ElGamal Signature

1
ElGamal Signature
p prime, g generator of Fp, a secret
exponent, A ga mod p.
p,g,A public key, a secret key, h 0,1 -gt
1,2,.. , p-1 hash function M message in 0,1
Signing (1) Generate a random number k in
1,2,..,p-2 (2) r gk mod p, s
k-1 (h(M) ar) mod p-1).
Verification(1) Check 0 lt r lt p.
(2) Check Ar rs gh(M) mod p.
Correctness of the verification Ar rs gar
gkk-1(h(M)-ar) gh(M) mod p.
2
Some Unsigned Addition Chains trade-off
efficiency memory
Efficiency
Additional Memory Targets
Binary method 1.5 n
---- general purpose 2k-ary
method (k2) 1.375 n 2 points
no memory constraint 2k-ary method (k3)
1.292 n 6 points no
memory constraint Sliding window (k2) 1.333
n 1 points no memory
constraint Sliding window (k3) 1.25 n
3 points no memory constraint
Lim-Lee (2 bases) 0.875 n 1
points (off-line) fixed base Walter method
1.25 n 1 register small
fixed exponent