List of my papers:
Not all free online, but papers 1, 9, 12 and 17 (and all issues of Math. Comp. 1943-2011) are now freely available from the AMS website here: www.ams.org/mcom/ ; also papers 12,16 and 17 can be obtained from __FactorWorld__ (which also has quotations from 18). Printed copies on request, by post. My papers are mainly on computational number theory, especially factoring and discrete logarithms: Factoring: 4,6,12,14-18 Discrete logarithms(*): 9,20,21. Most cited papers: 1,4,6,9,12-17. The above pictures illustrate some algorithms for factoring or discrete logarithms of which I am the inventor or joint inventor (see comments below).
1. The fast Fourier transform in a finite field, Math. Comp. 25(1971), 365-374.
2. An algorithm for testing the primality of any integer, Bull. London Math. Soc. 3(1971), 337-340. {obsolete paper}
3. A generalisation of the theorem of Cauchy and Davenport, J. London Math. Soc. (2), 8(1974), 460-462. {a theorem discovered by computer calculations}
4. Theorems on factorisation and primality testing, Proc. Camb. Phil. Soc. 76(1974), 521-528. {includes the two-stage p-1 method of factoring}
5. Addition properties of residue classes, J. London Math. Soc.(2), 11(1975), 147-152. {an extension of [3]}
6. A Monte Carlo method for factorization, BIT 15(1975), 331-334. {proposed the rho method for factoring}
7. Combinatorial properties of a queueing system with limited availability, Advances in Applied Prob. 7(1975), 864-877.
8. Implementation of number theoretic transforms, Elect. Lett., 22nd July 1976, 378-379. {connected with [1]}
9. Monte Carlo methods for index computation (mod p), Math. Comp. 32(1978), 918-924. {proposed the rho and kangaroo methods for discrete logarithms(*)}
10. Remarks on the convolution algorithm of Agarwal and Cooley, Elect. Lett., 13th Sept. 1979, 593-594. {connected with [1,8]}
11. On not storing the path of a random walk, BIT 19(1979), 545-548. {an algorithm looking for a problem?}
12. (With R.P.Brent), Factorisation of the eighth Fermat number, Math. Comp. 36(1981), 627-630. {an application of the rho method[6]}
13. (With C.P.Schnorr), An efficient solution of the congruence x^2 + ky^2 = m (mod n), IEEE Trans. Inf. Theory, IT-33, No. 5, Sept. 1987, 702-709. {broke several versions of the Ong-Schnorr-Shamir signature scheme}
14. Factoring with cubic integers, in “The development of the number field sieve", A.K.Lenstra and H.W.Lenstra(eds), Lecture Notes in Mathematics 1554, Springer-Verlag 1993, 4-10. {First implementation of the number field sieve}
15. The lattice sieve, in ditto, 43-49.
16. (With A.K.Lenstra, H.W.Lenstra and M.S.Manasse), The number field sieve, in ditto, 11-40.
17. (With the same coauthors), The factorisation of the ninth Fermat number, Math. Comp. 61(1993), 319-349. {an application of the special number field sieve}
18. Unforgettable Fermat factors, Math. Gazette 82(1998), 77-79. {not a research paper - mnemonics for some Fermat factors!}
19. Kruskal`s card trick, Math. Gazette 84(2000), 265-267. {connected with [20]} |