Editing RSA numbers (section)

==RSA-129==
RSA-129, having 129 decimal digits (426 bits), was not part of the 1991 RSA Factoring Challenge, but rather related to [[Martin Gardner]]'s [[Mathematical Games column]] in the August 1977 issue of ''[[Scientific American]]''.<ref name="RSA Honor Roll" />

RSA-129 was factored in April 1994 by a team led by [[Derek Atkins]], [[Michael Graff]], [[Arjen Lenstra|Arjen K. Lenstra]] and [[Paul Leyland]], using approximately 1600 computers<ref>{{cite web |last1=Atkins |first1=Derek |last2=Graff |first2=Michael |last3=Lenstra |first3=Arjen K. |last4=Leyland |first4=Paul C. |title=The Magic Words Are Squeamish Ossifrage |url=http://web.mit.edu/warlord/www/rsa129.ps |url-status=live |archive-url=https://web.archive.org/web/20230909141922/http://web.mit.edu/warlord/www/rsa129.ps |archive-date=2023-09-09 |access-date=2009-11-24 |website=Derek Atkins |type=PostScript document |via=Massachusetts Institute of Technology}}</ref> from around 600 volunteers connected over the [[Internet]].<ref>{{Cite web |last=Janeba |first=Mark |date=1994 |orig-date=links and formatting updated September 24, 2002 |title=Factoring Challenge Conquered - With a Little Help From Willamette |url=https://willamette.edu/~mjaneba/rsa129.html |url-status=live |archive-url=https://web.archive.org/web/20230902110801/https://willamette.edu/~mjaneba/rsa129.html |archive-date=2023-09-02 |access-date=2008-03-10 |website=Prof. Mark Janeba's Framed Home Page |via=Willamette University}}</ref> A [[United States dollar|US$]]100 token prize was awarded by RSA Security for the factorization, which was donated to the [[Free Software Foundation]].

The value and factorization are as follows:

 RSA-129 = 114381625757888867669235779976146612010218296721242362562561842935706935245733897830597123563958705058989075147599290026879543541

 RSA-129 = 3490529510847650949147849619903898133417764638493387843990820577
         × 32769132993266709549961988190834461413177642967992942539798288533

The factorization was found using the [[Multiple Polynomial Quadratic Sieve]] algorithm.

The factoring challenge included a message encrypted with RSA-129. When decrypted using the factorization the message was revealed to be "[[The Magic Words are Squeamish Ossifrage]]".

In 2015, RSA-129 was factored in about one day, with the CADO-NFS open source implementation of number field sieve, using a commercial cloud computing service for about $30.<ref>{{cite web |last=McHugh |first=Nathaniel |date=2015-03-26 |title=The Magic Words are Squeamish Ossifrage - factoring RSA-129 using CADO-NFS |url=https://natmchugh.blogspot.com/2015/03/the-magic-words-are-squeamish-ossifrage.html |url-status=live |archive-url=https://web.archive.org/web/20230902110041/https://natmchugh.blogspot.com/2015/03/the-magic-words-are-squeamish-ossifrage.html |archive-date=2023-09-02 |access-date=2016-05-25 |website=Nat McHugh: Transient Random-Noise Bursts with Announcements |place=Sheffield, South Yorkshire, UK |via=Blogger}}</ref>