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252 CHAPTER 12. RSA
(b) Compute d and decipher 2024, 1553, 469, 299.
6. Decipher 498, 1, 280, 248, 143, 37, if the RSA system used P = 19,
Q = 29 and e = 13.
7. Encipher composite in three-letter blocks using the parameters P = 1223,
Q = 563 and e = 23.
8. (a) [RSA] The “Small Example” given in the original description of RSA
uses p = 27, q = 59 and d = 157. (This paper chooses d first and
then computes e.) Compute e.
(b) Using the usual translation of letters to two-digit numbers, with 00
representing a space, translate Its all greek to me into numbers.
(c) Encipher the message.
9. [Hellman] In his Scientific American paper about Knapsack Ciphers and
RSA, Hellman uses the letter-to-number translation in which a to z are 0
to 25, A to Z are 26 to 51, a space is represented by 62, and is 66.
(a) Hellman’s example message is How are you What is the numerical
equivalent
(b) Use e = 11 and N = 11023 to encipher the message in two-letter
pairs. (Hellman called these E and n.) Hint: 73 divides 11023.
(c) Find the deciphering exponent.
10. In the following examples, the sender has tried to prove his identity by
signing the message, as described in the text. Decipher the message.
(a) The message is 54, 135, 112, 112. It is to Andy (parameters P =
17, Q = 11, e = 7) from Bridget (parameters P = 19, Q = 13,
e = 5).
(b) The message is 14756, 9105, 191. It is to Alice (parameters P =
137, Q = 191, e = 7) from Bob (parameters P = 173, Q = 127,
e = 5).
11. We started the chapter by considering raising a message to the 3rd power.
That is translating letters to numbers and raising each number to the 3rd
power modulo 26. Why didn’t we instead raise 3 to the letter’s power
So, for example, e would encipher to 3 5 = 243 ≡ 9 (mod 26) = I. Would
this method produce a good cipher (Hint: encipher a couple of words
and study the outcome.)
12. Your RSA parameters are P = 67, Q = 97, e = 59 and d = 179. One day
you receive the message
5689, 3415, 347.