Quantum-Resistant Cryptography and Its Implications for Blockchain and Cryptocurrency: A Comprehensive Mathematical Analysis

https://doi.org/10.65161/reciVMFDoYuEGfYeh

Modern public key cryptosystems rely on two assumptions regarding computational difficulty: the integer factorization problem (RSA) and the discrete logarithm problem (elliptic curve cryptography). These problems have stood the test of time for four decades of cryptanalysis. Yet, their algebraic and periodic nature makes them vulnerable to quantum algorithms, most notably Shor's algorithm (1994). This paper presents a detailed comparison between classical and quantum-resistant cryptographic systems with an emphasis on lattice-based systems. The Learning With Errors (LWE) problem and its variants (Ring-LWE, Module-LWE) do not have the same periodicity that makes problems like integer factorization and discrete logarithms susceptible to quantum algorithms. Furthermore, LWE problems have reductions from worst-case lattice problems and have mathematical proofs of quantum resistance. Due to the vulnerability of ECDSA algorithms for cryptocurrencies, it is estimated that current cryptocurrencies will no longer be secure once quantum computer technology matures within the next 10–30 years, potentially compromising holdings estimated at between $260 billion and $390 billion as of August 2026. The implications of cryptanalysis on public key cryptography systems motivate mathematical recommendations regarding the security of current cryptosystems and the need for a shift to post-quantum cryptographic standards.