CS 6260: Applied Cryptography August 28, 2008
Homework 1
Lecturer: Sasha Boldyreva Due: September 4, 2008
Recommended reading is chapters Introduction and Block ciphers from the lecture
notes of Bellare and Rogaway.
Problem 1.0, 0 points. Read all the information and rules on the course web
page.
Problem 1.1, 5 points. Explain how the complementation property of DES (for
any key Kand amy message Mit is true that E(K, M ) = E(K, M ) ) may help to
speed up exhaustive key search by a factor of 2. Explain what kind of attacks (e.g.
chosen-plaintext attacks) you are assuming.
Problem 1.2, 11 points. There are 40 cards with numbers 1,...,40 written on
them. So each card has a unique number on one side and the other side is blank.
Alice randomly shuffles the cards, picks some number x≤40 of cards without looking
at them and gives them to Bob so no one else could see what cards are given (but
Alice and Bob can see what card they have, of course). Now Alice will somehow try
to communicate a secret 32-bit message to Bob. What is smallest possible xso that
a message can be communicated with perfect security? Is that x enough to send a
33-bit message?
Hints. It does not really matter how exactly Alice communicates a message. You
may need to use a scientific calculator.
Problem 1.3, 4 points. Solve the puzzle at www.cc.gatech.edu/∼aboldyre/
teaching/puzzle.pdf