Advances in Cryptology 1984
DOI: 10.1007/978-1-4684-4730-9_9
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Factorization Using the Quadratic Sieve Algorithm

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Cited by 24 publications
(24 citation statements)
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“…Pollard [10] introduces the lattice sieve method based on an idea proposed in [20]. Here, we describe the lattice sieve (its sieving-by-rows variant) for the rational sieve only.…”
Section: The Lattice Sieve Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…Pollard [10] introduces the lattice sieve method based on an idea proposed in [20]. Here, we describe the lattice sieve (its sieving-by-rows variant) for the rational sieve only.…”
Section: The Lattice Sieve Methodsmentioning
confidence: 99%
“…Let q ∈ M be a medium prime (also called a special q in the notation of [20]). Unlike the line sieve described in earlier chapters, we now take into account a region R in the (a, b) plane.…”
Section: The Lattice Sieve Methodsmentioning
confidence: 99%
“…Maxim position calculation is the integer number of the maximum number being tested radical divided by 30 [2][3][4].…”
Section: Calculation Algorithmmentioning
confidence: 99%
“…While some of the arguments that follow have been detailed by Pomerance elsewhere [9], we present ours in a manner which is more oriented towards implementation of the algorithm. The basic algorithm depends on constructing a solution to the following equation, where TV is the number you wish to factor: This version of the quadratic sieve generates a set of quadratic residues of N using the following single polynomial: (2) Q(x) = (xA[fW])2-N = H2modN.…”
Section: By Robert D Silvermanmentioning
confidence: 99%
“…Finally, collect all of the factorizations found and reduce the matrix over GF (2). For each linear dependency S, Px = Y\Hj mod kN for ; e S, (17) ' P2 m Y}pfjvJ'/2 mod kN for all p, e FB and j e S. i…”
Section: By Robert D Silvermanmentioning
confidence: 99%