Shorfaktorizálás

Shorfaktorizálás, also known as Shor's algorithm, is a quantum algorithm for integer factorization. Developed by Peter Shor in 1994, it can factor an integer into its prime factors exponentially faster than the best known classical algorithms. This has significant implications for cryptography, as many widely used public-key cryptosystems, such as RSA, rely on the difficulty of factoring large numbers.

The core of Shor's algorithm lies in its ability to efficiently solve the problem of finding the period of a modular exponentiation function. This period-finding subroutine is performed on a quantum computer. Once the period is found, classical post-processing can be used to determine the prime factors of the original number. The quantum part of the algorithm, specifically the quantum Fourier transform, is what provides the exponential speedup.

While Shor's algorithm is theoretically powerful, its practical implementation faces significant challenges. Building a sufficiently large and stable quantum computer capable of running the algorithm on cryptographically relevant numbers is a major engineering hurdle. Current quantum computers are still relatively small and prone to errors, limiting their ability to perform complex computations like factoring large integers. Nevertheless, research and development in quantum computing continue to advance, bringing the potential realization of Shor's algorithm closer. The development of Shor's algorithm has spurred significant research into quantum-resistant cryptography.