# Factoring by electronic mail

- First Online:

DOI: 10.1007/3-540-46885-4_35

- Cite this paper as:
- Lenstra A.K., Manasse M.S. (1990) Factoring by electronic mail. In: Quisquater JJ., Vandewalle J. (eds) Advances in Cryptology — EUROCRYPT ’89. EUROCRYPT 1989. Lecture Notes in Computer Science, vol 434. Springer, Berlin, Heidelberg

## Abstract

In this paper we describe our distributed implementation of two factoring algorithms, the elliptic curve method (ecm) and the multiple polynomial quadratic sieve algorithm (mpqs).

Since the summer of 1987, our ecm-implementation on a network of MicroVAX processors at DEC’s Systems Research Center has factored several most and more wanted numbers from the Cunningham project. In the summer of 1988, we implemented the multiple polynomial quadratic sieve algorithm on the same network. On this network alone, we are now able to factor any 100 digit integer, or to find 35 digit factors of numbers up to 150 digits long within one month.

To allow an even wider distribution of our programs we made use of electronic mail networks for the distribution of the programs and for inter-processor communication. Even during the initial stage of this experiment, machines all over the United States and at various places in Europe and Australia contributed 15 percent of the total factorization effort.

At all the sites where our program is running we only use cycles that would otherwise have been idle. This shows that the enormous computational task of factoring 100 digit integers with the current algorithms can be completed almost for free. Since we use a negligible fraction of the idle cycles of all the machines on the worldwide electronic mail networks, we could factor 100 digit integers within a few days with a little more help.