## Professor Andre Scedrov

Office: Room 4E6 in David Rittenhouse Laboratory
Telephone: eight five nine eight three ( Math. Dept. Office: eight eight one seven eight )
Fax: three four zero six three
E-mail: lastname at math
Office Hours: By appointment

"What is to distinguish a digital dollar when it is as easily reproducible as the spoken word? How do we converse privately when every syllable is bounced off a satellite and smeared over an entire continent? How should a bank know that it really is Bill Gates requesting from his laptop in Fiji a transfer of \$100,000,.....,000 to another bank? Fortunately, the mathematics of cryptography can help. Cryptography provides techniques for keeping information secret, for determining that information has not been tampered with, and for determing who authored pieces of information." (From the Foreword by R. Rivest to the "Handbook of Applied Cryptography" by Menezes, van Oorschot, and Vanstone.)

This course for graduate students and advanced undergraduates will discuss security protocol design and analysis and the related areas of cryptography. The course will complement but not presuppose CIS 677 and Math 524 from Fall 2003 and is intended to be more advanced than CIS 551 in Spring 2004. We will cover the necessary background for students who have not taken CIS 677 or Math 524.

## Take-Home Midterm Due in Class on Wednesday, March 24

• Suppose that four-digit PINs are distributed uniformly at random. How many people must be in a room for the probability that two of them have the same PIN to be at least 1/2 ?
• Prove that the Caesar cipher does not have perfect secrecy.
• Use exhaustive key search to decrypt the following ciphertext, which was encrypted using a shift cipher: JBCRCLQRWCRVNBJENBWRWN .
• Prove that if (2^n) - 1 is a prime, then n is a prime, and if (2^n) + 1 is a prime, then n is a power of 2. The first type of prime is called a Mersenne prime, and the second type is called a Fermat prime.
• Using the Fundamental Theorem of Arithmetic, prove that the product of (1 - 1/p) over all primes p is zero.
• Consider the following linear recurrence over Z_2 of degree four: z_(i+4) = (z_i + z_(i+3)) mod 2, for i greater or equal to 0. For each of the 16 possible initialization vectors (z_0 , z_1 , z_2 , z_3) determine the period of the resulting keystream.
This is a complete list of midterm assignments due March 24, 2004.