**Instructor:** Poorvi Vora

**Text:** None. See this website for references.

**Schedule:** Tues., 6:10 - 8:40 pm, Tompkins 205.

**Course Content:**Special topics chosen according to student and instructor interests.

**Grading:** Class participation, paper presentations
and reviews, and a final project.

**Prerequisites:** both CS 6331 (intro graduate crypto) and CS 6212 (graduate algorithms) or equivalent exposure to modern algebra and mathematical proofs.

**14 January**

Lecture 1: Warm-up: review algebra. Cryptography over Elliptic Curves. Efficient exponentiation.
*References*

Wenbo Mao, Modern Cryptography, pp. 139-152. (Will give handout in next class)

Certicom Tutorial

FIPS 186-2 Digital Signature Standard (DSS)

**21 January**

Lecture 2: Fully-Homomorphic Encryption Over the Integers, an informal introduction.
*References*

For the lecture: Craig Gentry. Computing arbitrary functions of encrypted data. Commun. ACM 53(3): 97-105 (2010)

More formal, potential paper for a student to present: Marten van Dijk, Craig Gentry, Shai Halevi, Vinod Vaikuntanathan. Fully Homomorphic Encryption over the Integers. IACR Cryptology ePrint Archive 2009: 616 (2009), appeared in EUROCRYPT 2010

**28 January**

Lecture 3: Existence of PRNGs.
*References*

1. Goldwasser and Bellare, Lecture Notes on Crypto, section 3.2

2. A. C. Yao. Theory and Applications of Trapdoor Functions. Proceedings of the 23rd FOCS, IEEE, 1982, pp. 80-91. FIX

3. Yehuda Lindell's lecture notes on hard-core predicates

**4 February**

Lecture 4: Next-bit Tests.
*References*

1. Goldwasser and Bellare, Lecture Notes on Crypto, section 3.3

2. A. C. Yao. Theory and Applications of Trapdoor Functions. Proceedings of the 23rd FOCS, IEEE, 1982, pp. 80-91. FIX

**11 February**

Lecture 5: Zero-knowledge Proofs and Bit Commitments.
*References*

1. Goldwasser and Bellare, Lecture Notes on Crypto, sections 11.1.3, 11.2

**18 February: Student Presentations**