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Lenstra elliptic-curve factorization
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==References== {{reflist}} *{{cite journal |last1=Bernstein |first1=Daniel J. |last2=Birkner |first2=Peter |last3=Lange |first3=Tanja |last4=Peters |first4=Christiane |title=ECM using Edwards curves |journal=Mathematics of Computation |year=2013 | volume=82 | number=282 |doi=10.1090/S0025-5718-2012-02633-0 | mr=3008853 | pages=1139β1179 |doi-access=free }} *{{cite book |last1=Bosma |first1=W. |last2=Hulst |first2=M. P. M. van der |title=Primality proving with cyclotomy |publisher=Ph.D. Thesis, Universiteit van Amsterdam |year=1990 |oclc=256778332 }} *{{cite journal |last=Brent |first=Richard P. |title=Factorization of the tenth Fermat number |journal=Mathematics of Computation |volume=68 |issue=225 |year=1999 |pages=429β451 |doi=10.1090/S0025-5718-99-00992-8 |bibcode=1999MaCom..68..429B | mr=1489968|doi-access=free }} *{{cite book |last=Cohen |first=Henri |title=A Course in Computational Algebraic Number Theory |volume=138 |publisher=Springer-Verlag |location=Berlin |year=1993 |isbn=978-0-387-55640-6 | mr=1228206 | doi=10.1007/978-3-662-02945-9|series=Graduate Texts in Mathematics |s2cid=118037646 }} *{{cite journal |last=Cosset |first=R. |title=Factorization with genus 2 curves |journal=Mathematics of Computation |volume=79 |issue=270 |year=2010 |pages=1191β1208 |doi=10.1090/S0025-5718-09-02295-9 | mr=2600562|arxiv=0905.2325 |bibcode=2010MaCom..79.1191C |s2cid=914296 }} *{{cite book |editor1-link=Arjen Lenstra |editor1-last=Lenstra |editor1-first=A. K. |editor2-last=Lenstra Jr. |editor2-first=H. W. |title=The development of the number field sieve |series=Lecture Notes in Mathematics |volume=1554 |publisher=Springer-Verlag |location=Berlin |year=1993 |pages=11β42 |mr=1321216 | doi=10.1007/BFb0091534|isbn=978-3-540-57013-4 |url=http://infoscience.epfl.ch/record/164684 }} *{{cite journal |last=Lenstra Jr. |first=H. W. |title=Factoring integers with elliptic curves |journal=[[Annals of Mathematics]] |volume=126 |year=1987 |issue=3 |pages=649β673 |mr=0916721 |doi=10.2307/1971363 |url=https://openaccess.leidenuniv.nl/bitstream/handle/1887/2140/346_079.pdf?sequence=1 |jstor=1971363 |hdl=1887/2140 |hdl-access=free }} *{{cite book | last1= Pomerance | first1 = Carl | author1-link = Carl Pomerance | first2 = Richard | last2 = Crandall | year = 2005 | edition = Second | title = Prime Numbers: A Computational Perspective | publisher = Springer | location = New York | isbn = 978-0-387-25282-7 | mr = 2156291}} *{{cite book |last=Pomerance |first=Carl |chapter=The quadratic sieve factoring algorithm |title=Advances in Cryptology, Proc. Eurocrypt '84 |series=Lecture Notes in Computer Science |volume=209 |publisher=Springer-Verlag |location=Berlin |year=1985 |pages=169β182 |mr=0825590 | doi=10.1007/3-540-39757-4_17|isbn=978-3-540-16076-2 }} *{{cite journal |last=Pomerance |first=Carl |title=A Tale of Two Sieves |journal=[[Notices of the American Mathematical Society]] |pages=1473β1485 |volume=43 |year=1996 |issue=12 |url=https://www.ams.org/notices/199612/pomerance.pdf |mr=1416721 }} *{{cite journal |last=Silverman |first=Robert D. |title=The Multiple Polynomial Quadratic Sieve |journal=[[Mathematics of Computation]] |volume=48 |issue=177 |year=1987 |pages=329β339 |doi=10.1090/S0025-5718-1987-0866119-8 | mr=0866119|doi-access=free }} *{{cite book | last1=Trappe | first1= W. | last2=Washington| first2=L. C. | title=Introduction to Cryptography with Coding Theory |edition=Second | publisher=Pearson Prentice Hall | year=2006| isbn=978-0-13-186239-5| mr=2372272| location=Saddle River, NJ}} *{{cite book | author=Samuel S. Wagstaff, Jr. | title=The Joy of Factoring | publisher=American Mathematical Society | location=Providence, RI | year=2013 | isbn=978-1-4704-1048-3 |url=https://www.ams.org/bookpages/stml-68 |author-link=Samuel S. Wagstaff, Jr. |pages=173β190 }} *{{cite book |last=Watras |first=Marcin |title=Cryptography, Number Analysis, and Very Large Numbers |publisher=Wojciechowski-Steinhagen |location=Bydgoszcz |year=2008 |id=PL:5324564 }}
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