Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor...

quantum algorithms exploit generally cannot be efficiently simulated on classical computers (see Quantum supremacy). The best-known algorithms are Shor's algorithm...

an algorithm created to run on a quantum computer. In 1994, further progress toward quantum supremacy was made when Peter Shor formulated Shor's algorithm...

particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical...

algorithms, such as Shor's algorithm,: 131  the quantum algorithm for linear systems of equations, and the quantum counting algorithm. The algorithm operates...

classical algorithms. Quantum algorithms that offer more than a polynomial speedup over the best-known classical algorithm include Shor's algorithm for factoring...

it in polynomial time. Shor's algorithm takes only O(b3) time and O(b) space on b-bit number inputs. In 2001, Shor's algorithm was implemented for the...

purpose – would be able to factor in polynomial time, breaking RSA; see Shor's algorithm. Finding the large primes p and q is usually done by testing random...

on Shor's algorithm and Grover's algorithm. Of the two, Shor's offers the greater risk to current security systems. Derivatives of Shor's algorithm are...

it especially important in the theory of quantum computing because Shor's algorithms for factoring and finding discrete logarithms in quantum computing...

running Shor's algorithm or possibly alternatives. As of 2024, quantum computers lack the processing power to break widely used cryptographic algorithms; however...

universal quantum computer and, in particular, cannot execute Shor's algorithm because Shor's algorithm requires precise gate operations and quantum Fourier transforms...

many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating...

computer. The quantum algorithm solving Simon's problem, usually called Simon's algorithm, served as the inspiration for Shor's algorithm. Both problems are...

popular public-key cryptosystems, it is resistant to attacks using Shor's algorithm. NTRUEncrypt was patented, but it was placed in the public domain in...

(to break 128 bits of security). In comparison, using Shor's algorithm to break the RSA algorithm requires 4098 qubits and 5.2 trillion Toffoli gates for...

taken by Grover's algorithm. Amplitude amplification Brassard–Høyer–Tapp algorithm (for solving the collision problem) Shor's algorithm (for factorization)...

general-purpose algorithm is RSA-240, which has 240 decimal digits (795 bits) and is the product of two large primes. Shor's algorithm can factor any integer...

that could break current cryptography systems using methods such as Shor's algorithm. These methods include quantum key distribution (QKD), a method of...

algorithm prime factorization algorithm Quadratic sieve Shor's algorithm Special number field sieve Trial division Lenstra–Lenstra–Lovász algorithm (also...

elliptic-curve cryptosystems—which could, theoretically, be defeated using Shor's algorithm on a quantum computer—some lattice-based constructions appear to be...

quantum computing, modular exponentiation appears as the bottleneck of Shor's algorithm, where it must be computed by a circuit consisting of reversible gates...

exponentially quicker than classical algorithms. This is essential for quantum algorithms such as Shor’s algorithm, where quantum phase estimation is used...

of the protocol" for its second revision. Post-quantum cryptography Shor's algorithm Signal Protocol Signal (software) Public-key cryptography End-to-end...

immune to attacks using Shor's algorithm and – more generally – measuring coset states using Fourier sampling. The algorithm is based on the hardness...

public key algorithms, such as RSA and ElGamal would become insecure if an effective quantum computer could be built (due to Shor's algorithm). The Merkle...

and capable of executing a program known as Shor's algorithm will easily accomplish the task. Shor's algorithm can also quickly break digital signatures...

conventional computer. This algorithm introduces the main ideas which were then developed in Peter Shor's factorization algorithm. Peter Shor, at AT&T's Bell Labs...

asymptotically faster than by using classical computers. A combination of Shor's algorithm, an integer factorization method, with the Pocklington primality test...

discrete logarithms, like ECDSA, problems solved in polynomial time with Shor's algorithm. Schneier, Bruce (2004). Secrets and Lies. Wiley Publishing, Inc. p...