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178 INTERNET SECURITY
The ElGamal authentication scheme is shown in Figure 5.6. The ElGamal authentication
algorithm given in Table 5.7 is illustrated by the following example.
Example 5.10 Take the finite field GF(11). Then the set of primitive elements of GF(11)
is {2, 6, 7, 8}. Choose a primitive element g = 7 from the set. Define the public key
m
Private
key
x
gx
g
u ≡ g m (mod p)
(g x ) u
Extended
euclidean
algorithm
c ≡ xu + mv
v
u v
c
c − xu
Inverse
v −1
A ≡ (g x ) u u v (mod p)
Figure 5.6 The ElGamal authentication scheme.
Table 5.7 ElGamal authentication algorithm
Sender
Receiver
Verifying:
p (a prime integer)
g