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Exponentiation is a heavily used operation in public key cryptography. Which of the following options is the tightest upper bound on the number of multiplications required to compute 
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Exponentiation is a heavily used operation in public key cryptography....
We need to divide
n recursively and compute like following:
  In this, we need to calculate bn/2 only once.
.
.
Recurrence relation: 
 
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Most Upvoted Answer
Exponentiation is a heavily used operation in public key cryptography....
We can use divide and conquer paradigm here as follows:

int exp(b,n,m)
{
   if(n == 0)
      return 1;
   if(n == 1)
    return b % m;
  else
  {
      int split = exp(b, n/2, m);
      if(n%2)
         return (((split * split) %m ) * n ) %m;
    else
         return (split * split ) % m;
  }
}

Here Recurrence relation would be T(n) = T(n/2) + k. On solving it we will get T(n) = 0(logn)
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Community Answer
Exponentiation is a heavily used operation in public key cryptography....
We need to divide
n recursively and compute like following:
  In this, we need to calculate bn/2 only once.
.
.
Recurrence relation: 
 
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