Congruential sieves on reconfigurable computer

IEEE Symposium on FPGAs for Custom Computing Machines, Proceedings

Volumn 2003-January, Issue , 2003, Pages 11-18

  Wake, H A ^a   Buell, D A ^a  

^a University of South Carolina   (United States)

Author keywords

Arithmetic; Bridges; Cathode ray tubes; Contracts; Field programmable gate arrays; Hardware; Integral equations; Polynomials; Testing; Trademarks

Indexed keywords

BRIDGES; CATHODE RAY TUBES; CATHODES; COMPUTER HARDWARE; COMPUTERS; CONTRACTS; DIGITAL ARITHMETIC; INTEGRAL EQUATIONS; LOGIC GATES; POLYNOMIALS; RECONFIGURABLE ARCHITECTURES; RECONFIGURABLE HARDWARE; SIEVES; TESTING; TRADEMARKS;

BRIDGE SYSTEMS; ELECTRO-MECHANICAL; ELECTRONIC DEVICE; PHYSICAL DEVICES; PRIME NUMBER; RECONFIGURABLE COMPUTER; RECONFIGURABLE COMPUTING; SOFTWARE PROGRAM;

FIELD PROGRAMMABLE GATE ARRAYS (FPGA);

EID: 84942928093     PISSN: 10823409     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FPGA.2003.1227237     Document Type: Conference Paper

References (18)

1. N. D. Bronson and D. A. Buell. Congruential sieves on FPGA computers. In W. Gautschi, editor, Proceedings of Symposia in Applied Mathematics, volume 48, pages 547-552. American Mathematical Society, 1994. 1, 2, 3, 6
2. J. Buchmann and H. C. Williams. A key-exchange system based on imaginary quadratic fields. Journal of Cryptology, 1:107-118, 1987. 2
3. D. A. Buell. Small class numbers and extreme values of L-functions of quadratic fields. Mathematics of Computation, 31:786-796, 1977. 2
4. D. A. Buell. The expectation of success using a Monte Carlo factoring method-Some statistics on quadratic class numbers. Mathematics of Computation, 43:313-327, 1984. 2
5. D. A. Buell, J. M. Arnold, and W. J. Kleinfelder. Splash 2: FPGAs in a Custom Computing Machine. IEEE Computer Society Press, 1996. 1
6. Clay Mathematics Institute. Millenium prize problems. http://www.claymath.org/Millenium-Prize-Problems. 2
7. M. Gokhale, W. Holmes, A. Kopser, S. Lucas, R. Minnich, D. Sweely, and D. Lopresti. Building and using a highly parallel programmable logic array. IEEE Computer, pages 81-89, 1991. 1
8. J. L. Hafner and K. S. McCurley. A rigorous subexponential algorithm for computation of class groups. Journal of the AMS, 2, 1989. 2
9. D. H. Lehmer, E. Lehmer, and D. Shanks. Integer sequences having prescribed quadratic character. Mathematics of Computation, 24:433-451, 1970. 2
10. R. F. Lukes. A very fast electronic number sieve. U. of Manitoba Ph. D. thesis, 1995. 1
11. R. F. Lukes, C. D. Patterson, and H. C. Williams. Numerical sieving devices: Their history and some applications. Nieuw Arch. Wisk., 13:113-139, 1995. 1
12. R. F. Lukes, C. D. Patterson, and H. C. Williams. Some results on pseudosquares. Mathematics of Computation, 65:361-372, 1996. 2
13. K. S. McCurley. Cryptographic key distribution and computation in class groups. In R. A. Mollin, editor, Number Theory and Applications, NATO ASI Series C 265, pages 459-479. Kluwer Academic, 1989. 2
14. D. Shanks. Systematic examination of littlewood's bounds on l(1, x). Proceedings of the Symposium in Pure Mathematics, 24:267-283, 1974. 2
15. A. J. Stephens and H. C. Williams. An open architecture number sieve. In J. H. Loxton, editor, Number Theory and Cryptography, volume 154 of London Math Society Lecture Note Series, pages 38-75. Cambridge University Press, 1990. 1, 2
16. U. Vollmer. Asymptotically fast discrete logarithms in quadratic number fields. In W. Bosma, editor, Proceedings, ANTS IV, volume 1838 of Lecture Notes in Computer Science, pages 581-594. Springer Verlag, 2000. 2
17. H. C. Williams. Edouard Lucas and Primality Testing. Wiley-Interscience, 1998. 1
18. H. S. Zuckerman, H. L. Montgomery, I. M. Niven, and A. Niven. An Introduction to the Theory of Numbers. Wiley, 1991. 3