Question

2. Write the following methods for the NodeTransitionFunction class. public NodeTransitionFunction (Integer exp, Integer KVal) 1t // CONSTUCTOR: Sets the class to calculate f (x) = (x ^ exp) mod KVal public Integer apply (Integer val) // PRE: //POST Implements f (val) Note that if you implement apply) in a straightforward way, you will almost certainly exceed Java's Integer.MAX_VALUE: try it for yourself with an instance of NodeTransitionFunction instantiated with values 3 and 33, comparing it against the value obtained from e.g. a spreads Instead, there is a useful identity that lets you make the calculation without this risk: (ab) mod p ((a mod p) (b mod p)) mod p Implement apply) using this identity. 3. Implement a constructor for class Node with the following signature: public Node (Integer n, Integer e, Integer d, Integer K, Boolean encrypt, Boolean useBI, Map<Integer,Node> , MessageTrackCheck t) //CONSTUCTOR n is node ID, e is the exponent for the function fO d is the exponent for the function gO K is the divisor in f) and gC) encrypt is true if messages are encrypted, false otherwise useBI is true if BigInteger should be used for NodeTransitionFunction, false otherwise m is a non-null map of node IDs to node objects t is an instance of MessageTrackCheck For the Pass level, encrypt and useBI will be set to false. The parameters e, d and K here correspond to the e, d, K from $2.2

Answer 1

NodeTransitionFunction(int exp, int KVal){
       this.exp = exp;
       this.KVal = KVal;
   }

//idea is if the exp is even we square the val and make exp = exp / 2

// otherwise we decrease exp by 1 and multiply the val with ans

int apply(int val){
       int ans = 1;
       int e = exp;
       while(e != 0){
           if(e % 2 == 0){
                val = (val * val) % KVal;
                e = e / 2;
           }
           else{
                ans = (ans * val) % KVal;
                e--;
           }
       }
       return ans;
   }

Q3)

   Node(int n, int e, int d, int k, boolean encrypt, boolean useBI, Map<Integer, Node> m, MessageTrackCheck t){
       this.n = n;
       this.e = e;
       this.d = d;
       this.k = k;
       this.encrypt = encrypt;
       this.useBI = useBI;
       this.m = m;
       this.t = t;
   }