Computer Science homework help

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Computer Science homework help.

QUESTION 1

  1. Reformulate Equation (2.1), removing the restriction that ais a nonnegative integer. That is, let a be any integer.

QUESTION 2

  1. For each of the following equations, find an integer x that satisfies the equation.
  2. a) 5x ≡4 (mod 3) answer?
  3. b) 7x ≡6 (mod 5) answer?
  4. c) 9x ≡8 (mod 7) answer?

QUESTION 3

  1. Determine the GCD of the following;
  2. a) gcd(24140, 16762) answer?
  3. b) gcd(4655, 12075) answer?

QUESTION 4

  1. Using Fermat’s theorem to find a number xbetween 0 and 28 with x85congruent to 6 modulo 29. (You should not need to use any brute-force searching.)

QUESTION 5

  1. Use Euler’s theorem to find a number abetween 0 and 9 such that ais congruent to 71000 modulo 10. (Note: This is the same as the last digit of the decimal expansion of 71000).

QUESTION 6

  1. Prove the following:

If p is prime, then φ(p1) = pi – pi-1. Hint: What numbers have a factor in common

QUESTION 7

  1. Six professors begin courses on Monday, Tuesday, Wednesday, Thursday, Friday,and Saturday, respectively, and announce their intentions of lecturing at intervals of 2, 3, 4, 1, 6, and 5 days, respectively. Theregulations of the university forbid Sunday lectures (so that a Sunday lecture must be omitted). When first will all six professors find themselves compelled to omit a lecture? Hint: Use the CRT.
  2. Welcome to Week 2.
  3. This week we are going to be looking at Chapter 2 in our text and delving into number theory, which is pervasive in cryptographic algorithms.
  4. The first three sections of Chapter 2 introduce basic concepts from number theory that are needed for understanding finite fields; these include divisibility, the Euclidianalgorithm, and modular arithmetic. Going over these sections now will set a foundation, but feel free to return and revisit these sections as we get ready to tackle Chapter 5 on finite fields.
  5. Sections 2.4 through 2.8 discuss aspects of number theory related to prime numbers and discrete logarithms. These topics are fundamental to the design of asymmetric (public-key) cryptographic algorithms. Again, you may want to return to these sections as we approach Chapters 9 and 10.
  6. In addition to your reading assignment for this week, we have a set of exercises to help reinforce the applications of the principles that we are discussing. These exercises come out of the problems at the end of the chapter, and you can feel free to work them out of your book if you are more comfortable. Once you have the solutions, just insert your answers into the Exercise 2 quiz and submit. These are set up as quizzes for simplicity and to allow you to continue to rework as needed up to the due date on Sunday. There is no time limit and you can rework your answers as many times as you like up to the due date.
  7. If you have any questions, please reach out to me and we will work through them.

Lacture Chapter 2
https://s3.us-east-1.amazonaws.com/blackboard.learn.xythos.prod/5a31b16bb2c48/7836486?response-content-disposition=inline%3B%20filename%2A%3DUTF-8%27%272020-05-03%2520-%252002.mp4&response-content-type=video%2Fmp4&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Date=20200513T194728Z&X-Amz-SignedHeaders=host&X-Amz-Expires=21600&X-Amz-Credential=AKIAIL7WQYDOOHAZJGWQ%2F20200513%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Signature=7d232dd083c4beccb986b0b05d85df51938dd2a6cfa50de48f956352646a3810
Use this test form to submit your answers for this week’s exercises. Answers may be submitted and reworked multiple times leading up to the due date.

Computer Science homework help