An Example Letp=2357,g=2,x=1751,y≡g=2751=1185 (mod2357) System parameters: (p, g)=(2357, 2) Public key: y=1185, Private key: X=1751 Encryption: Say M=2035 1. Pick a random number k=1520 2.compUtes S=g=2150=1430mod2357) Myk=2035X1185150=697(mod2357) The ciphertext C=(s, t)=(1430, 697) Decryption 1. Computes u≡Sx≡1430175≡2084(mod2357) 2M=tu1=697X2084=2035(mod2357)13 An Example • Let p =2357, g = 2, x = 1751, y  g x  2 1751  1185 (mod 2357) • System parameters: (p, g) = (2357, 2) Public key: y = 1185, Private key: x = 1751 • Encryption:say M = 2035 1.Pick a random number k = 1520 2.Computes s = gk  2 1520  1430 (mod 2357) t = Myk  2035 x 11851520  697 (mod 2357) – The ciphertext C = (s, t) = (1430, 697) • Decryption: 1.Computes u  s x  14301751  2084 (mod 2357) 2.M  t u-1  697 x 2084-1  2035 (mod 2357)