Question

Suppose we use p = 7 and q = 5 to generate keys for RSA.

a) What is n ? ___________________

b) What is φ(n) ? _______________________

c) One choice of e is 5. What are the other choices for e? _________________________________________________________________________________  

d) Explain how you got your answer for part c.  

e) For the choice of e = 5 what is d? _________________________ Show work.

f) Using the public key (n, e), what is the message 3 encrypted as? _____________________Show work as if not using a calculator.

g) Show that your result for part f decrypts back to 3, using the private key (n, d). Show work as if not using a calculator.

h) Suppose you know only the public key (n,e) and want to figure out the private key. Explain how you can do it in the case of our value for n. Why doesn't this work for very large values of n?

Here is a hint for doing calculations (mod n): Sometimes it's better to replace a big number by a negative number that it's congruent to (mod n). For example if the number is 48 and you are doing calculations (mod 50) then it's probably better to work with -2 since that's smaller in absolute value than 48 and it's congruent to 48 (mod 50)..

Answer 1