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Mohamed G. Gouda                                     Network Protocol Security
CS 395T                                              MT2 Solution
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1. 

This protocol is based on dr=0 and dl < k.

process p

const k  : integer,
      dl : integer
var   sk : integer,
      x  : integer
      s  : 0 .. k-1,
      m  : integer

begin
   true ->  x := any;
            m := MD.(x|s|sk);
            send data(x,s,m) to q;
            s := s+1 mod k;
            if s=0  -> sk := MD.(sk)
            [] s!=0 -> skip
            fi
end

process q

const k      : integer,      /k.q=k.p
      dl     : integer       /dl.q=dl.p < k.p
var   sk, tk : integer,      /init. sk.q=sk.p
      x      : integer,
      exp, s : 0 .. k-1,     /init. exp.q=s.p=0
      m      : integer

begin
   rcv data(x,s,m) from p ->
       if exp>s  -> tk := MD.(sk)
       [] exp<=s -> tk := sk
       fi;
       if m!= MD.(x|s|tk) -> skip /not fresh
       [] m = MD.(x|s|tk) -> /fresh
                             sk := tk;
                             exp := s+1 mod k;
                             if exp=0  -> sk := MD.(sk)
                             [] exp!=0 -> skip
                             fi
       fi
end

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2.

C -> ac : C1, S
ac -> C : I.C1<sk, S, I.S<sk, S>>
C -> S  : I.S<sk, S>, C2, m
C <- S  : sk<password?, m>, n
C -> S  : sk<P, n>

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