ELLIPTICAL CURVE CRYPTOGRAPHY

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ELLIPTICAL CURVE CRYPTOGRAPHY

• -Anusha Uppaluri

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• 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

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

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Difficulty of forward and inverse operation
against key length
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• ECCs inverse operation gets harder much faster

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What is ECC?

• Elliptic curve is defined by the equation
• y2x3axb

Elliptic curve
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• 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.

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• Discrete Logarithm Problem is the inverse of
  point multiplication given points Q,P find k
  such that QkP
• Pollards rho attack is the best possible attack
  on ECC
• Pollards rho attack gets lot harder much faster
  with increase in key size.

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ECC compared with RSA
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• 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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References

• http//www.deviceforge.com/articles/AT4234154468.h
  tml
• http//www.rsa.com/rsalabs/node.asp?id2013
• http//searchsecurity.techtarget.com/sDefinition/0
  ,,sid14_gci784941,00.html

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Questions?