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We explore the use of subfield arithmetic for efficient implementations of Galois Field arithmetic especially in the context of the Rijndael block cipher. Our technique involves mapping field elements to a composite field representation. We describe how to select a representation which minimizes the computation cost of the relevant arithmetic, taking into(More)
We consider the following simple algorithm for feedback arc set problem in weighted tournaments --- order the vertices by their weighted indegrees. We show that this algorithm has an approximation guarantee of 5 if the weights satisfy <i>probability constraints</i> (for any pair of vertices <i>u</i> and <i>v, w</i><inf><i>uv</i></inf> +(More)
Motivated by applications in online dating and kidney exchange, we study a stochastic matching problem in which we have a random graph G given by a node set V and probabilities p(i, j) on all pairs i, j ∈ V representing the probability that edge (i, j) exists. Additionally, each node has an integer weight t(i) called its patience parameter. Nodes represent(More)
Efficient join processing is one of the most fundamental and well-studied tasks in database research. In this work, we examine algorithms for natural join queries over many relations and describe a novel algorithm to process these queries optimally in terms of worst-case data complexity. Our result builds on recent work by Atserias, Grohe, and Marx, who(More)
Consider a random graph model where each possible edge e is present independently with some probability p e . Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we can find out whether an edge is present or not is to query it, and if the edge is indeed present in the graph, we are forced(More)
We present an efficient randomized algorithm to test if a given function f : F/sub p/ /sup n/ /spl rarr/ F/sub p/ (where p is a prime) is a low-degree polynomial. This gives a local test for generalized Reed-Muller codes over prime fields. For a given integer t and a given real /spl epsiv/ > 0, the algorithm queries f at 1//spl epsiv/ + t/spl middot/p/sup(More)