Modern Public Key Cryptography – 705016 – Sommersemester 2026

Content

• Advanced Cryptographic Primitives • Public Key Cryptography (public key encryption schemes, signature schemes, commitment schemes, zero knowledge, ...) • Provable Security (security models, basic ideas of reductionist security proofs)

Material

Date	Lecturer	Lecture title	Exercise
04/03/2026	Lena	Course Information Introduction to reductions	Handout warmup exercise
11/03/2026	Shibam	Commitment Schemes	Correct warmup
18/03/2026	Shibam	Zero-Knowledge Proofs	Handout ZKP exercises
25/03/2026	Fabian	Game-based and simulation-based proofs	Correct ZKP exercises
15/04/2026	Lena	Lattices, SIS, R-SIS and LWE	Talk about Seminar Topics
22/04/2026	cancelled	cancelled	Choose Project Topics
29/04/2026	Daniel Escudero	MPC Crash course
06/05/2026	Lena	Lattices and (Oblivious) Pseudorandom Functions
13/05/2026	Fabian	Zero-Knowledge friendly cipher design
20/05/2026	Christian	Collusion assumptions
27/05/2026	tbd	Invited Talk II
03/06/2026	You!	Seminar Talks I
10/06/2026	You!	Seminar Talks I

Seminar topics (choose until the 22nd of April!)

• Choose your topic by e-mailing your chosen supervisor and forwarding the email with the date suggestion to Lena.
• Presentation can be done alone (20 minutes) or in pairs (40 minutes)
• After, we will discuss the topic in class. Students get bonus points for good questions.
• Hand in the slide draft for feedback three days before your presentation
• Overall, you get 60 points for the presentation:
  • 20 for the slide draft
  • 20 for the presentation delivery
  • 20 for discussion

Topics with Lena:

• Timelock encryption: Timelocks can send a message "to the future" where it can only be decrypted at a later date. https://people.seas.harvard.edu/~salil/research/timelock.pdf
• Bulletproofs:  https://eprint.iacr.org/2017/1066.pdf, also explain bulletproofs (shortened sigma proofs).
• Anonymous Credit Tokens: How can a credential keep a balance private? See: https://datatracker.ietf.org/doc/draft-schlesinger-privacypass-act/
• Proving a range in zero-knowledge: https://crypto.stanford.edu/~dabo/cryptobook/BonehShoup_0_6.pdf#subsection.20.4.1
• anonymous group messaging: How to use systems like Clarion to hide who is a member of a group: https://www.ndss-symposium.org/wp-content/uploads/2022-141-paper.pdf

Topics with Fabian:

• Lookup arguments in cryptographic proofs (https://eprint.iacr.org/2025/1876) explore the landscape of proving non-trivial relations.
• The BFV scheme (https://eprint.iacr.org/2012/144.pdf) explain one of the foundational arithmetic homomorphic encryption schemes.
• Function Secret Sharing (https://www.iacr.org/archive/eurocrypt2015/90560300/90560300.pdf) computing on shared data is much easier with a helper.
• Arithmetic-Binary-Yao (https://eprint.iacr.org/2018/403.pdf) 3 MPC schemes, 3 parties, and blazingly fast performance.
• ColliderScript (https://eprint.iacr.org/2024/1802.pdf) How Hash functions in weird settings enable arbitrary computation in constrained blockchains.

Topics with Shibam:

• ZK in Anonymous credentials, helps you prove ID without revealing more info https://eprint.iacr.org/2026/330.pdf
• Plonk constraints, Allows to write constraints for zkSNARKS https://www.mit.edu/~linust/files/zkSNARK_PlonK.pdf
• Threshold and Ring Signatures (both classic and PQ), https://arxiv.org/html/2311.05514v2, https://www.cs.umd.edu/~jkatz/papers/ring_sigs.pdf
• ZK/MPC friendly OWFs and Hashes, allows to write efficient ZK circuits, https://core.taceo.io/articles/how-to-choose-your-zk-friendly-hash-function/, https://eprint.iacr.org/2016/542
• VOLE(ith) applications, https://csrc.nist.gov/csrc/media/Projects/pqc-dig-sig/documents/round-1/spec-files/FAEST-spec-web.pdf, https://eprint.iacr.org/2025/113.pdf, https://eprint.iacr.org/2026/109, https://csrc.nist.gov/csrc/media/Projects/threshold-cryptography/documents/TCall-1/Schmivitz-PW01.pdf, https://eprint.iacr.org/2024/1431

Administrative Information

Previous Knowledge

We recommend Information Security and Cryptography. Mathematical Foundations of Cryptography or Privacy Enhancing Technologies are also a plus.

Prerequisites Curriculum

A course in cryptography (e.g. Information Security, Cryptography, Privacy Enhancing Technologies or equivalent).

Objective

“In this course you will get to know the details of many public-key cryptosystems; … be able to show the security of common cryptographic schemes by constructing a security proof; … learn more about advanced aspects of cryptography and cryptographic research.”

Language

English

Teaching Method

* Lectures * Exercises * Final presentation at the end of the lecture.

How to get a grade

Participation in class, exercises, and a final presentation.

Registration

https://online.tugraz.at/tug_online/ee/rest/pages/slc.tm.cp/course-registration/592116

Lecture Dates

Date	Begin	End	Location	Event	Type	Comment
2026/05/13	13:00	15:00	Seminarraum	Abhaltung	VU	fix/
2026/05/20	13:00	15:00	Seminarraum	Abhaltung	VU	fix/
2026/05/27	13:00	15:00	Seminarraum	Abhaltung	VU	fix/
2026/06/03	13:00	15:00	Seminarraum	Abhaltung	VU	fix/
2026/06/10	13:00	15:00	Seminarraum	Abhaltung	VU	fix/
2026/06/17	13:00	15:00	HS i3 "LENZING Hörsaal"	Abhaltung	VU	fix/
2026/06/24	13:00	15:00	Seminarraum	Abhaltung	VU	fix/

Lecturers