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Probabilistic algorithm for computing discrete logarithms
In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete
Index_calculus_algorithm
Baby-step giant-step Index calculus algorithm Pohlig–Hellman algorithm Pollard's rho algorithm for logarithms Euclidean algorithm: computes the greatest
List_of_algorithms
Algorithm in computational number theory
algorithm, see the index calculus algorithm. The algorithm is well known by two names. The first is "Pollard's kangaroo algorithm". This name is a reference
Pollard's_kangaroo_algorithm
Problem of inverting exponentiation in groups
sieve Index calculus algorithm Number field sieve Pohlig–Hellman algorithm Pollard's rho algorithm for logarithms Pollard's kangaroo algorithm (aka Pollard's
Discrete_logarithm
Algorithm to solve the discrete logarithm problem
to the sieving step in other sieving algorithms such as the Number Field Sieve or the index calculus algorithm. Instead of numbers one sieves through
Function_field_sieve
Best results achieved to date
than 550 CPU-hours. This computation was performed using the same index calculus algorithm as in the recent computation in the field with 24080 elements.
Discrete_logarithm_records
Operation in mathematical calculus
integral, called integration, is one of the two fundamental operations of calculus, along with differentiation. Integration was initially used to solve problems
Integral
Specialized notation for multivariable calculus
while the tensor index notation is preferred in physics. Two competing notational conventions split the field of matrix calculus into two separate groups
Matrix_calculus
Differential calculus on function spaces
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and
Calculus_of_variations
Small set of prime numbers used in sieving algorithms
between these algorithms is essentially the methods used to generate (x, y) candidates. Factor bases are also used in the Index calculus algorithm for computing
Factor_base
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
Collection of random variables
processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical
Stochastic_process
Ancient algorithm for generating prime numbers
In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking
Sieve_of_Eratosthenes
{\textstyle {\frac {n}{p}}\leq 4} usually suffices. The index calculus algorithm is another algorithm that can be used to solve DLP under some circumstances
Hyperelliptic curve cryptography
Hyperelliptic_curve_cryptography
Number, approximately 3.14
definition because, as Remmert 2012 explains, differential calculus typically precedes integral calculus in the university curriculum, so it is desirable to
Pi
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
Mathematical notation
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory
Multi-index_notation
Branch of mathematical analysis
Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number
Fractional_calculus
Rafael E. Núñez Algebra — Serge Lang Algebra: Chapter 0 — Paolo Aluffi Calculus on Manifolds — Michael Spivak Principles of Mathematical Analysis — Walter
List_of_mathematics_books
Overview of and topical guide to algorithms
Lambda calculus — formal system used in the study of computation Von Neumann architecture — computer architecture influencing practical algorithm implementation
Outline_of_algorithms
Infinitesimal calculus on functions defined on a geometric algebra
In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to
Geometric_calculus
Mathematical-logic system based on functions
In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and
Lambda_calculus
Algorithms to complete a sudoku
computer programs that will solve Sudoku puzzles using a backtracking algorithm, which is a type of brute force search. Backtracking is a depth-first
Sudoku_solving_algorithms
Algorithm for integer multiplication
The Karatsuba algorithm is a fast multiplication algorithm for integers. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a
Karatsuba_algorithm
Programming language designed 1942 to 1945
1938, Zuse discovered that the calculus he had independently devised already existed and was known as propositional calculus. What Zuse had in mind, however
Plankalkül
Algorithm in computational number theory
Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
Method for computing the relation of two integers with their greatest common divisor
and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common
Extended_Euclidean_algorithm
Algorithm to multiply two numbers
multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient
Multiplication_algorithm
Algorithm that employs a degree of randomness as part of its logic or procedure
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random
Randomized_algorithm
Mathematical notion of infinitesimal difference
differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives
Differential_(mathematics)
writing definitions for existing ones. This glossary of calculus is a list of definitions about calculus, its sub-disciplines, and related fields. Contents:
Glossary_of_calculus
Multiplication algorithm
The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers, published by Arnold Schönhage and Volker Strassen
Schönhage–Strassen_algorithm
Integer factorization algorithm
Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. It uses only a small amount of space, and
Pollard's_rho_algorithm
Decomposition of a number into a product
efficient non-quantum integer factorization algorithm is known. However, it has not been proven that such an algorithm does not exist. The presumed difficulty
Integer_factorization
Largest integer that divides given integers
|a|. This case is important as the terminating step of the Euclidean algorithm. The above definition is unsuitable for defining gcd(0, 0), since there
Greatest_common_divisor
Operation on differential forms
in its current form by Élie Cartan in 1899. The resulting calculus, known as exterior calculus, allows for a natural, metric-independent generalization
Exterior_derivative
Branch of mathematics
infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus. Differential calculus studies
Calculus
Discrete (i.e., incremental) version of infinitesimal calculus
Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of
Discrete_calculus
Algebraic object with geometric applications
Elwin Bruno Christoffel, and others – as part of the absolute differential calculus. The concept enabled an alternative formulation of the intrinsic differential
Tensor
Method in computational algebra
Berlekamp's algorithm is a well-known method for factoring polynomials over finite fields (also known as Galois fields). The algorithm consists mainly
Berlekamp's_algorithm
Algorithm used in modular arithmetic
The Tonelli–Shanks algorithm (referred to by Shanks as the RESSOL algorithm) is used in modular arithmetic to solve for r in a congruence of the form r2
Tonelli–Shanks_algorithm
Theorem in computability theory
represents an algorithm Fb and P(b) = "yes". We can then define an algorithm H(a, i) as follows: 1. construct a string t that represents an algorithm T(j) such
Rice's_theorem
Problem in computer science
in its computational power to Turing machines, such as Markov algorithms, Lambda calculus, Post systems, register machines, or tag systems. What is important
Halting_problem
Study of discrete mathematical structures
mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers;
Discrete_mathematics
Number of times a curve wraps around a point in the plane
study in algebraic topology, and they play an important role in vector calculus, complex analysis, geometric topology, differential geometry, and physics
Winding_number
Algorithm for generating prime numbers
Sundaram is a variant of the sieve of Eratosthenes, a simple deterministic algorithm for finding all the prime numbers up to a specified integer. It was discovered
Sieve_of_Sundaram
Algorithm for factoring polynomials over finite fields
the Cantor–Zassenhaus algorithm is a method for factoring polynomials over finite fields (also called Galois fields). The algorithm consists mainly of exponentiation
Cantor–Zassenhaus_algorithm
Notation of differential calculus
In differential calculus, there is no single standard notation for differentiation. Instead, several notations for the derivative of a function or a dependent
Notation_for_differentiation
Algorithm for integer factorization
elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer factorization, which employs elliptic curves. For general-purpose
Lenstra elliptic-curve factorization
Lenstra_elliptic-curve_factorization
Leibniz also develops his version of infinitesimal calculus. 1675—Isaac Newton invents an algorithm for the computation of functional roots. 1680s – Gottfried
Timeline_of_mathematics
Extension of propositional modal logic
theoretical computer science, the modal μ-calculus (Lμ, Lμ, or propositional mu-calculus, sometimes just μ-calculus, although this can have a more general
Modal_μ-calculus
Calculus of functions generalization
In mathematics, calculus on Euclidean space is a generalization of calculus of functions in one or several variables to calculus of functions on Euclidean
Calculus_on_Euclidean_space
Mathematical identities
are important identities involving derivatives and integrals in vector calculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)} in three-dimensional
Vector_calculus_identities
Mathematical algorithm
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, analogous to Pollard's
Pollard's rho algorithm for logarithms
Pollard's_rho_algorithm_for_logarithms
Algorithm checking for prime numbers
test and the cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena
AKS_primality_test
Algorithm for computing logarithms
theory, the Pohlig–Hellman algorithm, sometimes credited as the Silver–Pohlig–Hellman algorithm, is a special-purpose algorithm for computing discrete logarithms
Pohlig–Hellman_algorithm
Number-theoretic algorithm
In computational number theory, Cornacchia's algorithm is an algorithm for solving the Diophantine equation x 2 + d y 2 = m {\displaystyle x^{2}+dy^{2}=m}
Cornacchia's_algorithm
Calculus for temporal reasoning (relating to time instances) of events
Allen's interval algebra is a calculus for temporal reasoning that was introduced by James F. Allen in 1983. The calculus defines possible relations between
Allen's_interval_algebra
In computational number theory, Cipolla's algorithm is a technique for solving a congruence of the form x 2 ≡ n ( mod p ) , {\displaystyle x^{2}\equiv
Cipolla's_algorithm
Algorithm for computing the greatest common divisor
The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor
Binary_GCD_algorithm
Mathematical procedure
a_{1}x_{1}+a_{2}x_{2}+\cdots +a_{n}x_{n}=0.\,} An integer relation algorithm is an algorithm for finding integer relations. Specifically, given a set of real
Integer_relation_algorithm
Fast greatest common divisor algorithm
GCD algorithm, named after D. H. Lehmer, is a fast GCD algorithm for multiple-precision arithmetic, which improves on the simpler Euclidean algorithm by
Lehmer's_GCD_algorithm
Association of one output to each input
concept of algorithm, several models of computation have been introduced, the old ones being general recursive functions, lambda calculus, and Turing
Function_(mathematics)
Certain vector fields are the sum of an irrotational and a solenoidal vector field
the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector fields can be resolved into the
Helmholtz_decomposition
Basic framework of mathematics
self-contradictory theories, and to have reliable concepts of theorems, proofs, algorithms, etc. in particular. This may also include the philosophical study of
Foundations_of_mathematics
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
Special-purpose integer factorization algorithm
number field sieve (SNFS) is a special-purpose integer factorization algorithm. The general number field sieve (GNFS) was derived from it. The special
Special_number_field_sieve
Method for division with remainder
A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or
Division_algorithm
Rational number sequence
Jordan, Charles (1950), Calculus of Finite Differences, New York: Chelsea Publ. Co.. Kaneko, M. (2000), "The Akiyama-Tanigawa algorithm for Bernoulli numbers"
Bernoulli_number
Formula for the derivative of a product
In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions
Product_rule
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
System of rapid mental calculation
This article presents some methods devised by Trachtenberg. Some of the algorithms Trachtenberg developed are for general multiplication, division and addition
Trachtenberg_system
Field of knowledge
study here are discrete, the methods of calculus and mathematical analysis do not directly apply. Algorithms—especially their implementation and computational
Mathematics
Probabilistic primality test
or Rabin–Miller primality test is a probabilistic primality test: an algorithm which determines whether a given number is likely to be prime, similar
Miller–Rabin_primality_test
Algorithm for solving the discrete logarithm problem
branch of mathematics, the baby-step giant-step is a meet-in-the-middle algorithm for computing the discrete logarithm or order of an element in a finite
Baby-step_giant-step
Vector operator in vector calculus
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters
Divergence
Special-purpose algorithm for factoring integers
Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special-purpose algorithm, meaning
Pollard's_p_−_1_algorithm
Type of logical system
First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system used in mathematics, philosophy
First-order_logic
Integer factorization algorithm
The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field
Quadratic_sieve
Algorithm to compare text strings using wildcard syntax
In computer science, an algorithm for matching wildcards (also known as globbing) is useful in comparing text strings that may contain wildcard syntax
Matching_wildcards
Pattern defining an infinite sequence of numbers
theorem (analysis of algorithms) Mathematical induction Orthogonal polynomials Recursion Recursion (computer science) Time scale calculus Jacobson, Nathan
Recurrence_relation
Generalization of the product rule in calculus
In calculus, the general Leibniz rule, named after Gottfried Wilhelm Leibniz, generalizes the product rule for the derivative of the product of two functions
General_Leibniz_rule
Methods to test or prove primality
Goldwasser and Joe Kilian in 1986 and turned into an algorithm by A. O. L. Atkin in the same year. The algorithm was altered and improved by several collaborators
Elliptic_curve_primality
Theoretical model of computation
related to lambda calculus, namely head reduction and call by name. A redex (one says also β-redex) is a term of the lambda calculus of the form (λ x.
Krivine_machine
scientists, List of basic computer science topics, List of terms relating to algorithms and data structures. Topics on computing include: Contents: Top 0–9 A
Index_of_computing_articles
Algorithms to generate prime numbers
In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently. These are used in various applications
Generation_of_primes
Computer system for solving algebra problems
structured Gaussian elimination and Lanczos algorithms for reducing sparse systems which arise in index calculus methods, while Magma uses Markowitz pivoting
Magma (computer algebra system)
Magma_(computer_algebra_system)
Greatest integer less than or equal to square root
y {\displaystyle y} and k {\displaystyle k} be non-negative integers. Algorithms that compute (the decimal representation of) y {\displaystyle {\sqrt {y}}}
Integer_square_root
Multivariate derivative (mathematics)
In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued
Gradient
Algorithm in number theory
(also Dixon's random squares method or Dixon's algorithm) is a general-purpose integer factorization algorithm; it is the prototypical factor base method
Dixon's_factorization_method
Integer factorization algorithm
theory, Williams's p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by
Williams's_p_+_1_algorithm
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
Efficient algorithm to count points on elliptic curves
Schoof's algorithm is an efficient algorithm to count points on elliptic curves over finite fields. The algorithm has applications in elliptic curve cryptography
Schoof's_algorithm
Addition of several numbers or other values
telescoping series and is the analogue of the fundamental theorem of calculus in calculus of finite differences, which states that: f ( n ) − f ( m ) = ∫ m
Summation
Integer factorization algorithm
most laborious but easiest to understand of the integer factorization algorithms. The essential idea behind trial division tests to see if an integer n
Trial_division
Relationship between programs and proofs
forms in lambda calculus matches Prawitz's notion of normal deduction in natural deduction, from which it follows that the algorithms for the type inhabitation
Curry–Howard_correspondence
Attempts to formalize the concept of algorithms
Algorithm characterizations are attempts to formalize the word algorithm. Algorithm does not have a generally accepted formal definition. Researchers
Algorithm_characterizations
theory topics Index of wave articles The fields of mathematics and computing intersect both in computer science, the study of algorithms and data structures
Lists_of_mathematics_topics
Integer factorization algorithm
In mathematics, the rational sieve is a general algorithm for factoring integers into prime factors. It is a special case of the general number field
Rational_sieve
Church, the λ-calculus is strong enough to describe all mechanically computable functions (see Church–Turing thesis). Lambda-calculus is thus effectively
Computable_topology
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
Boy/Male
Sikh
Protector of Indra, Variant of Inder
Boy/Male
Hindi
Supreme god.
Girl/Female
Welsh
Legendary daughter of GanKy.
Girl/Female
Hindu, Indian
Index Finger
Male
French
Variant spelling of French Adrien, ANDRION means "from Hadria." This form of the name can be found in An Index to the Given Names in the 1292 Census of Paris, by Colm Dubh.Â
Boy/Male
Tamil
Inder Kant | இநà¯à®¤à®°à®•à®¾à®¨à¯à®¤
Indra devta
Inder Kant | இநà¯à®¤à®°à®•à®¾à®¨à¯à®¤
Surname or Lastname
English
English : occupational name for an officer of justice or a nickname for a solemn and authoritative person thought to behave like a judge, from Middle English, Old French juge (Latin iudex, from ius ‘law’ + dicere to say), which replaced the Old English term dēma. Compare Dempster.Irish : part translation of Gaelic Mac an Bhreitheamhain, later Mac an Bhreithimh ‘son of the judge (breitheamhnach)’. Compare Brain.
Boy/Male
Sikh
Lakh-w-inder-meaning is the Man who has defeated lakhs of inders indian Lord Indra)
Girl/Female
American, Australian, British, English
The Country India
Surname or Lastname
English
English : nickname for a virile man, from Middle English male ‘masculine’ (Old French masle, madle, Latin masculus).Belgian (van Male) : habitational name from any of a number of places in Flanders named Male.
Boy/Male
Bengali, Celebrity, Gujarati, Hindu, Indian, Kannada, Marathi, Punjabi, Sanskrit, Sikh, Sindhi, Traditional
The God of Weather and War; Lord of the Devas; King of Gods
Surname or Lastname
English and Scottish
English and Scottish : probably a variant of Sewatt, which is from the common Old Norse personal name Sigvarðr, composed of sigr ‘victory’ + varðr ‘guardian’. The International Genealogical Index records several UK ancestors called Suit(t), though the name is hardly found in Britain today.
Boy/Male
Hindu
Indra devta
Boy/Male
Indian, Punjabi, Sikh
Pushp means Flower and Inder is a God; Better
Girl/Female
Indian
Light of Lord Inder
Girl/Female
Indian, Sikh
Love with (God) Inder
Male
Celtic
, Mars, the divinity.
Boy/Male
Sikh
Ruler of all that is wild and untamed., Born of tooth and fang
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
Boy/Male
Arabic, Muslim
Very Good
Girl/Female
Tamil
Well being, Harmonious, Healing and spiritual frame of mind
Girl/Female
Arabic, Assamese, Greek, Hebrew, Indian, Kannada, Muslim
Virgin; Beauty; Fire; Noble
Girl/Female
Tamil
As a Lakshmi
Girl/Female
Hindu
Achievement, Determination
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Lord of Celebration
Girl/Female
Arabic, Gujarati, Hindu, Indian, Kannada, Marathi, Muslim, Telugu
Successful
Boy/Male
Arabic, Muslim
The Awaiting
Boy/Male
Irish American Celtic English Scottish
From the knolls.
Biblical
the right hand
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
v. t.
To provide with an index or table of references; to put into an index; as, to index a book, or its contents.
n.
Index; indication.
a.
Caused, or characterized, by the presence of a calculus or calculi; a, a calculous disorder; affected with gravel or stone; as, a calculous person.
n.
A concretion, or calculus, formed in the gall bladder or biliary passages. See Calculus, n., 1.
pl.
of Index
n.
A calculous concretion, especially one in the kidneys or bladder; the disease arising from a calculus.
imp. & p. p.
of Index
n.
A urinary calculus.
pl.
of Index
p. pr. & vb. n.
of Index
a.
Of or pertaining to the center of gravity. See Barycentric calculus, under Calculus.
n.
A method of computation; any process of reasoning by the use of symbols; any branch of mathematics that may involve calculation.
a.
Of the nature of a calculus; like stone; gritty; as, a calculous concretion.
pl.
of Calculus
n.
Any solid concretion, formed in any part of the body, but most frequent in the organs that act as reservoirs, and in the passages connected with them; as, biliary calculi; urinary calculi, etc.
pl.
of Index
n. pl.
See Index.
n.
The calculus; fluxions.
n.
The second digit, that next pollex, in the manus, or hand; the forefinger; index finger.
n. pl.
See Calculus.