Florida Atlantic University...Elliptic curves, generic curves, Montgomery curves, Edwards curves,...

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Transcript of Florida Atlantic University...Elliptic curves, generic curves, Montgomery curves, Edwards curves,...

Page 1: Florida Atlantic University...Elliptic curves, generic curves, Montgomery curves, Edwards curves, Hassian and Huff curves. Implementations of Elliptic Curve Cryptography over prime
Page 2: Florida Atlantic University...Elliptic curves, generic curves, Montgomery curves, Edwards curves, Hassian and Huff curves. Implementations of Elliptic Curve Cryptography over prime
Page 3: Florida Atlantic University...Elliptic curves, generic curves, Montgomery curves, Edwards curves, Hassian and Huff curves. Implementations of Elliptic Curve Cryptography over prime
Page 4: Florida Atlantic University...Elliptic curves, generic curves, Montgomery curves, Edwards curves, Hassian and Huff curves. Implementations of Elliptic Curve Cryptography over prime
Page 5: Florida Atlantic University...Elliptic curves, generic curves, Montgomery curves, Edwards curves, Hassian and Huff curves. Implementations of Elliptic Curve Cryptography over prime
Page 6: Florida Atlantic University...Elliptic curves, generic curves, Montgomery curves, Edwards curves, Hassian and Huff curves. Implementations of Elliptic Curve Cryptography over prime

Key Management and Elliptic Curves

Key Management and Elliptic Curves

Discrete Logarithms on Elliptic Curves

Discrete Logarithms on Elliptic Curves

1 Elliptic curves cryptography CHAPTER 8: Elliptic Curves Cryptography and factorization Cryptography based on manipulation of points of so called elliptic.

1 Elliptic curves cryptography CHAPTER 8: Elliptic Curves Cryptography and factorization Cryptography based on manipulation of points of so called elliptic.

Rational points on elliptic curves

Rational points on elliptic curves

Torsion Points on Elliptic curves

Torsion Points on Elliptic curves

Applications of elliptic curves in public key cryptographyEHU-UPV20110516-20AD.pdf1. Public Key Cryptography 2. Elliptic curves over the rationals 3. Elliptic curves over finite fields

Applications of elliptic curves in public key cryptographyEHU-UPV20110516-20AD.pdf1. Public Key Cryptography 2. Elliptic curves over the rationals 3. Elliptic curves over finite fields

Elliptic Curves 2

Elliptic Curves 2

CONTROL THEOREMS FOR ELLIPTIC CURVES

CONTROL THEOREMS FOR ELLIPTIC CURVES

Elliptic Curves in Cryptography

Elliptic Curves in Cryptography

Moduli Spaces of Elliptic Curves

Moduli Spaces of Elliptic Curves

Primality Testing Using Elliptic Curves

Primality Testing Using Elliptic Curves

ELLIPTIC CURVES, RANK IN FAMILIES AND RANDOMkowalski/elliptic-curves-families.pdf · ELLIPTIC CURVES, RANK IN FAMILIES AND RANDOM MATRICES E. KOWALSKI This survey paper contains two

ELLIPTIC CURVES, RANK IN FAMILIES AND RANDOMkowalski/elliptic-curves-families.pdf · ELLIPTIC CURVES, RANK IN FAMILIES AND RANDOM MATRICES E. KOWALSKI This survey paper contains two

Elliptic Curves and Elliptic Curve Cryptography

Elliptic Curves and Elliptic Curve Cryptography

Introduction To Elliptic Curves - uni-heidelberg.dehb3/publ/pseoul.pdfThe torsion subgroup of elliptic curves de ned over Q can be computed using pari. Elliptic curves are described

Introduction To Elliptic Curves - uni-heidelberg.dehb3/publ/pseoul.pdfThe torsion subgroup of elliptic curves de ned over Q can be computed using pari. Elliptic curves are described

Elliptic Curves and Mordell's Theorem...rational points for a class of cubic curves (elliptic curves) Aurash Vatan, Andrew Yao (MIT PRIMES) Elliptic Curves and Mordell’s Theorem

Elliptic Curves and Mordell's Theorem...rational points for a class of cubic curves (elliptic curves) Aurash Vatan, Andrew Yao (MIT PRIMES) Elliptic Curves and Mordell’s Theorem

Elliptic Curves - University of Washington

Elliptic Curves - University of Washington

Theory of Elliptic Curves

Theory of Elliptic Curves

J.S. Milne: Elliptic Curves

J.S. Milne: Elliptic Curves

Elliptic Curves - staff.science.uu.nl

Elliptic Curves - staff.science.uu.nl

ELLIPTIC CURVES - tomlr.free.frtomlr.free.fr/.../Elliptic%20Curves%20... · ELLIPTIC CURVES 1 Introduction An elliptic curve over a field k is a nonsingular complete curve of genus

ELLIPTIC CURVES - tomlr.free.frtomlr.free.fr/.../Elliptic%20Curves%20... · ELLIPTIC CURVES 1 Introduction An elliptic curve over a field k is a nonsingular complete curve of genus