Deterministic Cryptographic Seed Generation via Cyclic Modular Inversion over $\mathbb{Z}/3^p\mathbb{Z}$

• URL: http://arxiv.org/abs/2507.03000v1
• Date: Wed, 02 Jul 2025 00:17:55 GMT
• Title: Deterministic Cryptographic Seed Generation via Cyclic Modular Inversion over $\mathbb{Z}/3^p\mathbb{Z}$
• Abstract summary: We present a framework for cryptographic seed generation based on cyclic modular inversion over $mathbbZ/3pmathbbZ$.<n>The mapping yields entropy-rich, cycle-complete seeds well-suited for cryptographic primitives such as DRBGs, KDFs, and post-quantum schemes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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