-Anusha Uppaluri.  ECC- A set of algorithms for key generation, encryption and decryption (public key encryption technique)  ECC was introduced by Victor.

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Presentation transcript:

-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 y 2 =x 3 +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.

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