1. -Anusha Uppaluri

2.  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

3.  Asymmetric cryptographic systems use  functions whose inverse is difficult to calculate.  Ex: RSA-factoring very large numbers, Diffie Helman Key exchange- discrete log problem

4. Difficulty of forward and inverse operation against key length

5.  ECC’s inverse operation gets harder much faster

6.  Elliptic curve is defined by the equation y 2 =x 3 +ax+b Elliptic curve

7.  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.

8.  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.

9. ECC compared with RSA

10.  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.

11.  http://www.deviceforge.com/articles/AT423 4154468.html http://www.deviceforge.com/articles/AT423 4154468.html  http://www.rsa.com/rsalabs/node.asp?id=20 13 http://www.rsa.com/rsalabs/node.asp?id=20 13  http://searchsecurity.techtarget.com/sDefiniti on/0,,sid14_gci784941,00.html http://searchsecurity.techtarget.com/sDefiniti on/0,,sid14_gci784941,00.html