"start":
- Client sends S, H if this is the first round of the protocol
- Client generates r in [0, |G|[ at random
- - Client sends x = h("g^r || m || g^r")
+ - Client generates t in [0, |G|[ at random
+ - Client sends x = h("g^r || g^t || m || g^r || g^t")
- Client sends m in plain
"challenge":
- Server receives S, H if this is the first round of the protocol
- Server verifies H = h'(I(S))
- Server receives x, m
- Server generates c in [0, 2^k0[ at random
- - Server generates R in [0, |G|[ at random
- - Server sends c and g^R
+ - Server generates T in [0, |G|[ at random
+ - Server sends c and g^T
"response":
- - Client receives c and g^R
+ - Client receives c and g^T
- Client verifies that the received values are in the allowed ranges
- Client sends y = r + s * c mod |G|
- - Client calculates K = (g^R)^r
+ - Client sends g^t
+ - Client calculates K = (g^T)^t
"verify":
- - Server receives y
+ - Server receives y and g^t
- Server calculates z = g^y S^-c
- Server calculates x' = h("z || m || z")
- Server verifies x == x'
- - Server calculates K = z^R
+ - Server calculates K = (g^t)^T
Protocol variant: g and G can be also part of the public ID. In this case, g
and G are sent as part of this protocol additionally to S, H.