Fast, twist-secure elliptic curve cryptography from Q-curves Benjamin Smith Team GRACE INRIA Saclay–ˆIle-de-France ´

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47 Doc. Math. J. DMV Selmer Groups and Torsion Zero Cycles on the Selfproduct of a Semistable Elliptic Curve

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On polynomials attached to curves F. Morain Laboratoire d’Informatique de l’École polytechnique logoUW ECOL E

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• Mathematical analysis
• Mathematics
• Special functions
• Analytic number theory
• Elliptic curve
• Group theory
• Analytic functions
• Orthogonal polynomials
• Barnes G-function

Introduction The present work grew out of an entirely unsuccessful attempt to answer some basic questions about elliptic curves over $. Start with an elliptic curve E over $, say given by a Weierstrass equation E: y2 = 4

Source URL: web.math.princeton.edu

• Mathematics
• Analytic number theory
• Number theory
• Mathematical analysis
• Elliptic curves
• Conjectures
• Diophantine geometry
• Millennium Prize Problems
• Birch and Swinnerton-Dyer conjecture
• Rank of an elliptic curve
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ON A PROPERNESS OF THE HILBERT EIGENVARIETY AT INTEGRAL WEIGHTS: THE CASE OF QUADRATIC RESIDUE FIELDS SHIN HATTORI Abstract. Let p be a rational prime. Let F be a totally real number field such that F is unramified over

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• Algebra
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• Eigenform
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1. Introduction 1.1. Background. L-functions and modular forms underlie much of twentieth century number theory and are connected to the practical applications of number theory in cryptography. The fundamental importance

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• Mathematics
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• Modular forms
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• Millennium Prize Problems
• Riemann hypothesis
• Elliptic curve
• Langlands program
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EMBARGOED FOR RELEASE March 31, 12:01 a.m. ET Bruce Shriver ACMMarie Gentile

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• Cryptography
• Public-key cryptography
• Identity-based cryptography
• Elliptic curve cryptography
• Dan Boneh
• ID-based encryption
• Association for Computing Machinery
• Pairing-based cryptography
• Boneh
• Infosys
• ID-based cryptography
• Computer science

447 Documenta Math. p-Adic Fourier Theory P. Schneider, J. Teitelbaum

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• Mathematics
• Algebra
• Mathematical analysis
• Field theory
• Algebraic geometry
• Valuation
• Fourier transform
• Distribution
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A generalisation of Miller’s algorithm and applications to pairing computations on abelian varieties David Lubicz1,2 , Damien Robert3 1

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• Mathematical analysis
• Abstract algebra
• Mathematics
• Elliptic functions
• Riemann surfaces
• Group theory
• Theta function
• Elliptic curve
• Divisor
• Algebraic number field
• ZQ

2015-ohp-english+pictures.pdf

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• Abstract algebra
• Algebra
• Mathematics
• Number theory
• Algebraic geometry
• Elliptic curves
• Group theory
• Hodge theory
• Inter-universal Teichmller theory
• HodgeArakelov theory
• Shinichi Mochizuki
• Tate curve