Talk:RSA code: Difference between revisions

: [[http://www.math.okstate.edu/~wrightd/numthry/rsa129.html summaries of rsa 129 status reports and full details of keys (see below)

-[[User:Dgamey|Dgamey]] 15:56, 22 April 2011 (UTC) update: --[[User:Dgamey|Dgamey]] 15:39, 24 April 2011 (UTC)

=== RSA 129 - Final Answer (April 27, 1994) ===

We are happy to announce that

RSA-129 = 11438162575788886766923577997614661201021 82967212423625625618429357069352457338978 30597123563958705058989075147599290026879543541

= 3490529510847650949147849619903898133417764638493387843990820577 * 32769132993266709549961988190834461413177642967992942539798288533

The encoded message published was

968696137546220614771409222543558829057599911245743198746951209 30816298225145708356931476622883989628013391990551829945157815154

This number came from an RSA encryption of the `secret' message using the public exponent 9007. When decrypted with he `secret' exponent

106698614368578024442868771328920154780709906633937862801226224 496631063125911774470873340168597462306553968544513277109053606095

this becomes

20080500130107090300231518041900011805 0019172105011309190800151919090618010705

Using the decoding scheme 01=A, 02=B, ..., 26=Z, and 00 a space between words, the decoded message reads

THE MAGIC WORDS ARE SQUEAMISH OSSIFRAGE

To find the factorization of RSA-129, we used the double large prime variation of the multiple polynomial quadratic sieve factoring method. The sieving step took approximately 5000 mips years, and was carried out in 8 months by about 600 volunteers from more than 20 countries, on all continents except Antarctica. Combining the partial relations produced a sparse matrix of 569466 rows and 524338 columns. This matrix was reduced to a dense matrix of 188614 rows and 188160 columns using structured Gaussian elimination. Ordinary Gaussian elimination on this matrix, consisting of 35489610240 bits (4.13 gigabyte), took 45 hours on a 16K MasPar MP-1 massively parallel computer. The first three dependencies all turned out to be `unlucky' and produced the trivial factor RSA-129. The fourth dependency produced the above factorization.

We would like to thank everyone who contributed their time and effort to this project. Without your help this would not have been possible.

Derek Atkins

Michael Graff

Arjen Lenstra

Paul Leyland

--[[User:Dgamey|Dgamey]] 15:39, 24 April 2011 (UTC)