Publications listed in MathSciNet in 2006

Sums of Squares of Integers

Cryptanalysis of Number Theoretic Ciphers

Factorizations of bn ± 1, b = 2, 3, 5, 6, 7, 10, 11, 12, up to High Powers

Two papers on probable primes These articles propose an algorithm for selecting industrial-grade primes for use in cryptography. This algorithm is recommended in ANSI Standards X9.31 and X9-80. The first paper states a famous challenge for primality testing.

Paper with Jason Gower on SQUFOF in Mathematics of Computation, 77 (2008), 551-588. (Corrected version.)

"Congruences for rs(n) modulo 2s," Journal of Number Theory 127 (2007) 326-329.

Same paper also available here.

Paper on the Cunningham Project, In "High primes and misdemeanours: lectures in honour of the 60th birthday of Hugh Cowrie Williams," A. Stein and A. van der Poorten, editors, Fields Institute Communications, v. 41 (2004), Amer. Math. Soc., pages 367--378. MR 2005m:11234.

An efficient time-bound hierarchical key management scheme for secure broadcasting, IEEE Transactions on Dependable and Secure Computing, vol. 5, no. 2, April-June, 2008, pages 65-299, joint paper with E Bertino and N Shang.

Paper on primes with a fixed number of 0 or 1 bits

Is there a shortage of primes for cryptography? International Journal of Network Security, vol. 3, no. 3, pages 296-299.

Factors of Bernoulli and Euler Numbers

The Number Field Sieve on Many Computers by R.-M. Elkenbracht-Huizing, Peter L. Montgomery, R. D. Silverman, R. K. Wackerbarth and S. S. Wagstaff, Jr., Proceedings of the Fifth Conference of the Canadian Number Theory Association, Rajiv Gupta and Kenneth S. Williams, editors. Centre de Recherches Mathematiques (CRM, Montreal) Proceedings and Lecture Notes Series, published by the American Mathematical Society (AMS), volume 19 (1999), pages 81-85.

MPQS with three large primes, P. Leyland, A.K. Lenstra, B. Dodson, A. Muffett, S.S. Wagstaff, Jr., in Algorithmic Number Theory, Proceedings ANTS 2002, volume 2369 of Springer-Verlag Lecture Notes in Computer Science, 2002, pages 448--462.

Factors of Bell Exponential Numbers

Paper on watermarking with quadratic residues

Implementing the hypercube quadratic sieve with two large primes, Brian Carrier and Samuel S. Wagstaff, Jr., in Proceedings of the International Conference on Number Theory for Secure Communications, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam, India, 20 & 21 December, 2003, pages 51--64. The PostScript version of the same paper.

Computing Euclid's primes, Samuel S. Wagstaff, Jr., in Bulletin of the Institute for Combinatorics and its Applications 8 (1993), pages 23--32. MR 94e:11139.

The New Mersenne Conjecture Paper with Paul Bateman and John Selfridge, American Mathematical Monthly 96 (1989), 125-128. The table for this paper.


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(This page last modified July 18, 2013)