A soft-matrix symmetric cryptosystem with involutory keys for context-aware message encryption
Muhammad Saeed, Iqra Batool, Fatima Razaq · Journal of Cyber Security Technology · 2026
Lightweight symmetric encryption increasingly serves short-message, resource-constrained systems where contextual data properties are operationally relevant. Ciphers such as Hill, AES, and DES treat plaintext as a uniform block, ignoring multi-attribute format. Soft set theory can parameterize such attributes, but most soft-set cryptosystems use nonstandard operators that hinder analysis and implementation. This paper introduces a symmetric key cryptosystem combining binary soft-matrix encoding with standard modular multiplication over Zm. Plaintext is represented as a soft matrix relating symbols to parameters (e.g. vowel/consonant class or ASCII parity), then encrypted with a self-invertible (involutory) key matrix. The involutory structure allows exact decryption with the same key, without matrix inversion, preserving algebraic transparency and computational simplicity. Algorithmic specifications and realistic short-message examples confirm exact decryption under an injective encoding. A Python prototype runs in tens of microseconds per message on a commodity CPU; a hardened timing harness (median, interquartile range) is released for reproduction on constrained targets. As a single linear round, the transformation offers intra-symbol but no inter-symbol diffusion, fails a NIST SP 800-22 subset, and, being deterministic, fails IND-CPA. Rather than rivaling modern nonlinear block ciphers, it offers a transparent, context-sensitive matrix architecture for controlled short-message use and cryptanalytic study. Introduces a soft-matrix symmetric cryptosystem integrating parameterized plaintext modeling with modular linear algebra over Zm.Develops a systematic construction of involutory key matrices satisfying R2 ≡ I (mod m), enabling identical encryption and decryption transformations.Formally characterizes the encryption process as a linear transformation on a finite Zm-module.Establishes structural equivalence with Hill-type matrix ciphers under fixed encoding while preserving contextual attribute modeling.Provides algebraic analysis of known-plaintext exposure and linear key-recovery behavior.Demonstrates computational feasibility through prototype implementation in resource-constrained environments. Introduces a soft-matrix symmetric cryptosystem integrating parameterized plaintext modeling with modular linear algebra over Zm. Develops a systematic construction of involutory key matrices satisfying R2 ≡ I (mod m), enabling identical encryption and decryption transformations. Formally characterizes the encryption process as a linear transformation on a finite Zm-module. Establishes structural equivalence with Hill-type matrix ciphers under fixed encoding while preserving contextual attribute modeling. Provides algebraic analysis of known-plaintext exposure and linear key-recovery behavior. Demonstrates computational feasibility through prototype implementation in resource-constrained environments.