HW 6: Number Theory
Introduction
In this homework you will gain practice with finding modular
inverses, computing powers using repeated squaring and Euler's
Theorem, and working with RSA encryption.
Exercises
Your solutions to these exercises should be typed up in LaTeX.
- Find an inverse of 19 mod 141.
- Use part (a) to solve the congruence 19x ≡ 4 mod
141.
- Compute 351 (mod 65).
- Problem 9.51 from the text.
- Problem 9.58 from the text.
- Problem 9.77 from the text.
- Problem 9.79 from the text.
- What is the ciphertext that is produced when the RSA cipher
with key (n,e) = (2669, 3) is used to encrypt the message THEY
PASSED? Use the letter-to-number translation as A=1,B=2, etc, and
encrypt groups of 2 letters at a time.
- If the ciphertext message produced by the RSA cipher with key
(n,e) = (2747, 13) is 2206 0755 0436 1165 1737, what is the
original message?
Submit
When you are done, submit the .pdf
file on
Moodle.