Basic Concepts of Cryptology: Substitution Ciphers, Permutation Ciphers, Vigenere Cipher, Rotor Machines, Attack Models. Symmetric Ciphers, Block Ciphers, One-Time Pad, Information-Theoretic Properties of One-Time Pad, Perfect Secrecy, Misuses of One-Time Pad, Malleability. Stream Ciphers, Linear Feedback Shift Register, Golomb's Randomness Postulates, Linear Complexity, Non-linear Filters, Knapsack Keystream Generator.
Introduction to Number Theory: Congruences, Chinese Remainder Theorem, Fermat's Little Theorem, Euler's Theorem, Modular Exponentiation by Repeated Squaring. Finite Fields. Splitting Fields. Quadratic Residues. Legendre Symbol. Jacobi Symbol. Law of Quadratic Reciprocity.
Public-Key Cryptosystems: Diffie-Hellman Key Exchange, Person-in-the Middle Attack. Discrete Logarithm. RSA Public-Key Cryptosystem. Attacks on RSA. ElGamal Public-Key Cryptosystem. Digital Signatures, Selective Forgery, Existential Forgery. Signature Schemes Based on RSA. Signature Schemes Based on Discrete Logarithm: ElGamal Signature Scheme, Digital Signature Algorithm (DSA).
Selected topics from modern cryptography and computer network security, including: Probabilistic Primality Testing, Euler Pseudoprimes, Solovay-Strassen Primality Test, Strong Pseudoprimes, Miller-Rabin Primality Test. Hash Functions.
The take-home final exam will be due in pdf online in Canvas on Tuesday, May 6, 2025 during the final exam period and will be worth 30% of the grade. The take-home final exam will also have at least a ten-day lead time, during which there will be no new homework. The take-home final exam will also include a 5-page written report on a topic of your choice related to the course and approved in advance by the instructor.
Most other weeks during the semester there will be homework due in pdf online in Canvas, each time with at least one week lead time. Total homework will be worth 20% of the grade.
First homework will be assigned on Tuesday, January 28, 2025 and it will be due in pdf online in Canvas on Tuesday, February 4, 2025.
First midterm will be assigned on Thursday, February 6, 2025 and it will be due in pdf online in Canvas on Tuesday, February 18, 2025.
Please bear in mind that everyone is expected to submit written solutions individually. That is, even if in some cases your work may be a result of group discussions, each person is responsible to write up the solutions in their own words by themselves. Please take the time to show all your work and provide a detailed explanation of your reasoning in your own words.
This is the complete set of problems for Homework #1 due in pdf in Canvas by 8 pm on Tuesday, February 4, 2025.
Please read sections 1.1, 1.1.1, 1.6, 1.7, 1.7.1, 1.7.2, 1.7.3. 1.7.4, 5.2, 5.2.1, 5.3, 5.3.1, 5.3.2, 5.3.4, and 5.3.5 from the textbook.
In addition, in order to give you more time to work on it, we are now also assigning:
Small project due February 18: Exercise 5.17 on p. 286 of the textbook. Please refer to textbook section 5.2.2.
This project is a part of Midterm #1. The other Midterm #1 problems will be assigned on February 4.
Please bear in mind that everyone is expected to submit written solutions individually. That is, even if in some cases your work may be a result of group discussions, each person is responsible to write up the solutions in their own words by themselves. Please take the time to show all your work and provide a detailed explanation of your reasoning in your own words.
This is the complete set of problems for Midterm #1 due in pdf in Canvas by 8 pm on Tuesday, February 18, 2025.
Please read textbook sections 5.6 and 5.6.1, Handbook Chapter 6 and those parts of Chapter 5, which are referred to in Chapter 6, and textbook sections 1.2, 1.3, and 1.4.
Please bear in mind that everyone is expected to submit written solutions individually. That is, even if in some cases your work may be a result of group discussions, each person is responsible to write up the solutions in their own words by themselves. Please take the time to show all your work and provide a detailed explanation of your reasoning in your own words.
This is the complete set of problems for Homework #2 due in pdf in Canvas by 8 pm on Tuesday, March 4, 2025.
Please read textbook sections 1.2, 1.3, 1.3.1, 1.3.2, 1.4, 1.5, 2.8. 2.8.1, 2.10, 2.10.1, 2.10.2, 2.10.3, 2.10.4, and 3.1.