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One major drawback of public-key algorithms is that they are relatively slow.

In Sect. 7.5.1 we learned that an acceleration technique is to use short exponents /e/.

Now we study short exponents in this problem in more detail.

1. Assume that in an implementation of the RSA cryptosystem one modular squaring

takes 75% of the time of a modular multiplication. How much quicker is

one encryption on average if instead of a 2048-bit public key the short exponent

/e/=216+1 is used? Assume that the square-and-multiply algorithm is being used

in both cases.

2. Most short exponents are of the form /e/ = 2/n/ +1. Would it be advantageous to

use exponents of the form 2/n?/1? Justify your answer.

3. Compute the exponentiation /xe/ mod 29 of /x/ = 5 with both variants of /e/ from

above for /n/ = 4. Use the square-and-multiply algorithm and show each step of

your computation.