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Why put emotion into games? The answers are art and money. Sure, it's an unholy alliance, but so are pineapple and pizza, windmills and tiny golf courses, the military and intelligence, and canned fruit and gelatin molds. Don't get me wrong. I think of myself as an artist first and a businessman second. But game companies that don't make a profit aren't(More)
We present a general framework for constructing families of elliptic curves of prime order with prescribed embedding degree. We demonstrate this method by constructing curves with embedding degree k = 10, which solves an open problem posed by Boneh, Lynn, and Shacham [6]. We show that our framework incorporates existing constructions for k = 3, 4, 6, and(More)
We present algorithms which, given a genus 2 curve C defined over a finite field and a quartic CM field K, determine whether the endomorphism ring of the Jacobian J of C is the full ring of integers in K. In particular, we present probabilistic algorithms for computing the field of definition of, and the action of Frobenius on, the subgroups J[ℓ d ] for(More)
Let X be a Banach space with a separable dual. We prove that X embeds isomorphically into a L∞ space Z whose dual is isomorphic to ℓ1. If X has a shrinking finite dimensional decomposition and X * does not contain an isomorph of ℓ1, then we construct such a Z, as above, not containing an isomorph of c0. If X is separable and reflexive, we show that Z can be(More)
α-synuclein dysregulation is a critical aspect of Parkinson's disease pathology. Recent studies have observed that α-synuclein aggregates are cytotoxic to cells in culture and that this toxicity can be spread between cells. However, the molecular mechanisms governing this cytotoxicity and spread are poorly characterized. Recent studies of viruses and(More)
We provide the first explicit construction of genus 2 curves over finite fields whose Jacobians are ordinary, have large prime-order subgroups, and have small embedding degree. Our algorithm works for arbitrary embedding degrees k and prime subgroup orders r. The resulting abelian surfaces are defined over prime fields Fq with q ≈ r 4. We also provide an(More)
Quantitation of trace levels of perchlorate ion in water has become a key issue since this species was discovered in water supplies around the United States. Although ion chromatographic methods presently offer the lowest limit of detection, #40 nM (4 ng ml 21), chromatographic retention times are not considered to be unique identi®ers and often cannot be(More)