**EchoPulse: Adaptive Symbolic Key Encapsulation Framework for Cybersecurity, Embedded Defense Systems, and Post-Quantum Resilience**

EchoPulse v5.2: Tableless Non-Linear Hybrid ARX Key Encapsulation Mechanism (KEM) for Constrained Embedded Systems

EchoPulse is a lightweight, non-lattice post-quantum Key Encapsulation Mechanism (KEM) specifically engineered for extreme edge environments, critical sovereign infrastructure, and resource-constrained microcontrollers (<6 KB RAM) where standard NIST lattice-based algorithms struggle with severe memory limitations.

By replacing traditional memory-bound cryptographic tables with a dynamic, tableless Non-Linear Hybrid MARX (Multiplicative-ARX) Sponge Construction, EchoPulse operates entirely within the CPU register file. This achieves a static memory footprint of exactly zero bytes for the internal state topology, fundamentally neutralizing cache-timing side-channel attacks while delivering highly deterministic, constant-time execution.

The Evolution: From Heuristics to Empirical Proofs

This Version 5.2 Zenodo release marks the culmination of a rigorous architectural journey. It transitions EchoPulse from an abstract theoretical model to a hardened, non-linear embedded core, forged through exhaustive formal cryptanalysis and machine-level empirical verification.

• v1.0 – v4.2 (The Tableless Breakthrough): Transitioned from RAM-bound "Symbolic Graph" models to a radical register-only affine KEM. Memory tables were eradicated in favor of fliegende transformations over \mathbb{Z}_{2^{32}}, achieving unprecedented embedded efficiency but leaving the architecture heuristically vulnerable to advanced SMT/lattice-based linearization.
• v5.0 – v5.1 (Structural Cryptanalysis & The Linear Boundary): Introduced the 256-bit ARX core. Automated SMT evaluation (Microsoft Z3) exposed inherent MSB-orbit vulnerabilities in pure ARX modular addition (carry-drop paths). Exhaustive deterministic Python brute-force screening mathematically proved that linear rotation parameter tuning cannot eradicate these zero-weight trails due to the necessary wide fan-out of the linear parity layer.
• v5.2 (The Non-Linear Hybrid Breakthrough): EchoPulse pivots to a Hybrid Permutation. By merging Multiplicative-ARX (MARX) with a value-dependent, quadratic Simon-style AND gate and asymmetric Alzette cross-rotations, the linear MSB-paths are physically severed. Verified via exact 16-bit Branch-and-Bound tracking and 32-bit hardware fuzzing, v5.2 achieves near-perfect random non-linear mixing: SAC Avalanche = 50.002%, eliminating the deterministic trails (Diff HW ~128/256 within 2 rounds) at a highly efficient +37.8% relative CPU overhead.

Included in this v5.2 Release

This release provides total transparency into the framework's evolution, structural failures, and subsequent mathematical hardening:

• EchoPulse v5.2 Academic Core: The foundational no_std Rust reference implementation of the Hybrid Variant, optimized for Cortex-M0+/RISC-V architectures with zero-byte RAM overhead.
• Open-Source Cryptanalysis Suite: The exact analytical toolchain used to test the cipher, including the 256-bit Z3 full-state models, the pure-Python linear MSB-orbit sniper (fast_orbit_sniper.py), and the exact 16-bit DDT rank computations (hybrid_16bit_bruteforce.py).
• Hardware Fuzzing Testbench: The 32-bit Rust empirical testbench (main.rs) proving the Strict Avalanche Criterion (SAC) and differential propagation.
• Architectural Verification Reports: Three comprehensive PDF supplements detailing the SMT timeouts, the linear boundary proof of v5.1, and the empirical validation of the v5.2 Non-Linear Hybrid.

Target Audience & Application

This release is intended as a transparent, auditable reference for researchers, cryptanalysts, and embedded systems engineers exploring non-lattice post-quantum primitives that prioritize extreme physical and memory efficiency over conventional RAM-heavy arrays.

Keywords: post-quantum cryptography, key encapsulation mechanism, tableless KEM, ARX sponge, Simon gate, Alzette, embedded security, side-channel resistance, Rust, open-science, IoT

Licensing:

CC BY-NC-ND 4.0 — Non-commercial use, works permitted without sovereign licensing approval. All core mathematical primitives, test vectors, analytical testbenches, and reference code are published to support independent research, peer review, and academic validation.

Contact:

tom.wartenberg01@gmail.com

tom.wartenberg@web.de