Publications listed in MathSciNet in 2006

Cryptanalysis of Number Theoretic Ciphers

Factorizations of b^{n} ± 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 Jason Gower on SQUFOF in Mathematics of Computation, 77 (2008), 551-588. (Corrected version.)

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

Same paper also available here.

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.

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.

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.

Send e-mail to Sam Wagstaff