# Generating a Product of Three Primes With an Unknown Factorization

**Authors:**

*D. Boneh and J. Horwitz*

** Abstract: **

We describe protocols for three or more parties to jointly generate a
composite N = pqr which is the product of three primes. After our
protocols terminate N is publicly known, but neither party knows the
factorization of N. Our protocols require the design of a new type
of distributed primality test for testing that a given number is a
product of three primes. We explain the cryptographic motivation and
origin of this problem.

** Reference:**

In Proceedings of the *third Algorithmic Number Theory Symposium*, Lecture Notes in Computer Science, Vol. 1423, Springer-Verlag, pp. 237--251, 1998

**Full paper:**
gzipped-PostScript
[first posted
1/1998 ]