- 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
α
^{b}=2^{5}= 10.Have public key (n,α,α^{b}) = (10,2,10) and private key b = 5. - Alice chooses k = 7 and calculates α
^{k}= 2^{7}= 7. - Alice looks up α
^{b}= 10 and encodes message as m = 3 then calculates m(α^{b})^{k}= 3 * 10^{7}= 8. - Alice sends (α
^{k},mα^{bk}) = (7,8). - Bob Calculates mα
^{bk}((α^{k})^{b})^{-1}= 8(7^{5})^{-1}= 3. - Thus Bob receives the message, 3, as sent by Alice

## 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.

Labels:
ElGamal
,
ElGamal example
,
GF(11)
,
GF(11) filed

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