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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2507.03000 |
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| _version_ | 1866912464900194304 |
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| author | Idowu, Michael A. |
| author_facet | Idowu, Michael A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deterministic Cryptographic Seed Generation via Cyclic Modular Inversion over $\mathbb{Z}/3^p\mathbb{Z}$ Idowu, Michael A. Cryptography and Security Information Theory Primary 05A17, Secondary 11D45, 11Y60, 94A60 F.2.1 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. |
| title | Deterministic Cryptographic Seed Generation via Cyclic Modular Inversion over $\mathbb{Z}/3^p\mathbb{Z}$ |
| topic | Cryptography and Security Information Theory Primary 05A17, Secondary 11D45, 11Y60, 94A60 F.2.1 |
| url | https://arxiv.org/abs/2507.03000 |