TFHE Deep Dive - Part III - Key switching and leveled multiplications

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.