{"ID":2898953,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.03000","arxiv_id":"2507.03000","title":"Deterministic Cryptographic Seed Generation via Cyclic Modular Inversion over $\\mathbb{Z}/3^p\\mathbb{Z}$","abstract":"We present a deterministic framework for cryptographic seed generation based on cyclic modular inversion over $\\mathbb{Z}/3^p\\mathbb{Z}$. The method enforces algebraic admissibility on seed inputs via the identity $d_k \\equiv -\\left(2^{k-1}\\right)^{-1} \\bmod 3^p$, thereby producing structured and invertible residue sequences. This mapping yields entropy-rich, cycle-complete seeds well-suited for cryptographic primitives such as DRBGs, KDFs, and post-quantum schemes. To assess the quality of randomness, we introduce the Entropy Confidence Score (ECS), a composite metric reflecting coverage, uniformity, and modular bias. Although not a cryptographic PRNG in itself, the framework serves as a deterministic entropy filter that conditions and validates seed inputs prior to their use by conventional generators. Empirical and hardware-based results confirm constant-time execution, minimal side-channel leakage, and lightweight feasibility for embedded applications. The framework complements existing cryptographic stacks by acting as an algebraically verifiable entropy filter, thereby enhancing structural soundness and auditability.","short_abstract":"We present a deterministic framework for cryptographic seed generation based on cyclic modular inversion over $\\mathbb{Z}/3^p\\mathbb{Z}$. The method enforces algebraic admissibility on seed inputs via the identity $d_k \\equiv -\\left(2^{k-1}\\right)^{-1} \\bmod 3^p$, thereby producing structured and invertible residue seq...","url_abs":"https://arxiv.org/abs/2507.03000","url_pdf":"https://arxiv.org/pdf/2507.03000v1","authors":"[\"Michael A. Idowu\"]","published":"2025-07-02T00:17:55Z","proceeding":"cs.CR","tasks":"[\"cs.CR\",\"cs.IT\"]","methods":"[]","has_code":false}