The state-of-the-art in hyperelliptic curve cryptography Craig Costello Workshop on Curves and Applications

Source URL: www.mathtube.org

• Finite fields
• Public-key cryptography
• Cryptographic protocols
• Hyperelliptic curve cryptography
• Hyperelliptic curve
• Elliptic curve cryptography
• Diffie–Hellman key exchange
• Diffie–Hellman problem
• Abelian variety
• Cryptography
• Abstract algebra
• Algebraic curves

References [1] M. Agrawal, N. Kayal, and N. Saxena. PRIMES is in P. Ann. of Math. (2), 160(2):781–793, [removed]L. V. Ahlfors. Complex Analysis. McGraw-Hill Book Co., New York, third edition, 1978. An introduction to

Source URL: www.math.brown.edu

• Elliptic curves
• Public-key cryptography
• Elliptic curve cryptography
• NTRU
• Elliptic Curve DSA
• Lattice problem
• Counting points on elliptic curves
• Hyperelliptic curve cryptography
• Elliptic curve
• Cryptography
• Post-quantum cryptography
• Finite fields

Results from MathSciNet: Mathematical Reviews on the Web c Copyright American Mathematical Society 2005 MR2085902 11G40 11G10 Agashe, Amod (1-TX) ;

Source URL: wstein.org

• Number theory
• Elliptic curves
• Analytic number theory
• Abelian varieties
• Diophantine geometry
• Birch and Swinnerton-Dyer conjecture
• Tate–Shafarevich group
• Modular form
• Arithmetic of abelian varieties
• Abstract algebra
• Mathematics
• Algebraic geometry

References [1] Bernardi, D., Perrin-Riou, B.: Variante p-adique de la conjecture de Birch et Swinnerton-Dyer (le cas supersingulier). C. R. Acad. Sci. Paris S´er. I Math[removed]), no. 3, 227–[removed]Besser, A.: Th

Source URL: www.math.sci.osaka-u.ac.jp

• Elliptic curves
• Field theory
• Algebraic geometry
• Algebraic number theory
• P-adic number
• Birch and Swinnerton-Dyer conjecture
• P-adic L-function
• Néron–Tate height
• Iwasawa theory
• Abstract algebra
• Mathematics
• Number theory

Numerical computation of Chow-Heegner points associated to pairs of elliptic curves∗† William Stein February 5, 2012 Abstract

Source URL: wstein.org

• Group theory
• Algebraic number theory
• Heegner point
• Algebraic curve
• Finite fields
• Abstract algebra
• Elliptic curves
• Analytic number theory

Elliptic Curves and Hilbert’s Twelfth Problem Henri Darmon Britton Lectures, McMaster University, November 2013

Source URL: www.math.mcmaster.ca

• Algebraic number theory
• Dirichlet character
• Class number formula
• Dirichlet L-function
• Number theory
• Explicit formula
• Galois group
• Johann Peter Gustav Lejeune Dirichlet
• Generalized Riemann hypothesis
• Abstract algebra
• Mathematics
• Algebra

LECTURE 2. ELLIPTIC CURVES AND THE BIRCH AND SWINNERTON-DYER CONJECTURE Abstract: The second lecture extends some of the themes explored in the first to the setting of elliptic curves, where it becomes important to repla

Source URL: www.math.mcmaster.ca

9th Central European Conference on Cryptography - Tˇ reb´ıˇ c’09

Source URL: conf.fme.vutbr.cz

• Algebraic curves
• Group theory
• Cryptography
• Finite fields
• Hyperelliptic curve cryptography
• Public-key cryptography
• Imaginary hyperelliptic curve
• Real hyperelliptic curve
• Elliptic curve cryptography
• Abstract algebra
• Algebra
• Mathematics

Explicit approaches to modular abelian varieties by William Arthur Stein

Source URL: wstein.org

• Modular forms
• Number theory
• Analytic number theory
• Algebraic curves
• Diophantine geometry
• Hecke operator
• Tate–Shafarevich group
• Elliptic curve
• Birch and Swinnerton-Dyer conjecture
• Abstract algebra
• Mathematics
• Algebraic geometry

Abelian Varieties J.S. Milne

Source URL: www.jmilne.org

• Abelian varieties
• Diophantine geometry
• Algebraic curves
• Elliptic curves
• Néron–Tate height
• Mordell–Weil theorem
• Weil pairing
• Algebraic variety
• Arithmetic of abelian varieties
• Abstract algebra
• Algebraic geometry
• Algebra