Benjamin A. Smith

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We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm reduces the complexity of genus 2 point counting over a finite field Fq of large characteristic from Õ(log q) to Õ(log q). Using our algorithm we compute a 256-bit prime-order(More)
We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Problem (DLP) from Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperelliptic genus 3 curves, where they are vulnerable to faster index calculus attacks. We provide explicit formulae for isogenies with kernel isomorphic to (ℤ/2ℤ)3 (over an algebraic(More)
Cell locomotion and endocytosis are powered by the rapid polymerization and turnover of branched actin filament networks nucleated by Arp2/3 complex. Although a large number of cellular factors have been identified that stimulate Arp2/3 complex-mediated actin nucleation, only a small number of studies so far have addressed which factors promote actin(More)
During cell locomotion and endocytosis, membrane-tethered WASP proteins stimulate actin filament nucleation by the Arp2/3 complex. This process generates highly branched arrays of filaments that grow toward the membrane to which they are tethered, a conflict that seemingly would restrict filament growth. Using three-color single-molecule imaging in vitro we(More)
Membrane protrusion at the leading edge of migrating cells is driven by the polymerization of actin. Recent studies using advanced imaging techniques raised a lively controversy about the morphology of these filaments; however, common ground between the two sides now appears to have been found. Here we discuss how the controversy has led to a deeper(More)
In passive Heymann nephritis (PHN) glomeruli exhibit marked basement membrane expansion around subepithelial immune deposits but they fail to show any change in mRNA levels of type IV collagen, laminin or fibronectin by Northern and slot-blot analysis, or in the amount or distribution of type IV collagen or laminin by immunohistology for up to 12 weeks(More)
Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated since the full torsion subgroup has rank 2g. In this paper we prove that distortion maps always exist for supersingular curves of genus g > 1 and we give several examples in genus 2.
Déchène has proposed generalized Jacobians as a source of groups for public-key cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific proposal gives rise to a group isomorphic to the semidirect product of an elliptic curve and a multiplicative group of a finite field. We explain why her proposal has no advantages over(More)