## CSci 4554 Lab 4: Diffie-Hellman key exchange

### Due Monday, Nov 4th at 11:59pm (by e-mail)

#### Overview and background

This lab is done in groups of 2 or individually.

The purpose of the lab is to implement cryptographic algorithms based
on the DLP problem and attacks on them.

### Tasks for the lab

#### Task 1: 30 points total

- Each group is given a random letter, you don't know which one is which.
- Each group generates at least two Diffie-Hellman public keys:
- Choose a safe prime p greater than 1000000000 (you will need a
smaller prime q, then compute 2q+1, and check if it is a prime as
well)
- Find a generator in the cyclic group mod p. To checkm if a number g
is a generator, check that g^2 and g^q are both not equal 1. This
means that g does not belong to any of the cyclic subgroups of p, so
it is a generator.

A small generator is
fine. Use square-and-multiply for computations.

- Post your group and your public materials in the google document
that is given. Specifify whom it
is addressed to.
- Choose more key exchange materials, some under your
group name, and one under another group's name (your goal is to
established a shared key with two groups under other group's name
for a successful "man-in-the-middle" attack).
- Respond to requests adressed to you by following the rest of the
protocol steps.
- At least a half of your posted materials must be under your own
group name, and you must respond to at least a half of requests
addressed to you.
- At the end all the shared keys would be revealed

#### Task 2: 15 points total

Apply one the following
methods: baby-step,
giant-step method
or Pollard's
rho algorithm, to find a secret key for an DLP problem
generated by another group. When we open all the keys, you will be
able to know if your computation was correct.

#### What to submit (by e-mail to me, CC your partner)

- A record of all the steps that you did (computations, postings, etc).
- All the computed keys
- All your code.

CSci 4554 course web site.

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