The challenge c in Sigma protocol (using Fiat Shamir) As is known to all, the following picture depicts a sigma protocol, and to eliminate the interactivity, Prover can generate c by hashing (t, y) using Fiat Shamir transform. My question is:
1). Can c be obtained as hash(0x1234, 0x4321) by the Prover, (where 0x1234, 0x4321 are public parameters at setup)?
2). If above answer is yes, can a same c be used by different Provers at the same time in Fiat Shamir transform?
No. Since 0x1234, 0x4321 is public and thus known ahead of the execution, the prover knows the challenge c before sending t. This violet the requirement of the sigma protocol: c is sent to P after t is received.