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, P_B, and a prime for C, P_C. A also chooses a generator for B, g_B, and a generator for C, g_C.

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 g_B^a₁*bmod P_B and A and C share a secret key of g_C^a₂*cmod P_C.

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