-anusha uppaluri. ecc- a set of algorithms for key generation, encryption and decryption (public...
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-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