My photo in 2006

Sums of Squares of Integers

Cryptanalysis of Number Theoretic Ciphers

History of Integer Factorization Chapter 4 (shown as Chapter 1 here) of Computational Cryptography, edited by Joppe W Bos and Martijn Stam, London Mathematical Society Lecture Notes Series 469, Cambridge University Press, 2021, pages 41--77.

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

Two papers on probable primes The first paper states a famous challenge for primality testing. Both 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. Here is an article by other authors that recommends using this test to construct large primes. It also exhibits problems with several other primality tests, but none with this one.

Paper with Robert Baillie and Andrew Fiori, "Stengthening the Baillie-PSW primality test" in Mathematics of Computation, 90 (2021), 1931-1955.

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

Paper with Clinton Bradford on SQUFOF in the Bulletin of the Polish Academy of Sciences Mathematics, 70 (2022), No. 1, 13-34.

Unpublished manuscript by Daniel Shanks on SQUFOF. It was the basis for the papers with Gower and Bradford above.

"Congruences for r_s(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.

.pdf file for paper "Primary Carmichael numbers," Integers 22A (2022), Art. A55. (High school algebra on steroids.)

.pdf file for paper "Pseudoprimes and Fermat numbers," Integers 24A (2024), Art. A23.

.pdf file for paper on Bell numbers with Peter Montgomery and Sangil Nahm.

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

History of Steganography, with Sherry Hsia, 2001.

Ramanujan's paper on Bernoulli numbers, J. Indian Math. Soc 45 (1981), 49--65. (Appeared in 1985.)

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.

Ramanujan's taxicab number and its ilk, Ramanujan Journal 64(3) (2024), pages 1--4. The version in the Ramanujan Journal. The full Table 2 from "Ramanujan's taxicab number and its ilk" in the Ramanujan Journal.

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.

Low threat security patches and tools, . Mohd A. Bashar, Ganesh Krishnan, Markus A. Kuhn, Eugene H. Spafford and Samuel S. Wagstaff, Jr., Proceedings of the International Conference on Software Maintenance, Bari, Italy, October 1-3, 1997, Mary Jean Harrold and Giuseppe Visaggio, eds., IEEE Computer Society, 1997, pp. 306-313.

Paper with six others, "Cognitive Processing of Cryptography Concepts: An fMRI Study" 2017 ASEE Annual Conference and Exposition, Columbus, Ohio, June 26, 2017, American Society for Engineering Education, Paper ID #20261 (2017).

Paper with Carl Pomerance on "Some thoughts on pseudoprimes" Bull. Cl. Sci. Math. Nat. Sci, Math. 46 (2021), pp. 53-72.

Paper with Carl Pomerance on "The Denominators of the Bernoulli Numbers" Acta Arithmetica 209 (2023), pp. 1-15.

Sum of reciprocals of Germain primes, Journal of Integer Sequences, 24(2021) Article 21.9.5.

Equal sums of two distinct like powers, Journal of Integer Sequences, 25(2022) Article 22.3.1.

Ph.D. thesis of my student Nicholas Egbert, December, 2021.

(This page last modified April 21, 2024)