RSA exercises: Answers
Answer the following questions, and show some of your computations:
1. You are a receiver with p = 5, q = 7. You make the modulus m = 35
public.
You also choose the exponent e = 5 and make that public.
Messages to you come one letter at a time. Letters correspond to
numbers as usual (A ↔ 0, B ↔ 1, and so forth).
The following message comes for you:
17 19 7 9 0 12 24
Decode it.
ANSWER: First you need to find d = e−1 mod n, where n = (p −
1)(q − 1). Thus d = 5. Then raise each number to the power d and
reduce mod m. For example, 17d mod m ≡ 175 mod 35 ≡ 12, which
is the letter M. The whole plaintext turns out to be:
M Y H E A R T
2. Bob’s modulus m is 15 and his exponent e is 3. Send him the
message
A C H E A N D
(Even though the modulus is 15, and this is less than 26, the above
letters all have numbers below 15.)
ANSWER: Each letter needs to be raised to the power e = 3 and
reduced mod m = 15. Thus the first plaintext letter A corresponds to
the number zero, and 03 mod 15 ≡ 0. The second plaintext letter C
is the number 2, and 23 mod 15 ≡ 8. The full answer is:
0 8 13 4 0 7 12
3. (Show your erudition–not required) The above two messages are the
first words of a famous poem. What is it? (I’ve dropped one letter in
the text to make this cipher work. Which letter is this?)
ANSWER: Well, do you know what this is??
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