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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)
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)
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