## Introduction to Cryptography CSCI-462-01, Fall 2020

In all cases show the details of your work, and give brief reasons for your answers. The homeworks are due in pdf format on myCourses. Convert to single pdf before submission, submit just one pdf file for each assignment.

### Assignment 1, due Tuesday, September 1

Warm-up assignment:
Solve problems 1.2, 1.3, 1.4 from chapter 1, pages 24-25.

### Assignment 2, due Tuesday, September 15

1. Easy mod. Solve problems 5, 6, 7, 8 from chapter 1 (i.e. 1.5, 1.6, etc.), pages 25-26.
2. More warm up. Solve problems 11, 13 from chapter 1, pages 26-27.
3. Some work. Solve problems 4, 5, 6 from chapter 2, pages 52-53.
4. Some more work. Solve problems 8, 10 from chapter 2, pages 53-54.

### Assignment 3, due Thursday, September 24

1. Solve problems 1, 2, 7, 12 from chapter 3, pages 83-86.
2. Solve problems 3, 4, 10 from chapter 3, pages 83-86.

### Assignment 4, due Sunday, October 4

Show the details of your work.
1. Solve exercises 4, 5 and 6 from chapter 4, page 118.
2. Find all irreducible polynomials in Z2[x] of degree 4.
3. Which of the following polynomials are reducible in Z2[x]: x5 + x4 + 1, x5 + x3 + 1, x5 + x4 + x2 + 1? If reducible, then show factors.
4. Find all irreducible monic polynomials (with the leading coefficient at x2 equal to 1) in Z5[x] of degree 2.
5. Compute 10011001*10001001 in GF(256), using the AES irreducible polynomial.
6. Solve problems 13.1, 14, 16, 17 from chapter 4, pages 120-121 (this is the complete page 121 from the textbook, some places on the web show only one of the problems 16 and 17).

### Assignment 5, due Tuesday, October 27

Show the details of your work.
1. Solve problems 2, 4 from chapter 6, page 170.
2. Solve problems 5, 6 from chapter 6, pages 170-171.
3. Trace the execution of the Extended Euclid Algorithm, as in example 6.6 page 163, for gcd(333,776). Find the mutual multiplicative inverses of 333 and 776 in their respective canonical intervals.
4. Find the value of the Euler totient function φ(n), for n = 829, 831, 833, 834, 835, 836 and 837. Show the details of computations.

### Assignment 6, due Tuesday, November 10

Show the details of your work.
1. Solve problems 1, 2, 4, 6, 7 from chapter 7, page 200.
2. Solve problems 11 and 13 from chapter 7, pages 201-202.
3. Read, understand and think about problems 10, 12, 14, 15, 16 pages 201-204. Do not submit answers to them. Many answers can be found on the web. A question similar to one of these problems may be included in the final exam.

### Assignment 7, due Tuesday, November 24

Show the details of your work.
1. Solve problems 2, 4, 7, 10 from chapter 8, pages 234-235.
2. Solve problems 5, 10, 11, 14 from chapter 10, pages 289-291.

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