29-07-2011, 02:29 PM
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CRYPTOGRAPHY
Science of securely transmitting information, such that nobody but the intended recipient may understand its content.
Two basic encryption algorithms:
Private key cryptography
Public key cryptography
CRYPTOGRAPHIC GOALS
Authentication: Allowing the recipient of information to determine its origin.
Data integrity: A condition in which data has not been altered or destroyed in an unauthorized manner.
Confidentiality: Provided by encryption.
ELLIPTICAL CURVE CRYPTOGRAPHY(ECC)
Introduced by Victor Miller and Neal Koblitz in 1985.
Alternative to RSA ,DSA and other forms of algorithm.
ECC- Public key cryptography.
4. Same security level with small key.
5. Digital Image and data encryption using ECC.
ECC –based on Elliptic curve algorithms over the points on an elliptic curve.
Security of ECC depends on difficulty of ECDLP(Elliptic Curve Discrete Logarithmic Process).
Mathematical operation of ECC is defined over the elliptical curve ,
y^2=x^3+ax+b where 4a^3+27b^2≠ 0
Values of ‘a’ and ‘b’ gives different elliptic curve.
For the representation of the curves , the notation E[GF(q)] can be used.
E equation , y^2=x^3+ax+b
q prime number
GF Galois Field
For application of cryptography finite fields of ‘q’ elements are considered.
