Factorization of {RSA}-140 using the Number Field Sieve
Identifieur interne : 00A786 ( Main/Exploration ); précédent : 00A785; suivant : 00A787Factorization of {RSA}-140 using the Number Field Sieve
Auteurs : Stefania Cavallar ; Bruce Dodson ; Arjen-K. Lenstra ; Paul Leyland ; Walter M. Lioen ; Peter L. Montgomery ; Brian Murphy ; Herman Te Riele ; Paul ZimmermannSource :
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Abstract
On February 2, 1999, we completed the factorization of the 140--digit number RSA--140 with the help of the Number Field Sieve factoring method (NFS). This is a new general factoring record. The previous record was established on April 10, 1996 by the factorization of the 130--digit number RSA--130, also with the help of NFS. The amount of computing time spent on RSA--140 was roughly twice that needed for RSA--130, about half of what could be expected from a straightforward extrapolation of the computing time spent on factoring RSA--130. The speed-up can be attributed to a new polynomial selection method for NFS which will be sketched in this paper. The implications of the new polynomial selection method for factoring a 512--bit RSA modulus are discussed and it is concluded that 512--bit (= 155--digit) RSA moduli are easily and realistically within reach of factoring efforts similar to the one presented here.
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" wicri:score="163">Factorization of {RSA}-140 using the Number Field Sieve</title></titleStmt><publicationStmt><idno type="RBID">CRIN:cavallar99b</idno><date when="1999" year="1999">1999</date><idno type="wicri:Area/Crin/Corpus">002766</idno><idno type="wicri:Area/Crin/Curation">002766</idno><idno type="wicri:explorRef" wicri:stream="Crin" wicri:step="Curation">002766</idno><idno type="wicri:Area/Crin/Checkpoint">002031</idno><idno type="wicri:explorRef" wicri:stream="Crin" wicri:step="Checkpoint">002031</idno><idno type="wicri:Area/Main/Merge">00AE37</idno><idno type="wicri:Area/Main/Curation">00A786</idno><idno type="wicri:Area/Main/Exploration">00A786</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Factorization of {RSA}-140 using the Number Field Sieve</title><author><name sortKey="Cavallar, Stefania" sort="Cavallar, Stefania" uniqKey="Cavallar S" first="Stefania" last="Cavallar">Stefania Cavallar</name></author><author><name sortKey="Dodson, Bruce" sort="Dodson, Bruce" uniqKey="Dodson B" first="Bruce" last="Dodson">Bruce Dodson</name></author><author><name sortKey="Lenstra, Arjen K" sort="Lenstra, Arjen K" uniqKey="Lenstra A" first="Arjen-K." last="Lenstra">Arjen-K. Lenstra</name></author><author><name sortKey="Leyland, Paul" sort="Leyland, Paul" uniqKey="Leyland P" first="Paul" last="Leyland">Paul Leyland</name></author><author><name sortKey="Lioen, Walter M" sort="Lioen, Walter M" uniqKey="Lioen W" first="Walter M." last="Lioen">Walter M. Lioen</name></author><author><name sortKey="Montgomery, Peter L" sort="Montgomery, Peter L" uniqKey="Montgomery P" first="Peter L." last="Montgomery">Peter L. Montgomery</name></author><author><name sortKey="Murphy, Brian" sort="Murphy, Brian" uniqKey="Murphy B" first="Brian" last="Murphy">Brian Murphy</name></author><author><name sortKey="Te Riele, Herman" sort="Te Riele, Herman" uniqKey="Te Riele H" first="Herman" last="Te Riele">Herman Te Riele</name></author><author><name sortKey="Zimmermann, Paul" sort="Zimmermann, Paul" uniqKey="Zimmermann P" first="Paul" last="Zimmermann">Paul Zimmermann</name></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>factoring</term><term>number field sieve</term><term>public-key cryptosystems</term><term>rsa</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en" wicri:score="3021">On February 2, 1999, we completed the factorization of the 140--digit number RSA--140 with the help of the Number Field Sieve factoring method (NFS). This is a new general factoring record. The previous record was established on April 10, 1996 by the factorization of the 130--digit number RSA--130, also with the help of NFS. The amount of computing time spent on RSA--140 was roughly twice that needed for RSA--130, about half of what could be expected from a straightforward extrapolation of the computing time spent on factoring RSA--130. The speed-up can be attributed to a new polynomial selection method for NFS which will be sketched in this paper. The implications of the new polynomial selection method for factoring a 512--bit RSA modulus are discussed and it is concluded that 512--bit (= 155--digit) RSA moduli are easily and realistically within reach of factoring efforts similar to the one presented here.</div></front></TEI><affiliations><list></list><tree><noCountry><name sortKey="Cavallar, Stefania" sort="Cavallar, Stefania" uniqKey="Cavallar S" first="Stefania" last="Cavallar">Stefania Cavallar</name><name sortKey="Dodson, Bruce" sort="Dodson, Bruce" uniqKey="Dodson B" first="Bruce" last="Dodson">Bruce Dodson</name><name sortKey="Lenstra, Arjen K" sort="Lenstra, Arjen K" uniqKey="Lenstra A" first="Arjen-K." last="Lenstra">Arjen-K. Lenstra</name><name sortKey="Leyland, Paul" sort="Leyland, Paul" uniqKey="Leyland P" first="Paul" last="Leyland">Paul Leyland</name><name sortKey="Lioen, Walter M" sort="Lioen, Walter M" uniqKey="Lioen W" first="Walter M." last="Lioen">Walter M. Lioen</name><name sortKey="Montgomery, Peter L" sort="Montgomery, Peter L" uniqKey="Montgomery P" first="Peter L." last="Montgomery">Peter L. Montgomery</name><name sortKey="Murphy, Brian" sort="Murphy, Brian" uniqKey="Murphy B" first="Brian" last="Murphy">Brian Murphy</name><name sortKey="Te Riele, Herman" sort="Te Riele, Herman" uniqKey="Te Riele H" first="Herman" last="Te Riele">Herman Te Riele</name><name sortKey="Zimmermann, Paul" sort="Zimmermann, Paul" uniqKey="Zimmermann P" first="Paul" last="Zimmermann">Paul Zimmermann</name></noCountry></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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