New Ideas for Factoring Large Integers

  • Carl Pomerance
  • J. W. Smith
  • S. S. WagstaffJr.


This is an extended abstract which summarizes papers [3], [4], and [5]. They describe improvements in the continued fraction factorization algorithm (CFRAC) and a special processor designed to execute this algorithm swiftly. The ideas in these papers will permit one to factor a 100 decimal digit integer in about a month on a processor which would cost about $1,000,000. Therefore, moduli for RSA cryptosystems should be chosen somewhat larger than 100 digits to be secure.


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  1. 1.
    M. A. Morrison and J. Brillhart, A method of factoring and the factorization of F7, Math. Comp. 29 (1975), 183–205.Google Scholar
  2. 2.
    C. Pomerance, Analysis and comparison of some integer factoring algorithms, in Computational Methods in Number Theory,Part 1, H. W. Lenstra, Jr. and R. Tijdeman, eds., Math. Centrum 154, Amsterdam (1982), 89–139.Google Scholar
  3. 3.
    C. Pomerance and S. S. Wagstaff, Jr., Implementation of the continued fraction integer factoring algorithm, Congressus Numerantium 37 (1983), 99–118.Google Scholar
  4. 4.
    J. W. Smith and S. S. Wagstaff, Jr., An extended precision operand computer, Proceedings of the 21st Southeast Region ACM Conference (1983), 209–216.Google Scholar
  5. 5.
    J. W. Smith and S. S. Wagstaff, Jr., How to crack an RSA cryptosystem, to appear in Congressus Numerantium.Google Scholar
  6. 6.
    M. C. Wunderlich and D. Parkinson, A memory-efficient algorithm for Gaussian elimination over GF(2) implemented on highly parallel computers, in preparation.Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Carl Pomerance
  • J. W. Smith
  • S. S. WagstaffJr.

There are no affiliations available

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