This page contains some links to pages with material relevant to the special topics in applied mathematics course, Cryptography. You will also find links to Java applets and Mathematica notebooks which you can download and modify for further exploration.

• Section 01 current semester syllabus
• Selected homework solutions
• Many of the Mathematica notebooks listed on this page make use of functions that are defined in a package. This package is distributed without warranty and with no guarantee of correctness. Use it at your own risk.
• The field trip to the National Cryptologic Museum.
• Student reports on topics from the history of cryptography.
• The current listing of semester project problems.
• List of typographical errors in the fourth printing of the textbook.
• List of typographical errors in the fifth printing of the textbook.
• Find the greatest common divisor (GCD) of two positive integers is a frequently occurring operation. The Euclidean Algorithm is a simple method for determining the GCD. If you prefer to use Mathematica, you may download a notebook and use it.
• The greatest common divisor (GCD) of two positive integers can be written as a linear combination of the two integers. The Extended Euclidean Algorithm is a simple method for determining this linear combination. If you prefer to use Mathematica, you may download a notebook and use it.
• Solve a system of simultaneous linear congruences using the Chinese Remainder Theorem.
• Modular exponentiation raises bases to (usually large) powers and then mods the result. The Modular Exponentiation Algorithm implements this in Java. If you prefer to use Mathematica, you may download a notebook and use it.
• Data Encryption Standard (DES) Resources
  • A Javascript implementation of DES.
  • An implementation of DES in Mathematica.
  • An example of the key scheduling algorithm in DES.
  • An example of the DES function in action.
• Two examples of the Pohlig-Hellman symmetric key exponentiation cipher.
• Three examples of the use of the Pohlig-Hellman Algorithm to solve the discrete logarithm problem.
• A list of some small-ish prime numbers for simulating the operation of the RSA cryptosystem.
• A list of some small-ish prime numbers for simulating the operation of the Rabin cryptosystem.
• Public keys for several public key cryptosystems are contained on the pages listed below.
  • RSA
  • Rabin
  • El Gamal
• Practice ciphertexts for the public key cryptosystems.
• An example of the use of Gauss's Algorithm to find the primitive roots of a prime number. A Mathematica notebook is also available.
• Examples of the use of the Miller-Rabin-Selfridge Probabilistic Primality Test. A Mathematica notebook is also available.
• Examples of the use of the Solovay-Strassen Probabilistic Primality Test. A Mathematica notebook is also available.
• An introduction to elliptic curve cryptography. A Mathematica notebook is also available.
• An introduction to quantum cryptography.