Shor's Algorithm is a quantum algorithm for integer factorization named after mathematician Peter Shor, who developed it in 1994. This algorithm is particularly significant due to its potential to undermine modern cryptographic systems based on the difficulty of factoring large numbers into their prime factors.
The development of Shor's Algorithm was a pivotal moment in quantum computing. Peter Shor, while working at Bell Labs, published his findings in the paper titled "Algorithms for Quantum Computation: Discrete Logarithms and Factoring." His work combined quantum mechanics with number theory, leading to an exponential speedup over the best-known classical algorithm for factoring large numbers.
Shor's Algorithm essentially works in two main stages:
The practical implementation of Shor's Algorithm would break many of the public-key cryptosystems currently in use, such as RSA, which relies on the computational difficulty of factoring large integers. This has led to significant research into post-quantum cryptography, focusing on developing cryptographic systems that are resistant to quantum attacks.
As of now, Shor's Algorithm has been successfully implemented on small-scale quantum computers. However, factoring numbers of the size used in practical cryptography requires a quantum computer with many more qubits than are currently available.