Digital Signal Processing

Quantum Resistant Cryptography and It's Implications on Blockchain and Cryptocurrency

Authors: Tehzeeb Ali
Comments: 14 Pages.

Modern public key cryptosystems rely on two fundamental computational hardness assumptions: integer factorization (RSA) and the discrete logarithm problem (elliptic curve cryptography). These problems, formulated using modular arithmetic and algebraic geometry, have withstood four decades of cryptanalytic attacks. However, their inherent algebraic structures and periodicity properties make them vulnerable to quantum algorithms, particularly Shor’s algorithm (1994), which achieves polynomial-time complexity on quantum computers. This research presents an extensive mathematical comparison between classical cryptographic systems and quantum-resistant alternatives, with particular emphasis on lattice-based cryptography. We focus on the Learning With Errors (LWE) problem and its variants (Ring-LWE, Module-LWE), demonstrating through rigorous mathematical analysis why these lattice problems lack the periodicity that quantum algorithms exploit. We provide formal security reductions for LWE problems relative to worst-case lattice problems and present mathematical proofs of quantum resistance. For cryptocurrency systems, this analysis reveals critical vulnerabilities: current ECDSA algorithms used for transaction signing will become cryptographically insecure within 10-30 years, potentially compromising over $100 billion in digital assets. This work bridges mathematical foundations, security analysis, and practical implications for real-world systems, providing proof-based recommendations for the transition to post-quantum cryptographic standards in blockchain technologies.
Category: Digital Signal Processing