Foundations of Cryptography

CS60088, Spring 2025, LTP: 3-1-0

Prerequisites

We assume basic familiarity with probability theory, algebraic structures (groups, rings, fields), linear algebra and algorithms. Some exposure to computational complexity is useful as well. These topics will not be covered in the course. No prior exposure to cryptography is necessary.

Syllabus (Tentative)

• Introduction to Cryptography
• Perfect secrecy -- definition, equivalent definitions, one-time pads, limitations of perfect secrecy, Shannon's theorem
• Computational secrecy -- motivating the need for computational secrecy, formalising security under different threat models, reductionist arguments and hardness assumptions
• Symmetric Encryption from psedorandom generators, pseudorandom functions and permutations
• Message authentication codes (MACs), hash functions and their security definitions, provably secure constructions
• Practical Constructions of symmetric encryption, MACs and hash functions
• Public key encryption
• Signatures
• Introduction to one-way functions, constructing one-way functions from assumptions such as RSA, Discrete logarithm, hard-core predicates, construction of pseudorandom objects from one-way functions

References

• Jonathan Katz and Yehuda Lindell, Introduction to Modern Cryptography, Chapman and Hall/CRC Press, 2007.
• Shafi Goldwasser and Mihir Bellare, Lecture Notes on Cryptography, 2008 (available here).
• Oded Goldreich, The Foundations of Cryptography, Volume 1 and Volume 2, Cambridge University Press, 2001 and 2004.
• Wenbo Mao, Modern Cryptography: Theory and Practice, first edition, Pearson Education, 2004.

Evaluation

Quizzes/Exams

Tutorials