Numbers contained in the ``factoring challenge'' of RSA Data Security, Inc. An additional number which is not part of the
actual challenge is the RSA-129 number. The RSA numbers which have been factored are RSA-100, RSA-110, RSA-120, RSA-129, and
RSA-130 (Cowie *et al. *1996).

RSA-129 is a 129-digit number used to encrypt one of the first public-key messages. This message was published by R. Rivest, A. Shamir, and L. Adleman (Gardner 1977), along with the number and a $100 reward for its decryption. Despite belief that the message encoded by RSA-129 ``would take millions of years of break,'' RSA-129 was factored in 1994 using a distributed computation which harnessed networked computers spread around the globe performing a multiple polynomial Quadratic Sieve Factorization Method. The effort was coordinated by P. Leylad, D. Atkins, and M. Graff. They received 112,011 full factorizations, 1,431,337 single partial factorizations, and 8,881,138 double partial factorizations out of a factor base of 524,339 Primes. The final Matrix obtained was square.

The text of the message was ``The magic words are squeamish ossifrage'' (an ossifrage is a rare, predatory vulture found in the mountains of Europe), and the Factorization (into a 64-Digit number and a 65-Digit number) is

**References**

Cipra, B. ``The Secret Life of Large Numbers.'' *What's Happening in the Mathematical Sciences, 1995-1996, Vol. 3.*
Providence, RI: Amer. Math. Soc., pp. 90-99, 1996.

Cowie, J.; Dodson, B.; Elkenbracht-Huizing, R. M.; Lenstra, A. K.; Montgomery, P. L.; Zayer, J. A.
``World Wide Number Field Sieve Factoring Record: On to Bits.'' In *Advances in Cryptology--ASIACRYPT '96 (Kyongju)*
(Ed. K. Kim and T. Matsumoto.) New York: Springer-Verlag, pp. 382-394, 1996.

Gardner, M. ``Mathematical Games: A New Kind of Cipher that Would Take Millions of Years to Break.'' *Sci. Amer.* **237**,
120-124, Aug. 1977.

Klee, V. and Wagon, S. *Old and New Unsolved Problems in Plane Geometry and Number Theory, rev. ed.*
Washington, DC: Math. Assoc. Amer., p. 223, 1991.

Leutwyler, K. ``Superhack: Forty Quadrillion Years Early, a 129-Digit Code is Broken.'' *Sci. Amer.* **271**, 17-20, 1994.

Leyland, P. ftp://sable.ox.ac.uk/pub/math/rsa129.

RSA Data Security. A Security Dynamics Company. http://www.rsa.com.

Taubes, G. ``Small Army of Code-breakers Conquers a 129-Digit Giant.'' *Science* **264**, 776-777, 1994.

Weisstein, E. W. ``RSA Numbers.'' Mathematica notebook RSANumbers.m.

© 1996-9

1999-05-25