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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
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 its
Pollard's_rho_algorithm
Problem of inverting exponentiation in groups
calculus algorithm Number field sieve Pohlig–Hellman algorithm Pollard's rho algorithm for logarithms Pollard's kangaroo algorithm (aka Pollard's lambda
Discrete_logarithm
Digital signature scheme
choices of parameters, except for the arbitrary choice of base point—for example, Pollard's rho algorithm for logarithms is expected to take approximately
EdDSA
Best results achieved to date
discrete logarithms in GF(29234) using about 400,000 core hours. New features of this computation include a modified method for obtaining the logarithms of
Discrete_logarithm_records
Algorithm for solving the discrete logarithm problem
Alternatively one can use Pollard's rho algorithm for logarithms, which has about the same running time as the baby-step giant-step algorithm, but only a small
Baby-step_giant-step
Topics referred to by the same term
spectral radius of a square matrix Pollard's rho algorithm, for integer factorization Pollard's rho algorithm for logarithms ρ, prime constant ρ, plastic ratio
Rho_(disambiguation)
Algorithm in computational number theory
The algorithm was introduced in 1978 by the number theorist John M. Pollard, in the same paper as his better-known Pollard's rho algorithm for solving
Pollard's_kangaroo_algorithm
British mathematician
His discrete logarithm algorithms include the rho algorithm for logarithms and the kangaroo algorithm. He received the RSA Award for Excellence in Mathematics
John_Pollard_(mathematician)
Baby-step giant-step Index calculus algorithm Pohlig–Hellman algorithm Pollard's rho algorithm for logarithms Euclidean algorithm: computes the greatest common
List_of_algorithms
Probabilistic algorithm for computing discrete logarithms
the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in ( Z / q Z ) ∗ {\displaystyle
Index_calculus_algorithm
Plethystic logarithm Pollard's kangaroo algorithm Pollard's rho algorithm for logarithms Polylogarithm Polylogarithmic function Prime number theorem Richter
Index_of_logarithm_articles
Type of cryptographic attack
fraudulent one. Pollard's rho algorithm for logarithms is an example for an algorithm using a birthday attack for the computation of discrete logarithms. The same
Birthday_attack
On finding a repeating loop in a sequence
classic example is Pollard's rho algorithm for integer factorization, which searches for a factor p of a given number n by looking for values xi and xi+λ
Cycle_detection
Approach to public-key cryptography
Okamoto, T.; Vanstone, S. A. (1993). "Reducing elliptic curve logarithms to logarithms in a finite field". IEEE Transactions on Information Theory. 39
Elliptic-curve_cryptography
Algorithm for computing greatest common divisors
essential step in several integer factorization algorithms, such as Pollard's rho algorithm, Shor's algorithm, Dixon's factorization method and the Lenstra
Euclidean_algorithm
Decomposition of a number into a product
small factors. For example, naive trial division is a Category 1 algorithm. Trial division Wheel factorization Pollard's rho algorithm, which has two
Integer_factorization
John Pollard 1974 – Quadtree developed by Raphael Finkel and J.L. Bentley 1975 – Genetic algorithms popularized by John Holland 1975 – Pollard's rho algorithm
Timeline_of_algorithms
Integer having only small prime factors
rapidly. For example, the Pohlig–Hellman algorithm for computing discrete logarithms has a running time of O(n1/2)—for groups of n-smooth order. Moreover,
Smooth_number
generic attacks on the discrete logarithm problem in finite abelian groups such as the Pohlig–Hellman algorithm and Pollard's rho method can be used to attack
Hyperelliptic curve cryptography
Hyperelliptic_curve_cryptography
Number divisible only by 1 and itself
factorization algorithms are known, they are slower than the fastest primality testing methods. Trial division and Pollard's rho algorithm can be used to
Prime_number
Key agreement protocol
time using the Pollards rho algorithm. The most famous example of Montgomery curve is Curve25519 which was introduced by Bernstein. For Curve25519, p =
Elliptic-curve_Diffie–Hellman
Volunteer computing project aimed at finding a MD5 collision
Lai and Yu for their discovery. A technique called Floyd's cycle-finding algorithm was used to try to find a collision for MD5. The algorithm can be described
MD5CRK
generic algorithms for computing the order of a group element that are more space efficient, such as Pollard's rho algorithm and the Pollard kangaroo
Counting points on elliptic curves
Counting_points_on_elliptic_curves
primality test Lucas–Lehmer test for Mersenne numbers AKS primality test Pollard's p − 1 algorithm Pollard's rho algorithm Lenstra elliptic curve factorization
List_of_number_theory_topics
Integer factorization algorithm
N {\displaystyle N} is large. For a number as small as 15347, this algorithm is overkill. Trial division or Pollard rho could have found a factor with
Quadratic_sieve
converse is not necessarily true. Grantham's stated goal when developing the algorithm was to provide a test that primes would always pass and composites would
Quadratic_Frobenius_test
In cryptography, XTR is an algorithm for public-key encryption. XTR stands for 'ECSTR', which is an abbreviation for Efficient and Compact Subgroup Trace
XTR
multiplication). The currently best known discrete logarithm attack is the generic Pollard's rho algorithm, requiring about 2 122.5 {\displaystyle 2^{122
FourQ
POLLARDS RHO-ALGORITHM-FOR-LOGARITHMS
POLLARDS RHO-ALGORITHM-FOR-LOGARITHMS
Male
Japanese
(ç¿”) Japanese name SHO means "to fly, to soar" or "wind instrument."
Boy/Male
British, English, Teutonic
Short Haired
Surname or Lastname
English
English : nickname from Middle English dull + -ard ‘dull or stupid person’. Compare Doll 5.Irish : either an importation to Ireland of the English name or, possibly, a reduced and altered form of de la Hyde (see Dollarhide).
Boy/Male
Spanish
River. Abbreviation of names ending with '-rio.
Surname or Lastname
English
English : variant of Wolford.
Male
Scandinavian
 Scandinavian form of Old Norse Þórr, TOR means "Thor" or "thunder." Compare with other forms of Tor.
Surname or Lastname
English
English : nickname for a person with a large or unusually shaped head, from Middle English poll ‘head’ (Middle Low German polle ‘(top of the) head’) + the pejorative suffix -ard. The term pollard in the sense denoting an animal that has had its horns lopped is not recorded before the 16th century, and as applied to a tree the word is not recorded until the 17th century; so both these senses are almost certainly too late to have contributed to the surname.English : pejorative derivative of the personal name Paul. The surname has been established in Ireland since the 14th century.
Surname or Lastname
English (Gloucestershire)
English (Gloucestershire) : from Middle English soler ‘solar’, ‘upper floor of a house’ (Old English solor), probably an occupational name for a servant whose duties were centered in the upper part of a house.
Female
Japanese
Variant spelling of Japanese Chou, CHO means "butterfly."
Surname or Lastname
English and French
English and French : from the personal name Coll + the pejorative suffix -ard.
Male
Portuguese
Portuguese form of Latin Marius, MÃRIO means "male, virile."
Male
Finnish
Finnish name URHO means "brave."
Girl/Female
Biblical
Who conceives, or shows, a hill.
Surname or Lastname
English (Devon)
English (Devon) : variant spelling of Roe.Korean : variant of No.
Biblical
who conceives, or shows; a hill
Surname or Lastname
English, French, and Catalan
English, French, and Catalan : nickname from Old French, Middle English, Catalan fort, ‘strong’, ‘brave’ (Latin fortis). In some cases it may be from the Latin personal name derived from this word; this was borne by an obscure saint whose cult was popular during the Middle Ages in southern and southwestern France.English and French : topographic name for someone who lived near a fortress or stronghold, or an occupational name for someone employed in one. Compare Fortier 1.Czech (Fořt) : variant of Forst.
Surname or Lastname
English and Irish
English and Irish : according to MacLysaght, this is a surname of Dutch origin which was taken to Ireland early in the 18th century.French : from a personal name composed of the Germanic elements boll ‘friend’, ‘brother’ + hard ‘hardy’, ‘strong’.
Surname or Lastname
English
English : topographic name for someone who lived near a ford, Middle English, Old English ford, or a habitational name from one of the many places named with this word, such as Ford in Northumberland, Shropshire, and West Sussex, or Forde in Dorset.Irish : Anglicized form (quasi-translation) of various Gaelic names, for example Mac Giolla na Naomh ‘son of Gilla na Naomh’ (a personal name meaning ‘servant of the saints’), Mac Conshámha ‘son of Conshnámha’ (a personal name composed of the elements con ‘dog’ + snámh ‘to swim’), in all of which the final syllable was wrongly thought to be áth ‘ford’, and Ó Fuar(th)áin (see Foran).Jewish : Americanized form of one or more like-sounding Jewish surnames.Translation of German Fürth (see Furth).
Surname or Lastname
English
English : variant of Holland 1.Dutch : variant of Holland 2.Dutch : habitational name from places called Holland in northern France, named with Middle Dutch onland(e) ‘marsh’.
Male
Portuguese
Portuguese form of Latin Desiderius, DESIDÉRIO means "longing."Â
POLLARDS RHO-ALGORITHM-FOR-LOGARITHMS
POLLARDS RHO-ALGORITHM-FOR-LOGARITHMS
Girl/Female
Teutonic
Noble humor.
Boy/Male
Indian
Brave
Girl/Female
Gujarati, Hindu, Indian, Sanskrit
Touch; Feel; Sensation
Girl/Female
Australian, British, English
Occupational Name; Tailor
Boy/Male
Assamese, Bengali, Celebrity, Gujarati, Hindu, Indian, Marathi, Mythological, Sanskrit, Tamil, Traditional
Divinity Jack
Boy/Male
Tamil
Kaartik | காரà¯à®¤à®¿à®•
Name of one of the months
Boy/Male
American, Australian, Bengali, Indian
One God
Boy/Male
Arabic, Muslim
Father of Glory
Girl/Female
Arabic, Nigerian
Twin Girl
Boy/Male
Indian, Tamil
Lord Shiva
POLLARDS RHO-ALGORITHM-FOR-LOGARITHMS
POLLARDS RHO-ALGORITHM-FOR-LOGARITHMS
POLLARDS RHO-ALGORITHM-FOR-LOGARITHMS
POLLARDS RHO-ALGORITHM-FOR-LOGARITHMS
POLLARDS RHO-ALGORITHM-FOR-LOGARITHMS
v. t.
To lop the tops of, as trees; to poll; as, to pollard willows.
n.
One who takes, or that which is said on, the affrimative side; that which is said in favor of some one or something; -- the antithesis of against, and commonly used in connection with it.
prep.
Indicating that on place of or instead of which anything acts or serves, or that to which a substitute, an equivalent, a compensation, or the like, is offered or made; instead of, or place of.
n.
A bollard timber. See under Bollard.
prep.
Indicating that in favor of which, or in promoting which, anything is, or is done; hence, in behalf of; in favor of; on the side of; -- opposed to against.
prep.
Indicating the antecedent cause or occasion of an action; the motive or inducement accompanying and prompting to an act or state; the reason of anything; that on account of which a thing is or is done.
prep.
In the most general sense, indicating that in consideration of, in view of, or with reference to, which anything is done or takes place.
prep.
Indicating the remoter and indirect object of an act; the end or final cause with reference to which anything is, acts, serves, or is done.
prep.
Indicating that in the character of or as being which anything is regarded or treated; to be, or as being.
n.
A hornless animal (cow or sheep).
n.
The doctrines or principles of the Lollards.
p. pr. & vb. n.
of Pollard
conj.
Because; by reason that; for that; indicating, in Old English, the reason of anything.
imp. & p. p.
of Pollard
n.
See Algorism.
prep.
Indicating the space or time through which an action or state extends; hence, during; in or through the space or time of.
n.
The art of calculating with any species of notation; as, the algorithms of fractions, proportions, surds, etc.
n.
The art of calculating by nine figures and zero.
n.
Alt. of Algorithm
n. pl.
Young cabbage, used as "greens"; esp. a kind cultivated for that purpose; colewort.