Quantum computers are a significant threat to public key cryptography, whose security relies on some problems that are not computationally tractable. The course provides a complete overview of the so-called post-quantum cryptosystems, which can be implemented on classical devices but resist cryptanalysis performed with quantum computers.

Students are expected to acquire the following: • Knowledge about the basis of quantum computing and the use of online simulators of quantum computers for implementing some quantum algorithms (e.g., Grover and Shor algorithms) • Knowledge of the main post-quantum cryptosystems (e.g., NTRU, McEliece, Oil and Vinegar) • Knowledge of the mathematical problems which guarantee the security of post-quantum cryptosystems (e.g., shortest vector problem, syndrome decoding problem, learning with errors) • Knowledge of the NIST selected candidates (e.g., Crystals-Kyber, Falcon, Bike) • Ability to discern the security of cryptosystems against quantum cryptanalysis

Having followed the courses Cryptography and Advanced Cryptography.

• Introduction to quantum computing • Code-based cryptography • Lattice-based cryptography • Multivariate cryptography • Hash-based cryptography • Isogeny-based cryptography • Post-quantum signatures • Protocols standardized by NIST

The course consists of 40 hours of lessons and 20 hours of exercises, distributed over 14 weeks. The lessons are dedicated to the presentation of the topics of the course program. The exercises will follow the topics of the lessons; in part, they will be carried out by the teacher, and in part, they will require the active participation of the students.

The lecturer will provide the reading material. A recommended book is “Daniel J. Bernstein, Johannes Buchmann, Erik Dahmen: Post-Quantum Cryptography”.

Slides; Dispense;

Modalità di esame: Prova scritta (in aula); Prova orale facoltativa;

Exam: Written test; Optional oral exam;

... The final exam is written. An oral exam is optional, upon request by the student or at the teacher's discretion. Students cannot consult books, notes, or other teaching materials during the written exam. The written exam is considered passed if its result is greater than or equal to 18/30. Only students who have passed the written exam can ask to take the oral exam. The oral exam contributes to determining the final grade of the exam and the written one. In particular, depending on the student's performance, the oral exam can either raise or lower the grade achieved in writing.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.