Public key cryptography using discrete logarithms

Public key cryptography using discrete logarithms... Multiplicative cyclic group• Let G be a finite multiplicative group... Algorithms for the DLP• Shank • Pollard Rho • Pohlig-Hellman •

Public key cryptography using

discrete logarithms

Multiplicative cyclic group

• Let G be a finite multiplicative group.

• For α having order n in G We define

• Example:

– G: the multiplicative group a finite field

DLP

Algorithms for the DLP

• Shank

• Pollard Rho

• Pohlig-Hellman

•• Index Calculus

Elliptic curves

Elliptic curve over the Reals

Group properties

Elliptic curves modulo a Prime

13

points

in total

An Example to compute doubling

ElGamal encryption and decryption

using elliptic curve