Schnorr’s interactive ZKP

The protocol that we saw in the previous section is a non-interactive protocol, where Peggy and Victor don’t interact with each other but there is simply a commitment between them. The commitment is that Peggy shows Victor that she knows the message [m] without revealing anything about it. Thus, she tries to demonstrate to Victor that she can overcome the RSA problem (or another hard mathematical problem) as proof of her honesty. However, we have also seen that this protocol can be bypassed using a mathematical trick.

Let’s see whether the following interactive ZKP is more robust and can prevent possibly devastating attacks.

We always have Peggy and Victor as our main actors. So let’s assume the following:

• p is a big prime number.
• g is the generator of (Zp).
• is the public parameter of Peggy.
• (p, g, B) are public parameters.
• [a] is the secret number object of the commitment.

Peggy...