Decrypting the Future: Quantum Computing and The Impact of Grover’s and Shor’s Algorithms on Classical Cryptography

EasyChair Preprint 14978

Abstract

This paper aims to provide a direct analysis of the capabilities of quantum computation algorithms, particularly the Shor and Grovers algorithm on the basis of their time complexity and brute force capability. Shor's algorithm provides us with the capability to find out the prime factors of large primes exponentially faster than with classical systems. This proves to be a threat to the classical cryptosystems of date that rely on the incapability of the classical algorithms to calculate the prime factors of large primes. Grover's algorithm provides us with a quadratic speed up in the search capabilities of the computer systems which will have a major impact in brute forcing capabilities of the cryptosystem keys and hashes. We have also analysed the implications of these algorithms to the classical cryptosystems existing today and any major areas of improvement in the security algorithms that can be done to make them more secure.

Keyphrases: Brute force, Cryptosystem threats, Discrete logarithms, Grover's algorithm, Shor's algorithm, digital signatures and public, exponential speedup, grover s algorithm time complexity, quadratic speedup, quantum algorithms on classical cryptography, quantum computing, search capabilities, time complexity

@booklet{EasyChair:14978,
  author    = {Aryan Sahni and Ridhima Sahni},
  title     = {Decrypting the Future: Quantum Computing and The Impact of Grover’s and Shor’s Algorithms on Classical Cryptography},
  howpublished = {EasyChair Preprint 14978},
  year      = {EasyChair, 2024}}