Foundations of Cryptography
CSCI66201, 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 Monday, August 31
Warmup assignment:
Solve problems 1.2, 1.3, 1.4 from chapter 1, pages 2425.
Assignment 2, due Monday, September 14

Easy mod. Solve problems 5, 6, 7, 8
from chapter 1 (i.e. 1.5, 1.6, etc.), pages 2526.

More warm up. Solve problems 11, 13 from chapter 1, pages 2627.

Some work. Solve problems 4, 5, 6 from chapter 2, pages 5253.

Some more work. Solve problems 8, 10 from chapter 2, pages 5354.
Assignment 3, due Wednesday, September 23

Solve problems 1, 2, 7, 12 from chapter 3, pages 8386.

Solve problems 3, 4, 9, 10 from chapter 3, pages 8386.
Assignment 4, due Sunday, October 4
Show the details of your work.

Solve exercises 4, 5 and 6 from chapter 4, page 118.

Find all irreducible polynomials in Z_{2}[x] of degree 4.

Which of the following polynomials are reducible in Z_{2}[x]:
x^{5} + x^{4} + 1,
x^{5} + x^{3} + 1,
x^{5} + x^{4} + x^{2} + 1?
If reducible, then show factors.

Find all irreducible monic polynomials
(with the leading coefficient at x^{2} equal to 1)
in Z_{5}[x] of degree 2.

Compute 10111001*10100001 in GF(256),
using the AES irreducible polynomial.

Solve problems 13.1, 14, 16, 17 from chapter 4, pages 120121
(this is the complete page 121 from the textbook,
some places on the web show only one of the problems 16 and 17).
Midterm Exam, Monday, October 5
Assignment 5, due Monday, October 26
Show the details of your work.

Solve problems 2, 4 from chapter 6, page 170.

Solve problems 5, 6 from chapter 6, pages 170171.

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.

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 Monday, November 9
Show the details of your work.

Solve problems 1, 2, 4, 6, 7 from chapter 7, page 200.

Solve problems 11 and 13 from chapter 7, pages 201202.

Read, understand and think about problems 10, 12, 14, 15, 16
pages 201204.
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 Monday, November 23
Show the details of your work.

Solve problems 2, 4, 7, 10 from chapter 8, pages 234235.

Solve problems 5, 10, 11, 14 from chapter 10, pages 289291.
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