Cryptography (CY 4770)

Pre-requisites:The main pre-requisite is mathematical maturity and comfort with understanding/writing proofs. Familiarity with basic probability and discrete math is assumed (e.g., of conditional probability, modular arithmetic, and the big O notation). Prior knowledge on number theory is not assumed, but may be useful - we will cover the required background in class.

Grading: The final grade will be based on:

• Participation (5%): As we are having a virtual course, and not all students can attend the lectures, participation can be expressed either by attending the lectures, or by being actively involved in Piazza discussions (asking/answering questions).
• Quizzes (20%): During the course we will have 11 short quizzes. These quizzes are meant to be easier than problem sets and are designed to be completed quickly (~15 minutes). They are not meant to cause grief, and the questions will be straightforward. The goals of the quizzes are to encourage careful study of the lecture material.
• Problem Sets (40%): We will have 6 problem sets during the course. Homeworks should be submitted in PDF format. We recommend using typesetting, e.g., using LaTeX, but scanned handwritten solutions will also be accepted, as long as they are clearly readable. The submission date of each problem set will be two weeks after publishing it.
• Final (35%): At the end of the semester we will have a final exam covering the material studied in the course.

Lateness and Collaboration Policy:

• In general, we will not accept late submissions (with the exception of extreme circumstances), however, the problem set with the lowest grade and the quiz with the lowest grade will not be taken into account when computing the final grade.
• Collaborating with other students in the class on homework problems is encouraged, though we urge you to first attempt working out all of the problems by yourself. It is ok to ask your peers about the concepts, algorithms, or approaches needed to do the assignments. We encourage you to do so; both giving and taking advice will help you to learn.
• However, you must write up, prepare, and submit your solutions, in your own words. Looking at written homework solutions from other people or the Web is strictly prohibited. The solution must be entirely the work of the student turning them in. If you have any questions about using a particular resource, ask the course staff or post a question to the class forum.
• If you consult any outside reference such as a textbook or lecture notes, you must acknowledge it on your submission, and make sure all the solutions you submit are your own.
• All students are subject to the Northeastern University’s Academic Integrity Policy. Per Khoury College policy, all cases of suspected plagiarism or other academic dishonesty must be referred to the Office of Student Conduct and Conflict Resolution (OSCCR). This may result in deferred suspension, suspension, or expulsion from the university.
• We are more than happy to answer/discuss any question about the material covered in class during office hours. However, we will not look at homework solutions or discuss an assignment before its submission date. In case there are questions about the meaning of a question in an assignment, please ask the question in the Piazza forum so that all students can benefit.

• Introduction: What is modern cryptography and historical perspectives.
• Perfectly-Secret Encryption: Definitions, the one-time pad, Shanon's theorem.
• Private-Key (Symmetric) Encryption: Passive security and constructions from PRG. CPA security and constructions from PRF. Modes of operation.
• Message Authentication Codes: Message integrity, security definition, MAC from PRF, CCA secure encryption.
• Collision-Resistant Hash Functions: Definitions, Birthday attacks, the Merkle-Damgard transform.
• Constructions of Pseudorandom Permutations (Block Ciphers) in Practice: Substitution-permutation and Feistel networks, DES, triple DES, AES.
• Number Theory: Basic group theory, factoring and RSA, discrete log in cyclic groups, CRH from discrete log.
• Public-Key (Asymmetric) Cryptography: Introduction, Diffie-Hellman key exchange.
• Public-Key (Asymmetric) Encryption: The model, ElGamal, RSA.
• Digital Signatures: Definition and applications, Hash and sign, RSA signatures, Schnorr signatures, Certificates and PKI, SSL/TLS.
• Advanced Cryptography: Secret sharing, oblivious transfer, secure computation, zero-knowledge proofs.