15-859I Theoretical Foundations of Cryptography

Class Schedule

Mon 1/13
Intro; Hardness Amplification
Herzberg and Luby, " Public Randomness in Cryptography. " Crypto 92
Wed 1/15
One-way Functions and Pseudorandomness I
Hastad, Impagliazzo, Levin, and Luby.  " A Pseudorandom Generator from any One-Way Function. " SIAM J. Computing Vol 28, #4. (1999)

Mon 1/20
No class - Martin Luther King, Jr Day

Wed 1/22
One-way Functions and Pseudorandomness II

Mon 1/27
One-way Functions and Pseudorandomness III
Wed 1/29
Pseudorandom Functions & Permutations
Goldreich, Goldwasser, and Micali. " How to Construct Random Functions."  J. ACM Vol 33, #4. (1986)
Naor and Reingold, " On the Construction of Pseudo-Random Permutations: Luby-Rackoff Revisited. "  29th STOC, 1997.

Mon 2/3
Symmetric Encryption
Bellare and Goldwasser. " Lecture Notes on Cryptography." Chapter 6.

Wed 2/5
No class

Mon 2/10
Security Notions for Symmetric Encryption
Katz and Yung, " Complete Characterization of Security Notions for Probabilistic Private-Key Encryption" 32nd STOC, 2000.
Wed 2/12
Message Authentication
Bellare and Goldwasser, "Lecture Notes on Cryptography." Chapter 8
Bellare, Killian, and Rogaway, " The security of the cipher block chaining message authentication code. " Crypto 94.

Mon 2/17
no class
snow day

Wed 2/19
IND-CCA security from  IND-CPA + MAC;
OWFs are neccessary for symmetric crypto

Bellare and Namprempre, " Authenticated Encryption: Relations among notions and analysis of the generic composition paradigm." Asiacrypt 2000.
Impagliazzo and Luby, " One-way Functions are Essential for Complexity Based Cryptography. "  30th FOCS,  1989.

Mon 2/24
Digital Signatures and One-way functions
Naor and Yung, " Universal One-Way Hash Functions and their Cryptographic Applications. " 21st STOC, 1989.
Rompel, " One-way functions are necessary and sufficient for secure signatures ." 22nd STOC, 1990.
Wed 2/26
Digital Signatures and Trapdoor functions

Bellare and Micali, " How to sign given any Trapdoor Permutation ." JACM 39 #1, 1992.

Presentation: Luis von Ahn
Blum, Blum, and Shub, " A Simple Unpredictable Pseudo-Random Number Generator ," SIAM J. Comput. 15(2): 364-383 (1986).

Mon 3/3
Digital Signatures from Clawfree Trapdoor Permutations

Goldwasser, Micali, and Rivest, "A Digital Signature Scheme Secure against Adaptive Chosen Message Attacks," SIAM J. on Computing 17: 1988, pp 281-308.

Presentation: Asad Samar
Russell Impagliazzo and Moni Naor,  Efficient Cryptographic Schemes Provably as Secure as Subset SumJ. of Cryptology  9(4):, 1996, pp. 199--216

Wed 3/5
Forward-Secure Digital Signatures
Malkin, Micciancio and Miner, " Efficient generic forward-secure signatures with an unbounded number of time periods." Eurocrypt 2002

Mon 3/10

Wed 3/12
Public-Key Encryption
Goldwasser and Micali, "Probabilistic Encryption." Journal of Computer and System Sciences vol 28, 270-299 (1984).

Presentation: Ke Yang
Paillier, " Public-Key Cryptosystems Based on Composite Degree Residuosity Classes," In: Eurocrypt 99.

Mon 3/17
Chosen-Ciphertext Security
Naor and Yung, " Public Key Cryptosystems Provably Secure against Chosen Ciphertext Attacks ," 22nd STOC, 1990.
Rackoff and Simon, " Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack. " CRYPTO 91.

Presentation: Vince Conitzer
Danielie Micciancio, Generalized compact knapsaks, cyclic lattices, and efficient one-way functions from worst-case complexity assumptions, 43rd  FOCS, 2002. pp. 356-365

Wed 3/19
Dolev, Dwork and Naor, " Non-Malleable Cryptography." SIAM J. Computing, Vol. 30, #2, 2000.

Mon 3/24 No class - Spring Break

Wed 3/26
No class - Spring Break

Mon 3/31
Relationships between notions
Bellare, Desai, Pointcheval, and Rogaway, " Relations Among Notions of Security for Public-Key Encryption Schemes. " CRYPTO 98.

Wed 4/2
Random Oracles I
Bellare and Rogaway, " Random Oracles are Practical: A Paradigm for Designing Efficient Protocols. "  1st CCS, 1993.
Fiat and Shamir, " How to prove yourself: practical solutions to identification and signature problems." CRYPTO 86.
Mon 4/7
Random Oracles II:  Asymmetric Encryption
Bellare and Rogaway, " Optimal asymmetric Encryption" Eurocrypt 94.
Shoup, " OAEP Reconsidered. "  CRYPTO 2001.
Fujisaki and Okamoto, " Secure Integration of Asymmetric and Symmetric Encryption Schemes ." CRYPTO 99.

Wed 4/9
Random Oracles III: Random Oracles are Bad.
Canetti, Goldreich and Halevi, " The Random Oracle Methodology, Revisited."  30th STOC, 1998.

Mon 4/14
Wed 4/16
What Can we provably not prove?
lecture 21, lecture 22
Impagliazzo and Rudich, " Limits on the Provable Consequences of One-way Permutations ." 21st STOC, 1989.

Wed 4/16
Presentation: Bartosz Przydatek
Moni Naor and Omer Reingold, Number-Theoretic constructions of efficient pseudo-random functions ,  In: 38th FOCS, 1997, pp. 458-467

Mon 4/21
Public cryptography is wierd...
Rudich, " The use of interaction in public cryptosystems. " CRYPTO 91.
HW6 due
Wed 4/23
Public-Key notions are separable
Gertner, Kannan, Malkin, Reingold, and Viswanathan, " The Relationship between Public Key Encryption and Oblivious Transfer. " 41st FOCS, 2000.

Mon 4/28
Trapdoor predicates and Trapdoor Functions
Bellare, Halevi, Sahai, and Vadhan, " Many-to-one trapdoor functions and their relations to public-key cryptosystems ."  29th STOC, 1997.
Gertner, Malkin, and Reingold, " On the Impossibility of Basing Trapdoor Functions on Trapdoor Predicates. " 42nd FOCS, 2001.

Wed 4/30 No plan: Fudge Factor