May 2022 Summaries

This blog post, part of a series on the Fully Homomorphic Encryption (FHE) scheme TFHE, delves into advanced homomorphic operations and building blocks, such as key switching, external product, internal product, and CMux operation. The post explores the challenges of performing homomorphic multiplication when dealing with large constant polynomials, proposing a decomposition technique to manage noise growth during such operations. Key switching is introduced as a method to switch encryption keys without revealing the original secret key, using a combination of decomposition and inner products with GLev ciphertexts. The external product enables homomorphic multiplication of two ciphertexts, employing one as a GLWE and the other as a GGSW, while the internal product extends this by allowing combinations of GGSW ciphertexts. The CMux operation, a homomorphic version of a multiplexer gate, is highlighted as a crucial component in the bootstrapping process of TFHE.

The blog post is part of a series dedicated to explaining the Fully Homomorphic Encryption (FHE) scheme known as TFHE, which is implemented in Rust by Zama as TFHE-rs. It focuses on performing operations like homomorphic addition and multiplication on GLWE ciphertexts, which are fundamental components of GLev and GGSW ciphertexts, and discusses the impact of these operations on noise. The post explains how messages are encoded and highlights the importance of encoding schemes, such as encoding integers in the most significant bits (MSB) and using padding bits, which facilitate efficient homomorphic operations. It provides a detailed explanation of performing homomorphic addition and multiplication by constants, using toy examples to illustrate the concepts. Additionally, the post touches upon the unique aspects of TFHE, like its torus-based visualization, and encourages readers to explore further concepts such as homomorphic multiplications and key switchings in subsequent parts of the series.

TFHE-rs is a Rust implementation of the Fully Homomorphic Encryption (FHE) scheme TFHE, designed for developers and researchers seeking control over encryption processes without delving into low-level implementations. The blog post is part of a series exploring TFHE, also known as CGGI, which enables computations over encrypted data and is based on the Learning With Errors (LWE) problem and its variants. TFHE distinguishes itself through fast bootstrapping that reduces noise while evaluating functions. The post details various types of ciphertexts, including GLWE, GLev, and GGSW, and explains that each type has specific properties beneficial for homomorphic operations. The process of encryption and decryption in TFHE is illustrated with examples, emphasizing the importance of managing noise. Although the blog post introduces complex concepts gradually, it aims to deepen understanding of FHE by discussing key elements such as ciphertext types and bootstrapping techniques, inviting readers to explore further in subsequent parts.