Alan Kaminsky • Department of Computer Science • Rochester Institute of Technology • 4572 + 2433 = 7005
 Foundations of Cryptography • CSCI 662-01 • Spring Semester 2018
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## CSCI 662-01—Foundations of Cryptography Homework 7

Prof. Alan Kaminsky—Spring Semester 2018
Rochester Institute of Technology—Department of Computer Science

### Questions

1. Find a safe prime p in the range 10000000 through 20000000. Explain how you found p, and prove that p is a safe prime.

2. If 576003 = 156238a (mod 772517), what is the value of a? Explain how you found a.

3. Alex and Blake are doing a Diffie-Hellman key exchange in the group Zp* with modulus p = 7072252427 and generator g = 3614340734. Alex chooses secret random number a = 2042649032. Blake chooses secret random number b = 3402083232.
1. What number does Alex send to Blake?
2. What number does Blake send to Alex?
3. What shared number do Alex and Blake compute?

4. Give the set of elements in the elliptic curve group y2 = x3 + 5x + 13 (mod 17).

5. Corey and Devon are doing an elliptic curve Diffie-Hellman key exchange in the elliptic curve group y2 = x3 + 5x + 13 (mod 17) with generator (1, 11). Corey sends (3, 15) to Devon. Devon sends (8, 2) to Corey. What shared point do Corey and Blake compute?

### Submission Requirements

Put your answers in a plain text file named "<username>.txt", replacing <username> with the user name from your Computer Science Department account. Send your plain text file to me by email at ark­@­cs.rit.edu. Include your full name and your computer account name in the email message, and include the plain text file as an attachment.

The submission deadline is Friday, April 27, 2018 at 11:59pm. The date/time at which your email message arrives in my inbox will determine whether your homework meets the deadline.

You may submit your homework multiple times up until the deadline. I will keep and grade only the most recent successful submission. There is no penalty for multiple submissions.

If you submit your homework before the deadline, but I do not accept it (e.g. a plain text file was not attached to your email), and you cannot or do not submit your homework again before the deadline, the homework will be late (see below). I STRONGLY advise you to submit the homework several days BEFORE the deadline, so there will be time to deal with any problems that might arise in the submission process.

Each homework question will be graded as follows, for a total of 10 points:
2 = Correct
1 = Partially correct
0 = Incorrect or missing