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Quantum algorithm for integer factorization
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
Shor's_algorithm
Algorithm to be run on quantum computers
In quantum computing, a quantum algorithm is an algorithm that runs on a realistic model of quantum computation, the most commonly used model being the
Quantum_algorithm
Computational benchmark
has a superpolynomial speedup over the best known or possible classical algorithm for that task. A notable property of quantum supremacy is that it can
Quantum_supremacy
American mathematician
particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the best currently-known algorithm running on a classical
Peter_Shor
Decomposition of a number into a product
best published algorithm for large n (more than about 400 bits). For a quantum computer, however, Peter Shor discovered an algorithm in 1994 that solves
Integer_factorization
Algorithm for public-key cryptography
Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 at Government
RSA_cryptosystem
Process of converting plaintext to ciphertext
encryption scheme usually uses a pseudo-random encryption key generated by an algorithm. It is possible to decrypt the message without possessing the key but
Encryption
Cryptography secured against quantum computers
running Shor's algorithm or possibly alternatives. As of 2026, quantum computers lack the processing power to break widely used cryptographic algorithms; however
Post-quantum_cryptography
Quantum algorithm for eigenvalue estimation
quantum algorithms, such as Shor's algorithm, the quantum algorithm for linear systems of equations, and the quantum counting algorithm. The algorithm operates
Quantum phase estimation algorithm
Quantum_phase_estimation_algorithm
Computer hardware technology that uses quantum mechanics
efficient discrete-logarithm algorithm would compromise Diffie–Hellman key exchange. The cryptographic implications of Shor's algorithm drew attention to quantum
Quantum_computing
Cryptographic primitives that involve lattices
elliptic-curve cryptosystems—which could, theoretically, be defeated using Shor's algorithm on a quantum computer—some lattice-based constructions appear to be
Lattice-based_cryptography
Quantum search algorithm
In quantum computing, Grover's algorithm, also known as the quantum search algorithm, is a quantum algorithm for unstructured search that finds with high
Grover's_algorithm
Very general problem in computer science
it especially important in the theory of quantum computing because Shor's algorithms for factoring and finding discrete logarithms in quantum computing
Hidden_subgroup_problem
An algorithm is a fundamental set of rules or defined procedures that are typically designed and used to be a simpler way to solve a specific problem
List_of_algorithms
Problem in computer science
computer. The quantum algorithm solving Simon's problem, usually called Simon's algorithm, served as the inspiration for Shor's algorithm. Both problems are
Simon's_problem
Topics referred to by the same term
Look up shor or Shor in Wiktionary, the free dictionary. Shor may refer to: Shor language, one of the Turkic languages Shors, an indigenous ethnic group
Shor
Number of bits in a key used by a cryptographic algorithm
in a key used by a cryptographic algorithm (such as a cipher). Key length defines the upper-bound on an algorithm's security (i.e. a logarithmic measure
Key_size
Algorithm for computing greatest common divisors
In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers
Euclidean_algorithm
Quantum physics-based metaheuristic for optimization problems
Apolloni, N. Cesa Bianchi and D. De Falco as a quantum-inspired classical algorithm. It was formulated in its present form by T. Kadowaki and H. Nishimori
Quantum_annealing
List of quantum computing algorithms
algorithms, including algorithms, algorithmic techniques, computational models, and problem frameworks used in quantum computing. A quantum algorithm
List_of_quantum_algorithms
Study of analyzing information systems in order to discover their hidden aspects
cryptographic algorithms, cryptanalysis includes the study of side-channel attacks that do not target weaknesses in the cryptographic algorithms themselves
Cryptanalysis
Number divisible only by 1 and itself
of any integer between 2 and n {\displaystyle {\sqrt {n}}} . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small
Prime_number
Public-key cryptosystem that uses lattice-based cryptography
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
NTRU
Change of basis applied in quantum computing
many quantum algorithms, notably Shor's algorithm for factoring and computing the discrete logarithm, the quantum phase estimation algorithm for estimating
Quantum_Fourier_transform
Method of exchanging cryptographic keys
cryptography using asymmetric algorithms. Expired US patent 4200770 from 1977 describes the now public-domain algorithm. It credits Hellman, Diffie, and
Diffie–Hellman_key_exchange
Inherent difficulty of computational problems
such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory
Computational complexity theory
Computational_complexity_theory
Unsolved problem in computer science
polynomial function on the size of the input to the algorithm. The general class of questions that some algorithm can answer in polynomial time is "P" or "class
P_versus_NP_problem
Particle
solution of the decision problem. For example, using this procedure, Shor's algorithm for factoring an integer would correspond to some large link. To relate
Fibonacci_anyons
Quantum algorithm for solving systems of linear equations
The Harrow–Hassidim–Lloyd (HHL) algorithm is a quantum algorithm for obtaining certain limited information about the solution to a system of linear equations
HHL_algorithm
Technological development using the laws of quantum mechanics
'quantum safe' in the advent of quantum computing systems utilizing Shor's algorithm to break current cryptography systems. This is done through a number
Quantum_engineering
Mathematics award
computational complexity theory, logic of programming languages, analysis of algorithms, cryptography, computer vision, pattern recognition, information processing
IMU_Abacus_Medal
Metaheuristic proposed by Xin-She Yang
firefly algorithm is a metaheuristic proposed by Xin-She Yang and inspired by the flashing behavior of fireflies. In pseudocode the algorithm can be stated
Firefly_algorithm
Challenge for factoring large semiprimes
advances in quantum computers make this prediction uncertain due to Shor's algorithm. In 2001, RSA Laboratories expanded the factoring challenge and offered
RSA_Factoring_Challenge
The following timeline of algorithms outlines the development of algorithms (mainly "mathematical recipes") since their inception. Before – writing about
Timeline_of_algorithms
Asymmetric encryption algorithm developed by Robert McEliece
encryption algorithm developed in 1978 by Robert McEliece. It was the first such scheme to use randomization in the encryption process. The algorithm has never
McEliece_cryptosystem
Approach to public-key cryptography
encryption scheme. They are also used in several integer factorization algorithms that have applications in cryptography, such as Lenstra elliptic-curve
Elliptic-curve_cryptography
Exponentation in modular arithmetic
multiplicative inverse d of b modulo m (for instance by using extended Euclidean algorithm). More precisely: c = be mod m = d−e mod m, where e < 0 and b ⋅ d ≡ 1
Modular_exponentiation
Mechanism in quantum computing
exponentially quicker than classical algorithms. This is essential for quantum algorithms such as Shor's algorithm, where quantum phase estimation is used
Phase_kickback
Discrete Fourier transform algorithm
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT), or its inverse (IDFT), of a sequence. A Fourier transform
Fast_Fourier_transform
Experimental technology level
approximate optimization algorithm (QAOA), which use NISQ devices but offload some calculations to classical processors. These algorithms have been successful
Noisy intermediate-scale quantum computing
Noisy_intermediate-scale_quantum_computing
Type of cryptographic algorithm
discrete logarithms, like ECDSA, problems solved in polynomial time with Shor's algorithm. Schneier, Bruce (2004). Secrets and Lies. Wiley Publishing, Inc. p
Knapsack_cryptosystems
Projected date when quantum computers could break modern encryption
any size that matters, not in a human lifetime, not in many of them. Shor's algorithm, on a large enough fault-tolerant quantum computer, would do both in
Quantum_Threat
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
Timeline of quantum computing and communication
Timeline_of_quantum_computing_and_communication
Algorithm that begins on possibly incomplete inputs
online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e., in the order that the input is fed to the algorithm, without
Online_algorithm
Parsing algorithm for context-free grammars
Cocke–Younger–Kasami algorithm (alternatively called CYK, or CKY) is a parsing algorithm for context-free grammars published by Itiroo Sakai in 1961. The algorithm is named
CYK_algorithm
Project by NIST to standardize post-quantum cryptography
the possibility of quantum technology to render the commonly used RSA algorithm insecure by 2030. As a result, a need to standardize quantum-secure cryptographic
NIST Post-Quantum Cryptography Standardization
NIST_Post-Quantum_Cryptography_Standardization
Information held in the state of a quantum system
quantum algorithms can be used to perform computations faster than in any known classical algorithm. The most famous example of this is Shor's algorithm that
Quantum_information
Deterministic quantum algorithm
The Deutsch–Jozsa algorithm is a deterministic quantum algorithm proposed by David Deutsch and Richard Jozsa in 1992 with improvements by Richard Cleve
Deutsch–Jozsa_algorithm
Alternative form of government or social ordering
also referred to as algorithmic regulation, regulation by algorithms, algorithmic governance, algocratic governance, algorithmic legal order, or algocracy
Government_by_algorithm
Amount of resources to perform an algorithm
computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given
Computational_complexity
through the model of quantum circuits, it is focused more on quantum algorithms than on the construction of quantum computers. It has 13 chapters, divided
Quantum Computing: A Gentle Introduction
Quantum_Computing:_A_Gentle_Introduction
Measure of cryptographic strength
provide 128 bits of quantum security, which is still considered plenty. Shor's algorithm promises a massive speedup in solving the factoring problem, the discrete
Security_level
Lossless data compression algorithms
LZ77 and LZ78 are the two lossless data compression algorithms published in papers by Abraham Lempel and Jacob Ziv in 1977 and 1978. They are also known
LZ77_and_LZ78
Computational complexity class of problems
decision problem is a member of BQP if there exists a quantum algorithm (an algorithm that runs on a quantum computer) that solves the decision problem
BQP
Computer science award
and the Association for Computing Machinery Special Interest Group on Algorithms and Computational Theory (ACM SIGACT). The award is named in honor of
Gödel_Prize
Digital signature scheme
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
Merkle_signature_scheme
String-searching algorithm
algorithm is a string-searching algorithm invented by Alfred V. Aho and Margaret J. Corasick in 1975. It is a kind of dictionary-matching algorithm that
Aho–Corasick_algorithm
Ability to easily switch cryptographic primitives
key length, and a hash algorithm. X.509 version v.3, with key type RSA, a 1024-bit key length, and the SHA-1 hash algorithm were found by NIST to have
Cryptographic_agility
Family of lightweight block ciphers
optimized for performance in hardware implementations, while its sister algorithm, Speck, has been optimized for software implementations. The NSA began
Simon_(cipher)
Post-quantum digital signature scheme
offer security comparable to the Digital Signature Algorithm or Elliptic Curve Digital Signature Algorithm. A signature scheme has a signing key, which is
Unbalanced oil and vinegar scheme
Unbalanced_oil_and_vinegar_scheme
common multiple Euclidean algorithm Coprime Euclid's lemma Bézout's identity, Bézout's lemma Extended Euclidean algorithm Table of divisors Prime number
List_of_number_theory_topics
Post-quantum cryptographic algorithm
(SIDH or SIKE) was an insecure proposal for a post-quantum cryptographic algorithm to establish a secret key between two parties over an untrusted communications
Supersingular isogeny key exchange
Supersingular_isogeny_key_exchange
Quantum algorithm for counting solutions to search problems
Quantum counting algorithm is a quantum algorithm for efficiently counting the number of solutions for a given search problem. The algorithm is based on the
Quantum_counting_algorithm
Combinatorial algorithm
its five inventors, Peter Shor, Shlomo Moran, Alok Aggarwal, Robert Wilber, and Maria Klawe. For the purposes of this algorithm, a matrix is defined to
SMAWK_algorithm
Quantum programming framework
framework designed to simplify the implementation and development of quantum algorithms. Initially developed by Fraunhofer FOKUS (Quality Engineering unit, Berlin)
Qrisp
Algorithmic runtime requirements for common math procedures
The following tables list the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Israeli-American computer scientist
algorithm to factor integers with ∼ O ( n 3 / 2 ) {\displaystyle \sim O(n^{3/2})} quantum gates which would be more efficient than Shor's algorithm which
Oded Regev (computer scientist)
Oded_Regev_(computer_scientist)
Commentz-Walter algorithm is a string searching algorithm invented by Beate Commentz-Walter. Like the Aho–Corasick string matching algorithm, it can search
Commentz-Walter_algorithm
Involutive change of basis in linear algebra
the Deutsch–Jozsa algorithm, Simon's algorithm, the Bernstein–Vazirani algorithm, and in Grover's algorithm. Note that Shor's algorithm uses both an initial
Hadamard_transform
Public-key cryptosystem
encapsulation or ciphertext of the secret key by the KEM's encapsulation algorithm. The receiver who knows the private key corresponding to the public key
Key_encapsulation_mechanism
Australian quantum computing company
precision in 2022. Grover's algorithm is one of the two foundational quantum algorithms (alongside Shor's algorithm). Grover's algorithm runs quadratically faster
Silicon_Quantum_Computing
lemma Bellman–Ford algorithm (to do) Euclidean algorithm Kruskal's algorithm Gale–Shapley algorithm Prim's algorithm Shor's algorithm (incomplete) Basis
List_of_mathematical_proofs
Quantum algorithm
In quantum computing, the Brassard–Høyer–Tapp (BHT) algorithm is a quantum algorithm that solves the collision problem. In this problem, one is given n
BHT_algorithm
Chinese quantum physicist
photons. For example, he used four entangled photons to demonstrate Shor's factoring algorithm and in 2007 led the first team to entangle six photons. Anton
Lu_Chao-Yang
Cryptographic algorithm for digital signatures
cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography
Elliptic Curve Digital Signature Algorithm
Elliptic_Curve_Digital_Signature_Algorithm
Type of public-key encryption
Matthew K. Franklin defined a set of four algorithms that form a complete IBE system: Setup: This algorithm is run by the PKG one time for creating the
Identity-based_encryption
thereby proves Fermat's Last Theorem. 1994 – Peter Shor formulates Shor's algorithm, a quantum algorithm for integer factorization. 1995 – Simon Plouffe
Timeline_of_mathematics
with varying pulse rates of emission and loudness. The Bat algorithm was developed by Xin-She Yang in 2010. The idealization of the echolocation of microbats
Bat_algorithm
On finding a repeating loop in a sequence
In computer science, cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values. For any
Cycle_detection
Family of block ciphers
optimized for performance in software implementations, while its sister algorithm, Simon, has been optimized for hardware implementations. Speck is an add–rotate–xor
Speck_(cipher)
Art genre
Algorithmic art or algorithm art is art, mostly visual art, in which the design is generated by an algorithm. Algorithmic artists are sometimes called
Algorithmic_art
Accomplishments in factoring large integers
E5-2687W v1 for the linear algebra. The largest number reliably factored by Shor's algorithm, rather than some other quantum method, is 21 which was factored in
Integer_factorization_records
Indian-American computer scientist (born 1961)
search algorithm used in quantum computing. Grover's 1996 algorithm won renown as the second major algorithm proposed for quantum computing (after Shor's 1994
Lov_Grover
Superconducting qubit implementation
qubits that have had the most success are ion traps and NMR, with Shor's algorithm even being implemented using NMR. However, it is hard to see these
Charge_qubit
Quantum algorithm
The Bernstein–Vazirani algorithm, which solves the Bernstein–Vazirani problem, is a quantum algorithm invented by Ethan Bernstein and Umesh Vazirani in
Bernstein–Vazirani_algorithm
Quantum computing implementation
algorithms were published, which further stirred interest in realizing quantum computers. Peter Shor proposed Shor's algorithm, a quantum algorithm for
Superconducting quantum computing
Superconducting_quantum_computing
Network of Q&A sites based in New York City
possible weaknesses of their encryption algorithm. The Stack Exchange Crypto group discussion on the algorithm was censored, but it was later restored
Stack_Exchange
Digital signature resilient to quantum cryptography
Public key cryptography provides a rich set of different cryptographic algorithms the create digital signatures. However, the primary public key signatures
Ring learning with errors signature
Ring_learning_with_errors_signature
2023 book by Minna Ruckenstein
of algorithms and their social and behavioral impact. Ruckenstein examines the cultural, social, and emotional dimensions of algorithmic systems. She tracks
The_Feel_of_Algorithms
European information security initiative
commonly used algorithms have key sizes of 128 bits or more, providing sufficient security also in the case that the chosen algorithm is slightly weakened
ECRYPT
Generalization of the discrete Fourier transform
transform, which is commonly used in quantum computing and other fields. Shor's algorithm uses both the Hadamard transform (by applying a Hadamard gate to every
Fourier transform on finite groups
Fourier_transform_on_finite_groups
Algorithm for determining whether a number is prime
A primality test is an algorithm for determining whether an input number is prime. Among other fields of mathematics, it is used for cryptography. Unlike
Primality_test
portal In the digital humanities, "algorithmic culture" is part of an emerging synthesis of rigorous software algorithm-driven design that couples software
Algorithmic_culture
Optimization algorithms using quantum computing
Quantum optimization algorithms are quantum algorithms that are used to solve optimization problems. Mathematical optimization deals with finding the
Quantum optimization algorithms
Quantum_optimization_algorithms
Classification of quantum processors
quantum information. It is likely that advances at both the hardware and algorithm level are necessary for the transition to occur. When quantum computers
Fault tolerant quantum computing
Fault_tolerant_quantum_computing
Triple DES Caesar cipher Exponentiating by squaring Knapsack problem Shor's algorithm Standard Model Symmetry in physics Burnside's problem Classification
List_of_group_theory_topics
condensates. 1997 – Peter Shor publishes Shor's algorithm, a quantum computing algorithm for finding prime factors of integers. The algorithm is one of the few
Timeline_of_quantum_mechanics
Video-focused social media platform
mental health concerns, misinformation, offensive content, addictive algorithm, its role during the Gaza war, and, following its 2026 divestiture in
TikTok
Process by which platform algorithms increase the reach of certain content
Algorithmic amplification is the process by which automated ranking and recommendation systems on digital platforms increase the visibility of certain
Algorithmic_amplification
problems remains infeasible when a quantum computer is available (see Shor's algorithm). Independently, new quantum digital signature schemes have been proposed
Quantum_digital_signature
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