Paper 2025/1615

The Chaotic Entropic Expansion (CEE): A Transparent Post-Quantum Data Confidentiality Primitive via Entropic Chaotic Maps

Abstract

Weintroduce the Chaotic Entropic Expansion (CEE), a new one-way function based on iterated polynomial maps over finite fields. For polynomials f in a carefully defined class Fd, we prove that N iterations preserve min-entropy of at least log2q − N log2d bits and achieve statistical distance ≤ (q − 1)(dN − 1)/(2√q) from uniform. We formalize security through the Affine Iterated Inversion Problem (AIIP) and provide reductions to the hardness of solving multivariate quadratic equations (MQ) and computing discrete logarithms (DLP). Against quantum adversaries, CEE achieves O(2λ/2) security for λ-bit classical security. We provide comprehensive cryptanalysis and parameter recommendations for practical deployment. While slower than AES, CEE’s algebraic structure enables unique applications in verifiable computation and post-quantum cryptography within the CASH framework.

Note: Additional Notes: This manuscript on the Chaotic Entropic Expansion (CEE) constitutes the formalization of the core confidentiality primitive for the broader research program on legally explainable post-quantum cryptography. It is the first defined component of the CASH framework (CEE, AOW, SH), which itself is a primitive-level instantiation of the abstract Q2CSI infrastructure (ePrint 2025/1380). The design of CEE directly enforces the Confidentiality property of the CRO Trilemma (ePrint 2025/1348), providing the entropic foundation necessary to resolve the incompatibility with Reliability and Opposability. This submission is a theoretical and foundational contribution. It focuses exclusively on the definition, entropy properties, security reductions, and cryptanalysis of the new CEE primitive. It does not include implementation artifacts or performance benchmarks. All contributions are original. This manuscript is not under submission or review elsewhere. The author may reference this work in future publications detailing the instantiation of the full CASH framework or its integration into higher-level protocols (e.g., the ZK-NR attestation protocol), ensuring no duplication of content and a clear progression from foundational primitive to applied construction.