abhijith_dushyant_EllipticCurveCryptography

# abhijith_dushyant_EllipticCurveCryptography - ELLIPTIC...

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ELLIPTIC CURVE CRYPTOGRAPHY By Abhijith

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Introduction What are Elliptic Curves? Curve with standard form y2 = x3 + ax + b a, b ϵ ℝ Characteristics of Elliptic Curve Forms an abelian group Symmetric about the x-axis Point at Infinity acting as the identity element
Examples of Elliptic Curves

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Finite Fields aka Galois Field GF(pn) = a set of integers {0, 1, 2, …, pn -1) where p is a prime, n is a positive integer It is denoted by {F, +, x} where + and x are the group operators
Group, Ring, Field

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Why Elliptic Curve Cryptography? Shorter Key Length Lesser Computational Complexity Low Power Requirement More Secure
Comparable Key Sizes for Equivalent Security Symmetric Encryption (Key Size in bits) RSA and Diffie-Hellman (modulus size in bits) ECC Key Size in bits 56 512 112 80 1024 160 112 2048 224 128 3072 256 192 7680 384 256 15360 512

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What is Elliptic Curve Cryptography? Implementing Group Operations Main operations - point addition and point multiplication Adding two points that lie on an Elliptic Curve – results in a third point on the curve Point multiplication is repeated addition If P is a known point on the curve (aka Base point; part of domain parameters) and it is multiplied by a scalar k, Q=kP is the operation of adding P + P + P + P… +P (k times)
Adding two points on the curve P and Q are added to obtain P+Q which What is Elliptic Curve Cryptography?

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A tangent at P is extended to cut the curve at a point; its reflection is 2P Adding P and 2P gives 3P
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## This note was uploaded on 01/17/2012 for the course CIS 6930 taught by Professor Staff during the Fall '08 term at University of Florida.

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abhijith_dushyant_EllipticCurveCryptography - ELLIPTIC...

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