Muhamad Felemban

SEC 595 · Fall 2026

SEC 595 Secure Computation and Post-Quantum Cryptography Fall 2026 (Term 261) · Information and Computer Science Department

Interactive labs

  • FHE Scheme Lab BFV, BGV, CKKS, GSW, and TFHE on toy parameters, step by step.
  • PQC Lab Lattice, code-based, hash-based, multivariate, and isogeny schemes, including ML-KEM and ML-DSA.

Course Information

Lectures
Sunday & Tuesday, 8:10–9:25 PM
Location
Building 24-137
Prerequisites
Graduate standing
Syllabus
Download (PDF)

Description

Mathematical foundations: algebraic structures, hardness assumptions, and lattice primitives (LWE/RLWE). Lattice-based post-quantum cryptography: key encapsulation mechanisms, digital signatures. Homomorphic encryption: partial (PHE), leveled (LHE), and fully homomorphic encryption (FHE); bootstrapping; BGV, BFV, and CKKS schemes; noise management, packing, and rescaling. Secure computation: secret sharing, oblivious transfer, garbled circuits and Yao's protocol. Zero-knowledge proofs. Applications: privacy-preserving machine learning.

Objectives

  • Introduce the students to the emerging field of encrypted computing.
  • Expose students to the state-of-the-art algorithms in homomorphic encryption and secure multiparty computation.

Learning Outcomes

After taking this course, students will have the ability to:

  1. Explain various encrypted computing techniques and algorithms.
  2. Identify the advantages and challenges of different encrypted computing algorithms.
  3. Apply appropriate encrypted computing techniques based on the application's requirements.
  4. Design new encrypted computing techniques and protocols.

Evaluation

Paper Presentation10%
Project50%
Midterm Exam20%
Final Exam20%

Lectures

Introduction

# Lecture Handout Slides
— Course introduction and overview — PDF

Mathematical Foundations

# Lecture Handout Slides
1 Zq, Groups, and the Arithmetic of Scaling Supplement: CRT example PDF PDF
2 Polynomials over Finite Fields: Interpolation, Identity Testing, and the NTT Supplement: Primitive roots of unity PDF PDF
3 The Ring Rq: Structure and Fast Arithmetic Supplement: NTT examples PDF PDF
4 Rq: Decompositions, Automorphisms, and Embeddings PDF PDF
5 Lattices: Geometry, Hardness, and Reductions PDF PDF
6 Noise and Hardness: Distributions and the LWE Family PDF PDF
7 Lattices, LWE, and Regev's Cryptosystem PDF PDF

Homomorphic Encryption

# Lecture Handout Slides
8 Homomorphic Encryption: Definitions and First Examples PDF PDF
9 Bilinear Groups and BGN PDF PDF
10 The BFV Scheme Supplement: Worked examples Lab: FHE Scheme Lab — BFV PDF PDF
11 The BGV Scheme Supplement: Worked examples Lab: FHE Scheme Lab — BGV PDF PDF
12 The CKKS Scheme: Approximate Arithmetic Lab: FHE Scheme Lab — CKKS PDF PDF
13 The GSW Scheme Lab: FHE Scheme Lab — GSW PDF PDF
14 Bootstrapping PDF PDF
15 The TFHE Scheme Supplement: TFHE in detail: a full bootstrapping on a toy instance Lab: FHE Scheme Lab — TFHE PDF PDF

Post-Quantum Cryptography

# Lecture Handout Slides
16 The Families of Post-Quantum Cryptography Lab: PQC Lab — overview PDF PDF
17 ML-KEM (FIPS 203) Lab: PQC Lab — ML-KEM PDF PDF
18 ML-DSA (FIPS 204) Lab: PQC Lab — ML-DSA PDF PDF

Secret Sharing and Secure Computation

# Lecture Handout Slides
19 Secret Sharing: Access Structures PDF PDF
20 Secret Sharing Schemes: Shamir, CRT, and Brickell PDF PDF
21 Secure Computation: Oblivious Transfer, Garbled Circuits, and PSI PDF —

Zero-Knowledge Proofs

# Lecture Handout Slides
22 Zero-Knowledge Proofs: Sigma Protocols, Fiat–Shamir, SNARKs and STARKs PDF PDF

Textbooks and References

  1. K. Chen, Q. Yang. Privacy-Preserving Computing: For Big Data Analytics and AI. Cambridge University Press, 2023.
  2. D. Boneh, V. Shoup. A Graduate Course in Applied Cryptography.
  3. D. Evans, V. Kolesnikov, M. Rosulek. A Pragmatic Introduction to Secure Multi-Party Computation.
  4. J. Katz, Y. Lindell. Introduction to Modern Cryptography, 3rd ed. CRC Press, 2021.
  5. D. J. Bernstein, J. Buchmann, E. Dahmen (eds.). Post-Quantum Cryptography. Springer, 2009.
  6. R. Cramer, I. Damgård, J. B. Nielsen. Secure Multiparty Computation and Secret Sharing. Cambridge University Press, 2015.
  7. J. Thaler. Proofs, Arguments, and Zero-Knowledge. 2022.
  8. C. Dwork, A. Roth. The Algorithmic Foundations of Differential Privacy. 2014.

Papers

  1. Computing Arbitrary Functions of Encrypted Data
  2. On Lattices, Learning with Errors, Random Linear Codes, and Cryptography
  3. The Learning with Errors Problem
  4. Homomorphic Encryption for Arithmetic of Approximate Numbers
  5. Craig Gentry's PhD thesis
  6. (Leveled) Fully Homomorphic Encryption without Bootstrapping
  7. Fully Homomorphic Encryption (lecture notes, B. Barak)
  8. On Ideal Lattices and Learning with Errors over Rings
  9. CRYSTALS-Kyber: A CCA-Secure Module-Lattice-Based KEM
  10. CRYSTALS-Dilithium: A Lattice-Based Digital Signature Scheme
  11. Falcon: Fast-Fourier Lattice-Based Compact Signatures over NTRU
  12. NIST FIPS 203/204/205 — PQC standards
  13. How to Share a Secret (Shamir, 1979)
  14. Foundations of Garbled Circuits
  15. Extending Oblivious Transfers Efficiently (IKNP OT extension)
  16. On the Size of Pairing-Based Non-Interactive Arguments (Groth16)
  17. Fast Reed-Solomon Interactive Oracle Proofs of Proximity (STARKs)
  18. PLONK: Permutations over Lagrange-bases for Oecumenical Noninteractive Arguments of Knowledge
  19. GAZELLE: A Low Latency Framework for Secure Neural Network Inference

Libraries and Useful Links