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ELLIPTICAL CURVE CRYPTOGRAPHY

ELLIPTICAL CURVE CRYPTOGRAPHY. -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

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ELLIPTICAL CURVE CRYPTOGRAPHY

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  1. ELLIPTICAL CURVE CRYPTOGRAPHY -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. What is ECC? • Elliptic curve is defined by the equation y2=x3+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. References • 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

  12. Questions?

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