Zobrazeno 1 - 7
of 7
pro vyhledávání: '"Andrew Shallue"'
Autor:
Andrew Shallue, Jonathan Webster
Publikováno v:
Research in Number Theory. 8
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::519c6420e2b5232c5d1b5441f5764953
https://doi.org/10.1007/s40993-022-00384-z
https://doi.org/10.1007/s40993-022-00384-z
Autor:
Andrew Shallue
Publikováno v:
ACM Transactions on Algorithms. 13:1-14
This article explores the asymptotic complexity of two problems related to the Miller-Rabin-Selfridge primality test. The first problem is to tabulate strong pseudoprimes to a single fixed base a . It is now proven that tabulating up to x requires O
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d5da669529e218e95a1b2ace9735f6d0
https://doi.org/10.1145/2957759
https://doi.org/10.1145/2957759
Autor:
Jonathan Webster, Andrew Shallue
We provide a new algorithm for tabulating composite numbers which are pseudoprimes to both a Fermat test and a Lucas test. Our algorithm is optimized for parameter choices that minimize the occurrence of pseudoprimes, and for pseudoprimes with a fixe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7b7ddab0c774bee61232b2e3ed15904a
http://arxiv.org/abs/1806.08697
http://arxiv.org/abs/1806.08697
Autor:
Andrew Shallue, Eric Bach
Publikováno v:
Mathematics of Computation. 84:3069-3089
The strong probable primality test is an important practical tool for discovering prime numbers. Its effectiveness derives from the following fact: for any odd composite number $n$, if a base $a$ is chosen at random, the algorithm is unlikely to clai
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::99b0244edaf46eea3aa4929044fd6e53
https://doi.org/10.1090/mcom/2949
https://doi.org/10.1090/mcom/2949
Publikováno v:
Mathematics of Computation. 83:899-915
We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with k prime factors for every k between 3 and 19,565,220. These computations are the product of implementations of two new algori
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::20326c6ae439ce32fa57fb08d6062f91
https://doi.org/10.1090/s0025-5718-2013-02737-8
https://doi.org/10.1090/s0025-5718-2013-02737-8
Autor:
Andrew Shallue
Publikováno v:
Lecture Notes in Computer Science ISBN: 9783540794554
ANTS
ANTS
Given sets L1, . . . , Lk of elements from Z/mZ, the k-setbirthday problem is to find an element from each list such that theirsum is 0 modulo m. We give a new analysis of the algorithm in [16],proving that it returns a solution with high probability
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::386c54c674e737c65d78a07fbd0b49dc
https://doi.org/10.1007/978-3-540-79456-1_28
https://doi.org/10.1007/978-3-540-79456-1_28
Publikováno v:
Lecture Notes in Computer Science ISBN: 9783540360759
ANTS
ANTS
We give a deterministic polynomial-time algorithm that computes a nontrivial rational point on an elliptic curve over a finite field, given a Weierstrass equation for the curve. For this, we reduce the problem to the task of finding a rational point
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f0915e27ff10ea691ec3a9c7558de213
https://doi.org/10.1007/11792086_36
https://doi.org/10.1007/11792086_36