CS-235. Problem Set 4
- Ex. 5 in Supplemental material
- Ex. 7 in Supplemental material
- Extra Credit: Ex.2.10
- Ex. 3.24 (a: assigned, b: extra credit)
- Solve the following equalities (or prove that there is no solution):
Note: "=" is used here in place of
the 3-bar "congruence" symbol
- 15x + 21 = 2 (mod 31)
- 15x + 21 = 2 (mod 33)
- 15x + 21 = 3 (mod 33)
- 15x + 21 = 2 (mod 31) AND 15x + 21 = 3 (mod 33)
[that is x must satisfy both]
- 2x+3 = 4 (mod 5) AND 4x+3=2 (mod 7) AND
8x+9=10 (mod 11)
- RSA: compute RSA public and private keys using the primes 11
and 13, and write Encrypt and Decrypt algorithms for it.
- You can pick any e,d. Test your result by encrypting and then
decrypting 1, 2, 3, 5, 10, 100.
- It is customary to fix e to be something small and always the same,
e.g., 3 or 5. What would be the corresponding d for each of these
values of e? Can you use e=4?
- Now, what would the public and secret key be if you use primes 101 and 113
Use the smallest possible value of