Cryptography (Fall 2026)

Syllabus

The course is meant to be an introduction to modern cryptography, with a focus on provable security. Below is a tentative list of topics.

Information-Theoretic Cryptography:

• Perfect secrecy, one-time pad, Shannon's theorem.
• Perfect authentication, universal hashing, extractors, leftover-hash lemma.

Computational Security:

• One-Way Functions (OWFs) and complexity theory.
• Candidate OWFs (Factoring, RSA, DL, LWE, SIS, LPN).
• Computational indistinguishability, decisional assumptions (DDH, LWE, LPN).

Symmetric Cryptography:

• Pseudorandom Generators (PRGs), hard-core bits, PRGs constructions.
• Pseudorandom Functions (PRFs), PRFs constructions, Feistel networks and blockciphers.
• Secret-key encryption (SKE) and modes of operation.
• Message authentication codes (MACs) and authenticated encryption.
• Collision-resistant hash functions and random oracles .

Public-Key Cryptography:

• Public-key encryption (PKE).
• Digital signatures.
• Identification schemes and applications to digital signatures.
• Identity-based encryption and applications to public-key cryptography.

Logistics

Important: The lectures are offered exclusively in-person (with no registration taking place).

Lecture time: Tuesday (8:00am - 10:00am) and Friday (04:00pm - 07:00pm).
Location: The lectures on tuesday are in Aula 1L (RM018) - Via del Castro Laurenziano 7a; the lectures on friday are in Aula 11 (RM005) - Via Scarpa 14.
Twitter: @SapienzaCrypto.
Google Group: SapienzaCrypto.

Grading

Written exam. The written exam lasts 3 hours and consists of 3 exercises and 3 open questions. Books, notes and electronic devices are not allowed during the exam.

References

We will not follow a single book; the following textbooks are suggested as reference and for deeper study:

• [1] Daniele Venturi, Crittografia nel Paese delle Meraviglie, Springer, Collana di Informatica, 2012.
• [2] Jonathan Katz and Yehuda Lindell, Introduction to Modern Cryptography, CRC Press, 3rd Edition, 2025.
• [3] Jonathan Katz, Digital Signatures, Springer, 2010.
• [4] Salil P. Vadhan, Pseudorandomness, Foundations and Trends in Theoretical Computer Science, Vol. 7, Issue 1-3, 2012. Freely available here.
• [5] Jonathan Katz, Lecture Notes for a course on Advanced Topics in Cryptography, (Sping 2004). Lecture 9 and Lecture 10 are about the Cramer-Shoup PKE scheme.
• [6] Sanjit Chatterjee and Palash Sarkar, Identity-Based Encryption, Springer, 2011.

You may also find useful the following lecture notes from a past edition of the course (although not reviewed by myself):

• [7] Simone Bianco, Lecture Notes for the Cryptography Course, Sapienza University of Rome, A. Y. 2025/2026 (work in progress).

Exams

The exam dates for academic year 2026/2027 will appear below when available.
Exam 0. Reserved to part-time and working students from the past academic year (you must make a formal request to the secretariat; registration via Infostud is still required). Date: 30/10/26. Aula: 4 De Lollis (RM158). Time: 08:30-11:30. Scores [pdf].

Announcements

22/09/2026: The course will start on September 25, 2026.
05/10/2026: The lectures on 30/10/2026 and 03/11/2026 will not take place.

Lectures