Math 690 Fall 2006, MW 10:30-12
Mathematical Foundations of Computer Security
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
About This Course
"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.
"Cryptography: Theory and Practice. Third Edition" by Stinson.
Chapman & Hall/CRC, 2005. ISBN: 1584885084.
"Foundations of Cryptography: Volume 1, Basic Tools" by Goldreich.
Cambridge University Press, 2001. ISBN: 0521791723.
O. Goldreich. Foundations of Cryptography - Volume 2.
R. Focardi, R. Gorrieri (Eds.) Foundations of Security Analysis and Design.
Springer Lecture Notes in Computer Science, Volume 2171, 2001.
"Handbook of Applied Cryptography" by
Menezes, van Oorschot, and Vanstone.
CRC Press, Fifth Printing, 2001. ISBN: 0-8493-8523-7.
Goldwasser-Bellare lecture notes on cryptography at MIT.
Dodis cryptography lecture notes at NYU.
J. Clark and J. Jacob. A Survey of Authentication Protocol Literature.
Version 1.0, November, 1997.
- R. Kemmerer, C. Meadows, and J. Millen. Three Systems for Cryptographic
Protocol Analysis. Journal of Cryptology, Vol. 7, no. 2, 1994.
Kerberos: The Network Authentication Protocol.
The Kerberos Network Authentication Service (V5) Internet Draft.
- F. Butler, I. Cervesato, A. Jaggard, and A. Scedrov.
A formal analysis of some properties of Kerberos 5 using MSR.
In: S. Schneider, ed., 15-th IEEE Computer Security Foundations Workshop,
Cape Breton, Nova Scotia, Canada, June, 2002. IEEE Computer Society Press,
2002, pp. 175-190. Preliminary version
The TLS Protocol Version 1.0 RFC 2246.
The SSL Protocol Version 3.0 Internet Draft.
- D. Wagner and B. Schneier.
Analysis of the SSL 3.0 Protocol.
- J. Mitchell, V. Shmatikov, and U. Stern.
Finite-State Analysis of SSL 3.0.
J.C. Mitchell, M. Mitchell, and U. Stern. Automated Analysis of Cryptographic
Protocols Using Murphi, IEEE Symp. Security and Privacy, Oakland, 1997, pages
J.P. Anderson. Computer Security Technology Planning Study.
ESD-TR-73-51, ESD/AFSC, Hanscom AFB, Bedford, MA (Oct. 1972)
[NTIS AD-758 206].
M. Bishop's History of Computer Security Web Site at UC Davis.
- O. Goldreich. "Modern Cryptography, Probabilistic Proofs and
Pseudo-randomness." Springer-Verlag, 1999. ISBN: 3-540-64766-X.
Ron Rivest's Cryptography and Security Page at MIT.
The Cypherpunks Home Page at UC Berkeley.
Crypto FAQ site at RSA Security.
Homework #1 Due in Class on Monday, October 2
This is the complete set of problems for Homework #1 due in class
on Monday, October 2.
- Exercise 1.5 on p. 39 of Stinson.
- Exercise 1.16ab on p. 40 of Stinson.
- Exercise 1.18 on p. 40 of Stinson.
- Exercise 1.26 on p. 43 of Stinson.
- Exercise 1.29ab on p. 44 of Stinson.
- Exercise 2.2 on p. 70 of Stinson.
- Prove that the Caesar cipher does not have perfect secrecy.
Take-Home Midterm Due in Class on Wednesday, November 8
This is the complete set of problems for take-home midterm due in class
on Wednesday, November 8.
- 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.
- Exercise 5.3c on p. 226 of Stinson.
- Exercise 5.7 on p. 226 of Stinson.
- Exercise 5.8 on p. 226 of Stinson.
- Exercise 5.10 on p. 226 of Stinson.
- Exercise 5.12 on p. 227 of Stinson.
- Exercise 5.13 on p. 227 of Stinson.
- Exercise 5.14 on p. 228 of Stinson.
- Exercise 5.15ab on pp. 228-229 of Stinson.
- Exercise 5.16ab on pp. 229-230 of Stinson.
- Exercise 5.20 on p. 230 of Stinson.
Take-Home Final Exam Due in DRL 4E6 on Wednesday, December 20
at 10 a.m.
This is the complete set of problems for take-home final exam due in
DRL 4E6 on Wednesday, December 20 at 10 a.m.
- Exercise 4.6 on p. 157 of Stinson.
- Exercise 4.9ab on p. 157 of Stinson.
- Exercise 4.10 on pp. 157-158 of Stinson.
- Exercise 5.25 on p. 231 of Stinson.
- Exercise 5.32 on p. 232 of Stinson.
- Exercise 6.12 on pp. 277-278 of Stinson.