Big-O notation; Algorithms with numbers Homework 2 Solution

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Description

As announced at the end of class on Wednesday, August 31, Problem #4 is being removed from this assignment and will be included on Homework #3.

Solve the following problems:

0.1 (9 points) You do not need to show any work for this problem: just give your answer for each part.

1.13 (5 points) Show your work and support your answer. (Hint: Use Fermat’s Little Theorem to determine what the two numbers are modulo 31. Note that 30,000 = 30 ∙ 1,000. Use long division to find 123,456 mod 30.)

Problem #3 (Programming problem; 6 points) Using the programming language of your choice, implement and test the modular exponentiation algorithm from page 19. Use your program to compute 211 mod 10. What answer did you get? (Write it on your homework submission.) Also, upload your program through Canvas.

Problem #4 (Calculation problem; 5 points) For this problem, you are free to use the modular exponentiation program that you wrote for Problem #3. Consider the RSA algorithm from Section 1.4.2.

Suppose Bob chooses p = 131, q = 137, and e = 3.

What is Bob’s public modulus N?

What is Bob’s secret exponent d?

Suppose Alice wishes to send Bob the message x = 36.

Derive the encoded message y that she actually sends.

Show the calculations by which Bob decodes the message.