I might add a few more advanced topics; an older minor version of the course had the syllabus below. Additionally, I plan to incorporate graded hands-on sessions, so basic familiarity with writing code will be helpful (assuming everyone has taken CS101).

This course is intended to provide a theoretical foundation in Cryptography (with some supporting hands-on sessions for several topics). We shall learn about basic cryptographic tools like encryption and message authentication, in the “private-key” and “public-key” settings, with a focus on mathematical definitions of security, “provably secure” constructions based on fundamental cryptographic primitives, and how they are used. The topics that will be covered include the following. We will mainly refer to two books: Katz-Lindell and Boneh-Shoup.

• Perfectly secret encryption: one-time pad, limitations of perfect security
• Private key encryption: defining encryption CPA security, constructing CPA secure scheme- pseudorandom functions and block ciphers, pseudorandom generators, stream ciphers, one-way functions, hardcore predicates, CCA security – motivates message authentication codes, some practical constructions.
• Hash Functions and applications: definition of hash functions, message authentication using hash functions, attacks, and some additional applications
• Public key encryption: CPA security, introduction to some related modular arithmetic, El Gamal, RSA, and Rabin constructions, some attacks on RSA.
• Zero Knowledge Proofs: introduction with motivation, definition of honest verifier zero knowledge, one protocol (graph coloring or some other NP complete problem) 

Mathematical maturity is the only prerequisite. Knowledge of elementary probability, elementary algebra, and elementary number theory will be a bonus, but we will recap the basics needed during the course.

I might add a few more advanced topics; an older minor version of the course had the syllabus below. Additionally, I plan to incorporate graded hands-on sessions, so basic familiarity with writing code will be helpful (assuming everyone has taken CS101).

This course is intended to provide a theoretical foundation in Cryptography (with some supporting hands-on sessions for several topics). We shall learn about basic cryptographic tools like encryption and message authentication, in the “private-key” and “public-key” settings, with a focus on mathematical definitions of security, “provably secure” constructions based on fundamental cryptographic primitives, and how they are used. The topics that will be covered include the following. We will mainly refer to two books: Katz-Lindell and Boneh-Shoup.

• Perfectly secret encryption: one-time pad, limitations of perfect security
• Private key encryption: defining encryption CPA security, constructing CPA secure scheme- pseudorandom functions and block ciphers, pseudorandom generators, stream ciphers, one-way functions, hardcore predicates, CCA security – motivates message authentication codes, some practical constructions.
• Hash Functions and applications: definition of hash functions, message authentication using hash functions, attacks, and some additional applications
• Public key encryption: CPA security, introduction to some related modular arithmetic, El Gamal, RSA, and Rabin constructions, some attacks on RSA.
• Zero Knowledge Proofs: introduction with motivation, definition of honest verifier zero knowledge, one protocol (graph coloring or some other NP complete problem) 

Mathematical maturity is the only prerequisite. Knowledge of elementary probability, elementary algebra, and elementary number theory will be a bonus, but we will recap the basics needed during the course.

I might add a few more advanced topics; an older minor version of the course had the syllabus below. Additionally, I plan to incorporate graded hands-on sessions, so basic familiarity with writing code will be helpful (assuming everyone has taken CS101).

This course is intended to provide a theoretical foundation in Cryptography (with some supporting hands-on sessions for several topics). We shall learn about basic cryptographic tools like encryption and message authentication, in the “private-key” and “public-key” settings, with a focus on mathematical definitions of security, “provably secure” constructions based on fundamental cryptographic primitives, and how they are used. The topics that will be covered include the following. We will mainly refer to two books: Katz-Lindell and Boneh-Shoup.

• Perfectly secret encryption: one-time pad, limitations of perfect security
• Private key encryption: defining encryption CPA security, constructing CPA secure scheme- pseudorandom functions and block ciphers, pseudorandom generators, stream ciphers, one-way functions, hardcore predicates, CCA security – motivates message authentication codes, some practical constructions.
• Hash Functions and applications: definition of hash functions, message authentication using hash functions, attacks, and some additional applications
• Public key encryption: CPA security, introduction to some related modular arithmetic, El Gamal, RSA, and Rabin constructions, some attacks on RSA.
• Zero Knowledge Proofs: introduction with motivation, definition of honest verifier zero knowledge, one protocol (graph coloring or some other NP complete problem) 

Mathematical maturity is the only prerequisite. Knowledge of elementary probability, elementary algebra, and elementary number theory will be a bonus, but we will recap the basics needed during the course.

Textbooks:

• Introduction to Modern Cryptography, Jonathan Katz and Yehuda Lindell
• A Graduate Course in Applied Cryptography, Dan Boneh and Victor Shoup
• The Joy of Cryptography, Mike Rosulek
• A Course in Cryptography, Rafael Pass and Abhi Shelat
• Lecture notes for fundamentals of cryptography, Leonid Reyzin
• Foundations of Cryptography, Volume I-II, Oded Goldreich

Background Material:

• Basic Probability: Section A.3 of Katz-Lindell, Recitation 1 from MIT6875
• Basic Number Theory: Section B of Katz-Lindell, Recitation 3 from MIT6875, the book Comutational Number Theory (Basics)
• Basic computation complexity can be found in Recitation 2 from MIT6875

Related Courses:

• Cryptography (CS406) by Prof. Manoj Prabhakaran, IITB
• Foundations of Cryptography (MIT6875) by Prof Vinod Vaikunthanathan
• Last year’s CS409M offered by me

• Introduction to Modern Cryptography, Jonathan Katz and Yehuda Lindell

• A Graduate Course in Applied Cryptography, Dan Boneh and Victor Shoup

• The Joy of Cryptography, Mike Rosulek

• A Course in Cryptography, Rafael Pass and Abhi Shelat

• Lecture notes for fundamentals of cryptography, Leonid Reyzin

• Foundations of Cryptography, Volume I-II, Oded Goldreich

• Comutational Number Theory (Basics)