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- Tapan S. Rai, Ezra Brown, Peter Haskell, Peter Linnell, John Rossi
- 2004

We develop a public key cryptosystem whose security is based on the intractability of the ideal membership problem for a noncommutative algebra over a finite field. We show that this system, which is the noncommutative analogue of the Polly Cracker cryptosystem, is more secure than the commutative version. This is due to the fact that there are a number of… (More)

- Ezra Brown
- 2001

Ezra (Bud) Brown (brown@math.vt.edu) has degrees from Rice and Louisiana State, and has been at Virginia Tech since the first Nixon Administration. His research interests include graph theory, the combinatorics of finite sets, and number theory—especially elliptic curves. In 1999, he received the MAA MD-DC-VA Section Award for Outstanding Teaching, and he… (More)

1. INTRODUCTION. The groups of invertible matrices over finite fields are among the first groups we meet in a beginning course in modern algebra. Eventually, we find out about simple groups and that the unique simple group of order 168 has two representations as a group of matrices. And this is where we learn that the group of 2 × 2 unimodular matrices over… (More)

We present a family of hyperelliptic curves whose Jacobians are suitable for cryptographic use, and whose parameters can be specified in a highly efficient way. This is done via complex multiplication and identity-based parameters. We also present some novel computational shortcuts for these families.

- Ezra Brown
- 1996

1. Introduction. Let a and n > 0 be integers, and define G(a, n) to be the directed graph with vertex set V = {0, 1,. .. , n − 1} such that there is an arc from x to y if and only if y ≡ ax (mod n). Recently, Ehrlich [1] studied these graphs in the special case a = 2 and n odd. He proved that if n is odd, then the number of cycles in G(2, n) is odd or even… (More)

Gauss's Cyclotomic Formula [3, pp.425-428, p.467] is a neglected mathematical wonder. Theorem 1.1. (Gauss) Let p be an odd prime and set p ′ = (−1) (p−1)/2 p. Then there exist integer polynomials R(x, y) and S(x, y) such that 4(x p + y p) x + y = R(x, y) 2 − p ′ S(x, y) 2 .

- Long Pan, Elisa D. Sotelino, Yang Cao, Ezra Brown, Eugene Santos, Eunice E. Santos
- 2007

Performing social network analysis (SNA) requires a set of powerful techniques to analyze structural information contained in interactions between social entities. Many SNA technologies and methodologies have been developed and have successfully provided significant insights for small-scale interactions. However, these techniques are not suitable for… (More)