%% oldest and most popular article about known attacks on RSA. @article{20years, title={Twenty years of attacks on the RSA cryptosystem}, author={Boneh, Dan and Rivest, Ron and Shamir, Adi and Adleman, Len and others}, journal={Notices of the AMS}, volume={46}, number={2}, pages={203--213}, year={1999} } %% reccomended limits of p-q @misc{DSS2009, title={FIPS PUB 186-3: Digital Signature Standard}, author={NIST}, year={2009} } %% here there's the descriptions for an efficient computation of fₚ(x) = y . y² ≡ x (mod p) %% [openssl implements it] @misc{ieee2001ieee, title = {IEEE P1363a D10 (Draft Version 10): Standard Specifications for Public Key Cryptography: Additional Techniques, IEEE P1363 Working Group, Working draft}, author = {IEEE P1363 Working Group and others}, year = {2001} } @misc{rfc6176, title = {Prohibiting Secure Sockets Layer (SSL) Version 2.0}, author = {S. Turner and T. Polk}, publisher = {RFC Editor}, url = {http://tools.ietf.org/html/rfc6176} } @book{bombelli:algebra, title = {L'Algebra}, author = {Rafael Bombelli}, year={1572}, url={http://mathematica.sns.it/opere/9/} } @book{AOCPv2, author = {Knuth, Donald E.}, title = {The Art of Computer Programming, Volume 2 (3rd Ed.): Seminumerical Algorithms}, year = {1997}, isbn = {0-201-89684-2}, publisher = {Addison-Wesley Longman Publishing Co., Inc.}, address = {Boston, MA, USA} } @book{MITalg, author = "T.~H. Cormen and C.~E. Leiserson and R.~L. Rivest and C.~Stein", edition = "3rd", publisher = "The MIT Press", title = "Introduction to Algorithms", year = 2009, isbn = "978-0-262-03384-8" } @book{Dijkstra:adop, author = {Dijkstra, Edsger Wybe}, title = {A Discipline of Programming}, year = {1997}, isbn = {013215871X}, edition = {1st}, publisher = {Prentice Hall PTR}, address = {Upper Saddle River, NJ, USA}, } @book{riesel, author = {Riesel, Hans}, title = {Prime Numbers and Computer Methods for Factorization}, year = {1985}, isbn = {0-8176-3291-3}, publisher = {Birkhauser Boston Inc.}, address = {Cambridge, MA, USA}, } @book{Crandall, author = {Richard Crandall and Carl Pomerance and Richard Crandall and Carl Pomerance}, title = {Prime numbers: a computational perspective. Second Edition}, year = {2005} } @article{wiener, author = {Michael J. Wiener}, title = {Cryptanalysis of short RSA secret exponents}, journal = {IEEE Transactions on Information Theory}, year = {1990}, volume = {36}, pages = {553--558}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.5261} } @article{pollard1974, author = {J. M. Pollard}, title = {Theorems on factorization and primality testing}, journal = {Mathematical Proceedings of the Cambridge Philosophical Society}, volume = 76, issue = 03, month = 11, year = 1974, issn = {1469-8064}, pages = {521--528}, numpages = 8, doi = {10.1017/S0305004100049252}, url = {http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2074504} } @article{Williams:p+1, title = {A $p + 1$ Method of Factoring}, author = {Williams, H. C.}, journal = {Mathematics of Computation}, volume = 39, number = 159, jstor_formatteddate = {Jul., 1982}, pages = {pp. 225-234}, url = {http://www.jstor.org/stable/2007633}, ISSN = 00255718, language = {English}, year = 1982, publisher = {American Mathematical Society}, } @article{dixon, title = {Asymptotically Fast Factorization of Integers}, author = {Dixon, John D.}, journal = {Mathematics of Computation}, volume = {36}, number = {153}, pages = {pp. 255-260}, url = {http://www.jstor.org/stable/2007743}, ISSN = {00255718}, year = {1981} }