I have a problem that I don't know how to solve
Assume that H is a cryptographic hash function with output size 80 bits. Assume that ABC123 is a specifically designed line of hardware chips for computing H. where ABC123 can create 10000 hash values a second. This product line is the best, fastest and affordable, in the market, priced at 1000$. Consider the following Bit-Commitment protocol which is used for applications in betting in football matches.
- A create R1 and R2 as 2 random binary strings with length 48 bits and 40 bits, respectively
- A send host B: M = H(R1 || R2 || b) || R1
- To announce bit b, A send host B: (R2, b) (b is a bit, 0 or 1, that A choose indicate that a football team win or lose, for simplify)
- B check validity by re-hashing H(R1 || R2 || b) and comparing with the value received from step 2
Question: how much money the host B has to invest in order to correctly guess b in 5 minutes?
Thank you very much. Any help is appreciated!