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- Benjamin A Smith, Hugo Roy, Paul De Koninck, Peter Grütter, Yves De Koninck
- Biophysical journal
- 2007

Neuronal dendritic spines are a key component of brain circuitry, implicated in many mechanisms for plasticity and long-term stability of synaptic communication. They can undergo rapid actin-based activity-dependent shape fluctuations, an intriguing biophysical property that is believed to alter synaptic transmission. Yet, because of their small size… (More)

- Benjamin A. Smith
- Journal of Cryptology
- 2008

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)

- Benjamin A Smith, Barbara Tolloczko, James G Martin, Peter Grütter
- Biophysical journal
- 2005

Complex rheology of airway smooth muscle cells and its dynamic response during contractile stimulation involves many molecular processes, foremost of which are actomyosin cross-bridge cycling and actin polymerization. With an atomic force microscope, we tracked the spatial and temporal variations of the viscoelastic properties of cultured airway smooth… (More)

- Steven D. Galbraith, Jordi Pujolàs, Christophe Ritzenthaler, Benjamin A. Smith
- IACR Cryptology ePrint Archive
- 2006

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.

- Pierrick Gaudry, David R. Kohel, Benjamin A. Smith
- ASIACRYPT
- 2011

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 O(log 8 q) to O(log 5 q). Using our algorithm we compute a 256-bit prime-order… (More)

- David R. Kohel, Benjamin A. Smith
- ANTS
- 2006

Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic Jacobians, but one obstruction is the lack of explicit models of curves together with an efficiently computable… (More)

- Steven D. Galbraith, Benjamin A. Smith
- IACR Cryptology ePrint Archive
- 2006

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)

- Steven D. Galbraith, Jordi Pujolàs, Christophe Ritzenthaler, Benjamin A. Smith
- J. Mathematical Cryptology
- 2009

- Benjamin A. Smith
- IACR Cryptology ePrint Archive
- 2007

We describe the use of explicit isogenies to reduce Discrete Logarithm Problems (DLPs) on Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperelliptic genus 3 curves, which are vulnerable to faster index calculus attacks. We provide algorithms which compute an isogeny with kernel isomorphic to (Z/2Z) 3 for any hyperelliptic genus 3 curve.… (More)