Math 5405. Cryptography, Spring 2013
Homework Assignments
1. Due Thursday, January 17.
Trappe and Washington, #4, 11, 13, 16, 18, 19, 20, 21, 24, 25 on Pages 104-108.
2. Due Thursday, January 24.
Savin, Page 138 # 1,2, Page 142 # 1,2,3, Page 145 # 1,3, Page 150 # 1,2,3.
3. Due Thursday, January 31.
Savin, Page 150 #4 (and factor these numbers using either the $p-1$ or $p+1$ method),
Page 154 #1, Page 156 #1,2.
4. Due Thursday, February 7.
Savin, Pages 159-60 #1-5.
Trappe-W, Pages 215-16 #4,8,10. Page 217 #4.
5. Due Thursday, February 14.
The next prime year is the year 2017.
5 is a primitive element (mod 2017).
I chose a mystery number x and computed 5^x (mod 2017) and got 1077.
Please find my number in three different ways.
(1) 2017 is not such a big prime, so use baby-step/giant-step to find x.
(2) 2016 has only small prime factors, so use Pohlig-Helmann to find x.
(3) Although it is a pain, use Index Calculus to find discrete logs of 2,3,5,7,11,13 and then find x.
6. Due Thursday, February 28.
Savin, Page 165 #1,2. Page 170 #1,2.`
7. Due Thursday, March 7.
Savin, Page 173 #1,2. Page 175 #1,2.`
8. Due Thursday, March 21.
Savin, Pages 180-181 #1-5.
9. Due Thursday, March 28.
Homework Number Nine
Supplementary Notes
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