Instructor: Poorvi Vora

Text: None. See this website for references.

Schedule: Thurs., 7:10 - 9:40 pm, Rome 202.

Course Content: Elliptic Curve Cryptography. Provably secure PRNGS. Zero-knowledge proofs. Special topics chosen according to student and instructor interests.

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

Prerequisites: both CS 284 (intro graduate crypto) and CS 212 (graduate algorithms) or equivalent exposure to algebra and mathematical proofs.

Course Outline

Planned Schedule

3 September 2009
Lecture 1: Cryptography over groups: review algebra, Diffie-Hellman, El Gamal, efficient exponentiation over groups, digital signatures. ElGamalEtc
References
Wenbo Mao, Modern Cryptography, pp. 139-152.
Blake et al, Elliptic Curves in Cryptography, pp. 1-10

10 September 2009
Lecture 2: Elliptic Curve Cryptography: elliptic curve algebra
References
Wenbo Mao, Modern Cryptography, pp. 166-173.
Neal Koblitz, A Course in Number Theory and Cryptography. pp. 179-182.
Neal Koblitz, Algebraic Aspects of Cryptography. pp. 132-133, 134-136.
Certicom Tutorial
FIPS 186-2 Digital Signature Standard (DSS)

17 September 2009
Lecture 3: Information theory of secrecy: perfect secrecy, unicity distance. Computational theory of secrecy for PRGs: definitions
References
1. Claude E. Shannon, Communication Theory of Secrecy Systems, Bell System Technical Journal, vol.28-4, page 656--715, 1949.
2. Doug Stinson, Chapter 2, "Cryptography: Theory and Practice", Third Edition, 2006.
3. Goldwasser and Bellare, Lecture Notes on Crypto, section 3.1.

24 September 2009
Lecture 4: 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
Student Presentation On: Shamir Secret Sharing. Reference for Presentation Adi Shamir, How to Share a Secret, CACM, 22:11 1979. Also see: Doug Stinson, "Cryptography: Theory and Practice", Third Edition, 2006, pp. 481-486

1 October 2009
Lecture 5: 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
Student Presentation On: Computational Secret Sharing. Reference for Presentation: Hugo Krawczyk. Secret sharing made short. In Advances in Cryptology: Proceedings of Crypto '93, pages 136-143. Springer-Verlag, 1993

8 October 2009
Lecture 6: Zero-knowledge Proofs and Bit Commitments.
References
1. Goldwasser and Bellare, Lecture Notes on Crypto, sections 11.1.3, 11.2
2. Oded Goldreich. Zero knowledge Twenty Years after its Invention. Part I.
3. Gaurav Jain. Zero Knowledge Proof Systems - A Survey

15 October 2009: Student Presentations

Undergrad Presentations
• Adi Shamir, How to Share a Secret, CACM, 22:11 1979. Also see: Doug Stinson, "Cryptography: Theory and Practice", Third Edition, 2006, pp. 481-486. Alex Florescu.
• Hugo Krawczyk. Secret sharing made short. In Advances in Cryptology: Proceedings of Crypto '93, pages 136-143. Springer-Verlag, 1993. Jan Rubio
• Moni Naor and Adi Shamir, Visual Cryptography. Eurocrypt 94. Simple explanation by Stinson. Jacob Alperin-Sheriff
  Anonymous Delivery
• David Chaum, The Dining Cryptographers Problem: Unconditional Sender and Recipient Untraceability, JoC, 1:1 1988. Edmond K. Machie
• David Chaum, Untraceable Electronic Mail, Return Addresses, and Digital Pseudonyms, CACM, 24:2 1981. Ryan Festag

22 October 2009: Student Presentations

Anonymous Delivery (contd)
• Jakobsson, Juels and Rivest, Making Mix Nets Robust For Electronic Voting By Randomized Partial Checking, USENIX 2002. Scotty Smith.
  Hard Problems in Algorithmic Number Theory
• Twenty years of attacks on the RSA cryptosystem. D. Boneh. In Notices of the American Mathematical Society (AMS), Vol. 46, No. 2, pp. 203--213, 1999. Rizwan Habib
  Electronic Cash and Blind Signatures
• Untraceable Electronic Cash. David Chaum, Amos Fiat and Moni Naor, Crypto 1988 Edmond K. Machie
• Fair Blind Signatures. Markus Stadler, Jean-Marc Piveteau, Jan Camenisch, Eurocrypt 1995. Anica Allen

29 October 2009: Student Presentations

Homomorphisms and Cryptography
• Ahituv, Lapid, Neumann. Processing Encrypted Data. CACM 30:9, 777-780, September 1987. Mohammed Obiedat
  Classical Voting Systems
• Benaloh, J. and Tuinstra, D. Receipt-Free Secret-Ballot Elections. STOC 1994. pp. 544--553. Scotty Smith.
  Voter-Verifiable Voting Systems
• Ronald L. Rivest and Warren D. Smith. ThreeVotingProtocols: ThreeBallot, VAV, and Twin. EVT'07 Jan Rubio
• David Chaum. Secret-Ballot Receipts: True Voter-Verifiable Elections. IEEE Security and Privacy, vol. 2, no. 1, pp. 38-47, 2004. An explanation, by Poorvi Vora. Also, Chaum, van de Graaf, Ryan and Vora, Secret Ballot Elections with Unconditional Integrity. Anica Allen

5 November 2009: Student Presentations

Non-commutative Groups and Cryptography
• Bettina Eick, Delaram Kahrobaei Polycyclic Groups A New Platform for Cryptology?. Mohammed Obiedat
  Symmetric-Key Cryptanalysis
• Joshua Mason, Kathryn Watkins, Jason Eisner, and Adam Stubblefield. A Natural-Language Approach to Automated Cryptanalysis of Two-Time Pads. CCS 2006. Ryan Festag.
• Alex Biryukov, Christophe De Canniere, and Michael Quisquater. On Multiple Linear Approximations CRYPTO 2004. Jacob Alperin-Sheriff

26 November 2009
No lecture. Thanksgiving.