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Supersingular isogeny graph

In mathematics, the supersingular isogeny graphs are a class of expander graphs that arise in computational number theory and have been applied in elliptic-curve cryptography. Their vertices represent

Korkine–Zolotarev lattice basis reduction algorithm

The Korkine–Zolotarev (KZ) lattice basis reduction algorithm or Hermite-Korkine–Zolotarev (HKZ) algorithm is a lattice reduction algorithm. For lattices in it yields a lattice basis with orthogonality

Lattice reduction

In mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different algorithms,

Computational hardness assumption

In computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently (where efficiently typically means "in polynomial time"

Lenstra–Lenstra–Lovász lattice basis reduction algorithm

The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982. Given a basis

Phi-hiding assumption

The phi-hiding assumption or Φ-hiding assumption is an assumption about the difficulty of finding small factors of φ(m) where m is a number whose factorization is unknown, and φ is Euler's totient fun

Computational number theory

In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory

Fast Library for Number Theory

The Fast Library for Number Theory (FLINT) is a C library for number theory applications. The two major areas of functionality currently implemented in FLINT are polynomial arithmetic over the integer

Algorithmic Number Theory Symposium

Algorithmic Number Theory Symposium (ANTS) is a biennial academic conference, first held in Cornell in 1994, constituting an international forum for the presentation of new research in computational n

Higher residuosity problem

In cryptography, most public key cryptosystems are founded on problems that are believed to be intractable. The higher residuosity problem (also called the n th-residuosity problem) is one such proble

Itoh–Tsujii inversion algorithm

The Itoh–Tsujii inversion algorithm is used to invert elements in a finite field. It was introduced in 1988, first over GF(2m) using the normal basis representation of elements, however, the algorithm

Quadratic residuosity problem

The quadratic residuosity problem (QRP) in computational number theory is to decide, given integers and , whether is a quadratic residue modulo or not.Here for two unknown primes and , and is among th

Table of costs of operations in elliptic curves

Elliptic curve cryptography is a popular form of public key encryption that is based on the mathematical theory of elliptic curves. Points on an elliptic curve can be added and form a group under this

ABC@Home

ABC@Home was an educational and non-profit network computing project finding abc-triples related to the abc conjecture in number theory using the Berkeley Open Infrastructure for Network Computing (BO

Odlyzko–Schönhage algorithm

In mathematics, the Odlyzko–Schönhage algorithm is a fast algorithm for evaluating the Riemann zeta function at many points, introduced by (Odlyzko & Schönhage ). The main point is the use of the fast

Evdokimov's algorithm

In computational number theory, Evdokimov's algorithm, named after Sergei Evdokimov, is the asymptotically fastest known algorithm for factorization of polynomials (until 2019). It can factorize a one

Factorization of polynomials over finite fields

In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for p

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