Public key crypto at toy security levels $[$note: the numbers here are small, but you will likely need to do a little bit of programming, or use an online calculator$]$ a$.$ Suppose Alice and Bob agree to use p$=10007$ and g$=3$ as public parameters i$.$ What is the order of g modulo p$?$ ii$.$ For Shamir$$s Three$-$Pass protocol, Alice wants to send the message m$=1337.$ She uses a temporary key a$=2461$ and Bob uses a temporary key b$=4319.$ What are a $-1$ and b $-1$ mod p$-1?$ What are the three values transmitted to send m from Alice to Bob? iii. For a Diffie$-$Hellman key exchange, Alice chooses a $=2461$ and Bob chooses b$=4319.$ What will their shared secret be$?$