Abstract
A new version of the Quadratic Sieve algorithm, used for factoring large integers, has recently emerged. The new algorithm, called the Multiple Polynomial Quadratic Sieve, not only considerably improves the original Quadratic Sieve but also adds features that ideally suit a parallel implementation. The parallel implementation used for the new algorithm, a novel remote batching system, is also described.
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Brillhart, J., Lehmer, D.H., Selfridge, J.L., Tuckerman, B., and Wagstaff, S.S. Jr. 1983. Factorizations of b n ± 1 for b = 2, 3, 5, 6, 7, 10, 11, 12, up to High Powers. American Mathematical Society, Providence, Rhode Island.
Coppersmith, D., Odlyzko, A.M., and Schroeppel, R. 1986. Discrete logarithms in GF(p). Algorithmica, 1: 1–15.
Davis, J.A., and Holdridge, D.B. 1983. Factorization using the quadratic sieve algorithm. Sandia National Laboratories Tech. Rept. SAND 83-1346.
Davis, J.A., Holdridge, D.B., and Simmons, G.J. 1985. Status report on factoring. Advances in Cryptology: Lecture Notes in Computer Science, pp 183–215.
Knuth, D.E. 1981. The Art of Computer Programming, vol. 2, Seminumerical Algorithms, 2nd ed. Addison-Wesley, Reading, Massachusetts, p. 365.
Montgomery, P. 1985. Personal communication.
Morrison, M., and Brillhart, J. 1975. A method of factoring and the factorization of F7. Math. Comput., 29: 183–205.
Pomerance, C. 1983. Analysis and comparison of some integer factoring algorithms. In Computational Methods in Number Theory (H.W. Lenstra Jr., and R. Tijdeman, Eds.), Mathematisch Centrum, Amsterdam, pp. 89–140.
Pomerance, C. 1985. A pipe-line architecture for factoring large integers with the quadratic sieve algorithm. SIAM J. Comput. Special Issue on Cryptography. To appear.
Silverman, R.D., 1987. The multiple polynomial quadratic sieve. Math. Comput. 48: 329–339.
Wagstaff, S.S. Jr. 1986. Personal communication.
Wiedemann, D. 1986. Solving sparse linear equations over finite fields. IEEE Trans. Information Theory, IT-32, 54–61.
Wunderlich, M. 1986. Personal communication.
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Caron, T.R., Silverman, R.D. Parallel implementation of the quadratic sieve. J Supercomput 1, 273–290 (1988). https://doi.org/10.1007/BF00154339
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DOI: https://doi.org/10.1007/BF00154339