-Anusha Uppaluri

ECC- A set of algorithms for key generation, encryption and decryption (public key encryption technique)

ECC was introduced by Victor Miller and Neal Koblitz in 1985

Good alternative to other asymmetric cryptography algorithms Greater security for a given key size Smaller key size= more compact

implementations

Is related to discrete logarithm cryptography

Asymmetric cryptographic systems use functions whose inverse is difficult to

calculate. Ex: RSA-factoring very large numbers, Diffie

Helman Key exchange- discrete log problem

Difficulty of forward and inverse operation against key length

ECC’s inverse operation gets harder much faster

Elliptic curve is defined by the equation y2=x3+ax+b

Elliptic curve

Consider a very large prime number P, a square graph PxP in size.

Define an elliptic curve satisfying the above equation.

Considering the points (x,y) on the curve a group which is a subset of all the points on the graph is created.

Point multiplication is the critical operation used: calculate kP where k is an integer and P is a point on curve.

Discrete Logarithm Problem is the inverse of point multiplication: given points Q,P find k such that Q=kP

Pollard’s rho attack is the best possible attack on ECC

Pollard’s rho attack gets lot harder much faster with increase in key size.

ECC compared with RSA

Smaller ECC keys implies – cryptographic operations in fewer processor cycles, faster operations, less power consumed, lower memory demands

Ideal for portable devices Few cases wherein elliptical curve

discrete logarithm problem becomes vulnerable to subexponential techniques.

http://www.deviceforge.com/articles/AT4234154468.html

http://www.rsa.com/rsalabs/node.asp?id=2013

http://searchsecurity.techtarget.com/sDefinition/0,,sid14_gci784941,00.html