Results 11  20
of
661,353
SIEVING BY LARGE INTEGERS AND COVERING SYSTEMS OF CONGRUENCES
, 2006
"... An old question of Erdős asks if there exists, for each number N, a finite set S of integers greater than N and residue classes r(n) (mod n) for n ∈ S whose union is Z. We prove that if � n∈S 1/n is bounded for such a covering of the integers, then the least member of S is also bounded, thus confirm ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
An old question of Erdős asks if there exists, for each number N, a finite set S of integers greater than N and residue classes r(n) (mod n) for n ∈ S whose union is Z. We prove that if � n∈S 1/n is bounded for such a covering of the integers, then the least member of S is also bounded, thus
SCRIBE: A largescale and decentralized applicationlevel multicast infrastructure
 IEEE Journal on Selected Areas in Communications (JSAC
, 2002
"... This paper presents Scribe, a scalable applicationlevel multicast infrastructure. Scribe supports large numbers of groups, with a potentially large number of members per group. Scribe is built on top of Pastry, a generic peertopeer object location and routing substrate overlayed on the Internet, ..."
Abstract

Cited by 648 (29 self)
 Add to MetaCart
This paper presents Scribe, a scalable applicationlevel multicast infrastructure. Scribe supports large numbers of groups, with a potentially large number of members per group. Scribe is built on top of Pastry, a generic peertopeer object location and routing substrate overlayed on the Internet
Factoring large integers using parallel Quadratic Sieve
, 2000
"... Integer factorization is a well studied topic. Parts of the cryptography we use each day rely on the fact that this problem is di�cult. One method one can use for factorizing a large composite number is the Quadratic Sieve algorithm. This method is among the best known today. We present a parallel i ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Integer factorization is a well studied topic. Parts of the cryptography we use each day rely on the fact that this problem is di�cult. One method one can use for factorizing a large composite number is the Quadratic Sieve algorithm. This method is among the best known today. We present a parallel
Arithmetic with Large Integers by Means of the Chinese Remainder Theorem and . . .
, 1996
"... used, since may be impossible to predict whether the result of a subtraction will be a negative number, which is not allowed.) To perform these operations one almost has to convert back to the form (). Another problem is that for a given underlying word size (say 2 16 ), there is an upper limit o ..."
Abstract
 Add to MetaCart
on the integers that can be represented, since there is a largest M that can be obtained as a product of prime (or relatively prime) numbers less than the word size. This limitation is seldom important in practice. The Extended Euclidean Algorithm One hole left in our description of the method is an algorithm
Factorisation of Large Integers on some Vector and Parallel Computers
 The Australian National University TRCS9501
, 1995
"... ..."
Shor’s Algorithm for Factoring Large Integers
, 2008
"... This work is a tutorial on Shor’s factoring algorithm by means of a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are reviewed. It is intended for nonspecialists which have basic knowledge on undergraduate Linear Algebra. ..."
Abstract
 Add to MetaCart
This work is a tutorial on Shor’s factoring algorithm by means of a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are reviewed. It is intended for nonspecialists which have basic knowledge on undergraduate Linear Algebra.
A Note on the Hermite Basis Computation of Large Integer Matrices
, 2004
"... A new algorithm is given and analyzed for the computation of the Hermite basis of a large integer matrix whose HNF has small essential part. The algorithm improves the results from [3] by dropping two key requirements on the matrix considered—sparsity and small kernel dimension—at the cost of relyin ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
A new algorithm is given and analyzed for the computation of the Hermite basis of a large integer matrix whose HNF has small essential part. The algorithm improves the results from [3] by dropping two key requirements on the matrix considered—sparsity and small kernel dimension—at the cost
A Limited Memory Algorithm for Bound Constrained Optimization
 SIAM Journal on Scientific Computing
, 1994
"... An algorithm for solving large nonlinear optimization problems with simple bounds is described. ..."
Abstract

Cited by 557 (9 self)
 Add to MetaCart
An algorithm for solving large nonlinear optimization problems with simple bounds is described.
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
Abstract

Cited by 601 (1 self)
 Add to MetaCart
. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum
Results 11  20
of
661,353