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...

Williston Shor (born August 14, 1959) is an American mathematician known for his work on quantum computation, in particular for devising Shor's algorithm, a...

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

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...

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

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

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...

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...

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...

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...

essential step in several integer factorization algorithms, such as Pollard's rho algorithm, Shor's algorithm, Dixon's factorization method and the Lenstra...

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

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

particular, cannot execute Shor's algorithm because Shor's algorithm is not a hillclimbing process.[citation needed] Shor's algorithm requires a universal quantum...

rho algorithm prime factorization algorithm Quadratic sieve Shor's algorithm Special number field sieve Trial division Multiplication algorithms: fast...

lemma Bellman–Ford algorithm (to do) Euclidean algorithm Kruskal's algorithm Gale–Shapley algorithm Prim's algorithm Shor's algorithm (incomplete) Basis...

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

Shor and Shorshor, a 1926 Soviet film Shor's algorithm, a quantum algorithm for integer factorization Toots Shor's Restaurant, New York City Schor (disambiguation)...

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...

(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...

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

easily solved on a sufficiently powerful quantum computer running Shor's algorithm or even faster and less demanding (in terms of the number of qubits...

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

Quantum computers running Shor's algorithm can solve these problems exponentially faster than the best-known algorithms for conventional computers....

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

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

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

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

Chapter 8 covers Shor's algorithm for integer factorization, and introduces the hidden subgroup problem. Chapter 9 covers Grover's algorithm and the quantum...