ⋆-action with the matrix multiplication. The deterministic version is not claimed to provide semantic security or IND-CPA security without additional randomization, nonce-dependent masking, and formal security proofs.
Source: Axioms
Authors: Ersen Akinci, Sukran Uygun
Institution: Gaziantep University
Language: English
Subfield: Information Systems
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W7168317482