Question: Design a protocol in which 3 parties A, B, C share one cryptographic secret but you must satisfy these constraints: 1. A chooses a prime

Design a protocol in which 3 parties A, B, C share one cryptographic secret but you must satisfy these constraints:

1. A chooses a prime for B, PB, and a prime for C, PC. A also chooses a generator for B, gB, and a generator for C, gC.

2. A does two separate diffie-hellman key exchanges: one with B and another with C.

3. A chooses secret key a1 and a2 and B choose secret key b and C chooses secret key c.

A and B share a secret key that is gBa1*bmod PB and A and C share a secret key of gCa2*cmod PC.

Continue this protocol until it is complete, such that the above secrets are used.

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