My niece in the United States, because the outbreak has not been in class, self-study at home, now have the title of the algorithm does not assembly, want to hand in on Friday morning, a great god help solve, thank you,

Assume that a, b both sides agreed to by publicly readable Internet communication,
Anyone can pretend to be someone else, A and B (in advance) agree on A large prime number p
Public, so it's not a secret), and two secret number a and b ∈ Zp (a, b are only a and b), the
Define a hash function x7 - h (x)=ax + b mod p,
When A to B sends A message (we assume by ASCII coding for integer x< them; P), A
Send the message and verify v x=ax + b mod p.b x convinced himself that the message has been sent
By verifying h (x)=v,
? Now imagine an evil entity C want to send message disguised as A and B (x0, where v0) (
X0=x 6), assuming that saw the legitimate messages from a to B C (x, v), if you don't know secret a and C
Define the hash function b (even if they know the hash function and the form of prime number p), prove that
C can't cheat believe the news (x0, where v0) from A send (you proved
C can send right where v0 is 1/p)
? Now suppose C intercepted two messages from A to B, in the form of (x, v) and (y, w), according to the C
Can now be pretending to be A, by attaching the correct where v0 pretending to be the was to persuade B accept any message x0
From A sending,
? Suggest change a and B prior consent communication solution method, to allow the
Most rivals C can be intercepted two pieces of information,
The bonus (:) at most k intercepted information?