Public key cryptography using discrete logarithms

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 Example 13 points in total An Example to compute doubling ElGamal encryption and decryption using elliptic curve