abhijith_dushyant_EllipticCurveCryptography

abhijith_dushyant_EllipticCurveCryptography - By Abhijith...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
By Abhijith Chandrashekar and Dushyant Maheshwary
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Introduction What are Elliptic Curves? Curve with standard form y 2 = x 3 + ax + b a, b ϵ Characteristics of Elliptic Curve Forms an abelian group Symmetric about the x-axis Point at Infinity acting as the identity element
Background image of page 2
Examples of Elliptic Curves
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Finite Fields aka Galois Field GF(p n ) = a set of integers {0, 1, 2, …, p n -1) where p is a prime, n is a positive integer It is denoted by {F, +, x} where + and x are the group operators
Background image of page 4
Group, Ring, Field
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Why Elliptic Curve Cryptography? Shorter Key Length Lesser Computational Complexity Low Power Requirement More Secure
Background image of page 6
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
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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) Q is the resulting public key and k is the private key in the public-private key pair
Background image of page 8
Adding two points on the curve P and Q are added to obtain P+Q which is a reflection of R along the X axis What is Elliptic Curve Cryptography?
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
A tangent at P is extended to cut the curve at a point; its reflection is 2P Adding P and 2P gives 3P Similarly, such operations can be performed as many times as desired to obtain Q = kP What is Elliptic Curve Cryptography?
Background image of page 10
What is Elliptic Curve Cryptography? Discrete Log Problem
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 23

abhijith_dushyant_EllipticCurveCryptography - By Abhijith...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online