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.
    1. Find an inverse of 19 mod 141.
    2. Use part (a) to solve the congruence 19x ≡ 4 mod 141.

  2. Compute 351 (mod 65).

  3. Problem 9.51 from the text.

  4. Problem 9.58 from the text.

  5. Problem 9.77 from the text.

  6. Problem 9.79 from the text.

  7. 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.

  8. 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?

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