The CKKS - HEAAN FHE Scheme

Explore the CKKS (also known as HEAAN) Fully Homomorphic Encryption scheme in this comprehensive lecture by Yongsoo Song from Microsoft Research. Delve into the theoretical foundations and practical applications of lattice-based cryptography. Learn about the motivation behind CKKS, its core algorithms, and key concepts such as learning with errors. Understand the encoding, decryption, and arithmetic operations involved in HEAAN. Examine the rescaling process and explore a practical example of function evaluation. Investigate the transition from theory to practice, including the two sides of HEAAN and its definition. Gain insights into modular reduction, sine evaluation, and pre- and post-processing techniques. This talk, part of the "Lattices: From Theory to Practice" series at the Simons Institute, offers a deep dive into advanced cryptographic concepts for researchers and practitioners in the field.

Intro
Motivation
Learning with Errors
Algorithms in HEAAN
Encoding & Decoding
Encrypt & Decrypt
Arithmetic Operations
Rescaling
Example: F(x) = x+
Leveled HE
From theory to practice
Two sides of HEAAN
Definition and necessity CHKKS18a
Main Idea
Step 2: Modular reduction
Step 2: sine evaluation
Pre- and post-processing
Conclusion