Tuesday, May 1, 2012

ElGamal example over GF(11) field

 This very simple example of ElGamal with small field. It's highly recommended that use large fields.
  • Our group is GF(11) = {1,2,3,4,5,6,7,8,9,10}
  • Lets take n = 10 and  α = 2. Bob randomly select b = 5 then αb =25 = 10.Have public key (n,α,αb) = (10,2,10) and private key b = 5.
  • Alice chooses k = 7 and calculates αk = 27 = 7.
  • Alice looks up αb = 10 and encodes message as m = 3 then calculates           m(αb)k = 3 * 107 = 8.
  • Alice sends (αk,mαbk) = (7,8).
  • Bob Calculates mαbk((αk)b)-1 = 8(75)-1 = 3.
  • Thus Bob receives the message, 3, as sent by Alice
You need some idea about finite fields and modular arithmetic

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