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RSA Factoring Challenge

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RSA Factoring Challenge

The RSA Factoring Challenge was a challenge put forward by RSA Laboratories on March 18, 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers and cracking RSA keys used in cryptography. They published a list of semiprimes (numbers with exactly two prime factors) known as the RSA numbers, with a cash prize for the successful factorization of some of them. The smallest of them, a 100 decimal digit number called RSA-100 was factored by April 1, 1991, but many of the bigger numbers have still not been factored and are expected to remain unfactored for quite some time, however advances in quantum computers make this prediction uncertain due to Shor's algorithm.

The RSA challenges ended in 2007.[1] RSA Laboratories stated: "Now that the industry has a considerably more advanced understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these challenges are no longer active."[2]

The factoring challenge was intended to track the cutting edge in integer factorization. A primary application is for choosing the key length of the RSA public-key encryption scheme. Progress in this challenge should give an insight into which key sizes are still safe and for how long. As RSA Laboratories is a provider of RSA-based products, the challenge was used by them as an incentive for the academic community to attack the core of their solutions — in order to prove its strength.

The RSA numbers were generated on a computer with no network connection of any kind. The computer's hard drive was subsequently destroyed so that no record would exist, anywhere, of the solution to the factoring challenge.[3]

The first RSA numbers generated, RSA-100 to RSA-500 and RSA-617, were labeled according to their number of decimal digits; the other RSA numbers (beginning with RSA-576) were generated later and labelled according to their number of binary digits.


  • The mathematics 1
  • The prizes and records 2
  • See also 3
  • Notes 4
  • External links 5

The mathematics

RSA Laboratories states that: for each RSA number n, there exist prime numbers p and q such that

n = p × q.

The problem is to find these two primes, given only n.

The prizes and records

The following table gives an overview over all RSA numbers.

The challenge numbers in white lines are numbers expressed in base 10, while the challenge numbers in yellow lines are numbers expressed in base 2. The prizes for RSA-576 and RSA-640 have been awarded. The remaining prizes have been retracted since the challenge became inactive in 2007.
RSA Number Decimal digits Binary digits Cash prize offered Factored on Factored by
RSA-100 100 330 US$1,000[4] April 1, 1991[5] Arjen K. Lenstra
RSA-110 110 364 US$4,429[4] April 14, 1992[5] Arjen K. Lenstra and M.S. Manasse
RSA-120 120 397 $5,898[4] July 9, 1993[6] T. Denny et al.
RSA-129 [**] 129 426 $100 USD April 26, 1994[5] Arjen K. Lenstra et al.
RSA-130 130 430 US$14,527[4] April 10, 1996 Arjen K. Lenstra et al.
RSA-140 140 463 US$17,226 February 2, 1999 Herman te Riele et al.
RSA-150 [*] ? 150 496   April 16, 2004 Kazumaro Aoki et al.
RSA-155 155 512 $9,383[4] August 22, 1999 Herman te Riele et al.
RSA-160 160 530   April 1, 2003 Jens Franke et al., University of Bonn
RSA-170 [*] 170 563   December 29, 2009 D. Bonenberger and M. Krone [***]
RSA-576 174 576 $10,000 USD December 3, 2003 Jens Franke et al., University of Bonn
RSA-180 [*] 180 596   May 8, 2010 S. A. Danilov and I. A. Popovyan, Moscow State University[7]
RSA-190 [*] 190 629   November 8, 2010 A. Timofeev and I. A. Popovyan
RSA-640 193 640 $20,000 USD November 2, 2005 Jens Franke et al., University of Bonn
RSA-200 [*] ? 200 663   May 9, 2005 Jens Franke et al., University of Bonn
RSA-210 [*] 210 696 September 26, 2013[8] Ryan Propper
RSA-704 [*] 212 704 $30,000 USD July 2, 2012 Shi Bai, Emmanuel Thomé and Paul Zimmermann
RSA-220 220 729  
RSA-230 230 762  
RSA-232 232 768  
RSA-768 [*] 232 768 $50,000 USD December 12, 2009 Thorsten Kleinjung et al.
RSA-240 240 795  
RSA-250 250 829  
RSA-260 260 862  
RSA-270 270 895  
RSA-896 270 896 $75,000 USD
RSA-280 280 928  
RSA-290 290 962  
RSA-300 300 995  
RSA-309 309 1024  
RSA-1024 309 1024 $100,000 USD
RSA-310 310 1028  
RSA-320 320 1061  
RSA-330 330 1094  
RSA-340 340 1128  
RSA-350 350 1161  
RSA-360 360 1194  
RSA-370 370 1227  
RSA-380 380 1261  
RSA-390 390 1294  
RSA-400 400 1327  
RSA-410 410 1360  
RSA-420 420 1393  
RSA-430 430 1427  
RSA-440 440 1460  
RSA-450 450 1493  
RSA-460 460 1526  
RSA-1536 463 1536 $150,000 USD
RSA-470 470 1559  
RSA-480 480 1593  
RSA-490 490 1626  
RSA-500 500 1659  
RSA-617 617 2048  
RSA-2048 617 2048 $200,000 USD

^ * The number was factored after the challenge became inactive.

^ ** RSA-129 was not part of the RSA Factoring Challenge, but was related to a column by Martin Gardner in Scientific American.

^ *** RSA-170 was also independently factored by S. A. Danilov and I. A. Popovyan two days later.[7]

See also


  1. ^ RSA Laboratories, The RSA Factoring Challenge. Retrieved on 2013-11-09.
  2. ^ RSA Laboratories, The RSA Factoring Challenge FAQ. Retrieved on 2013-11-09.
  3. ^ RSA Laboratories. "The RSA Factoring Challenge FAQ". Retrieved 2008-08-05. 
  4. ^ a b c d e
  5. ^ a b c RSA Honor Roll
  6. ^ On the factorization of RSA-120 - Springer. Retrieved on 2014-05-11.
  7. ^ a b
  8. ^ RSA-210 factored,

External links

  • RSA Security: The RSA factoring challenge
  • MathWorld: RSA Number
  • Mathematica package for RSA numbers
  • The original challenge announcement on sci.crypt
  • Certicom ECC Challenge
  • MTC3 Thanks to RSA Inc, the crypto contest MTC3 contains all unsolved RSA numbers and offers users additional information and feedback about these factorization challenges.
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