Self-assembly is a ubiquitous process by which objects autonomously assemble into complexes. In the context of computation, self-assembly is important to both DNA computing and amorphous computing.… (More)

In 1864, Waage and Guldberg formulated the “law of mass action.” Since that time, chemists, chemical engineers, physicists and mathematicians have amassed a great deal of knowledge on the topic. In… (More)

We describe a new class of list decodable codes based on Galois extensions of function fields and present a list decoding algorithm. This work is an extension of Folded Reed Solomon codes to the… (More)

We describe a deterministic algorithm for finding a generating element of the multiplicative group of the finite field with p elements. In time polynomial in p and n, the algorithm either outputs an… (More)

In [Jou], Joux devised an algorithm to compute discrete logarithms between elements in a certain subset of the multiplicative group of an extension of the finite field F p n in time polynomial in p… (More)

We study the discrete logarithm problem for the multiplica tive group and for elliptic curves over a finite field by using a lifting of the corresponding object to an algebraic number field and… (More)

We consider computational problems concerning algebras over finite fields. In particular, we propose an algorithm for finding a small generating set for the multiplicative group of GF(p)[x]/F, where… (More)

Recent breakthrough methods [GGMZ, Jou, BGJT] on computing discrete logarithms in small characteristic finite fields share an interesting feature in common with the earlier medium prime function… (More)

It has been suggested that a major obstacle in finding an index calculus attack on the elliptic curve discrete logarithm problem lies in the difficulty of lifting points from elliptic curves over… (More)