Decryption Through Polynomial Ambiguity: Noise-Enhanced High-Memory Convolutional Codes for Post-Quantum Cryptography

TL;DR

This paper introduces a new post-quantum cryptographic scheme using noise-enhanced high-memory convolutional codes with directed-graph decryption, offering superior security, scalability, and efficient implementation for quantum-resistant encryption.

Contribution

It presents a novel cryptographic construction that employs polynomial ambiguity and noise injection to achieve high security and flexibility in post-quantum encryption schemes.

Findings

Achieves security surpassing Classic McEliece by over 2^200.

Supports arbitrary plaintext lengths with linear-time decoding.

Enables efficient hardware and software implementations.

Abstract

We present a novel approach to post-quantum cryptography that employs directed-graph decryption of noise-enhanced high-memory convolutional codes. The proposed construction generates random-like generator matrices that effectively conceal algebraic structure and resist known structural attacks. Security is further reinforced by the deliberate injection of strong noise during decryption, arising from polynomial division: while legitimate recipients retain polynomial-time decoding, adversaries face exponential-time complexity. As a result, the scheme achieves cryptanalytic security margins surpassing those of Classic McEliece by factors exceeding 2^(200). Beyond its enhanced security, the method offers greater design flexibility, supporting arbitrary plaintext lengths with linear-time decryption and uniform per-bit computational cost, enabling seamless scalability to long messages. Practical deployment is facilitated by parallel arrays of directed-graph decoders, which identify the correct plaintext through polynomial ambiguity while allowing efficient hardware and software implementations. Altogether, the scheme represents a compelling candidate for robust, scalable, and quantum-resistant public-key cryptography.