Math ∩ Programming

Table of Contents This is part of a tutorial series on the CKKS homomorphic encryption scheme. In the last article, we described the ciphertext-ciphertext addition and multiplication operations. We ended with two challenges, one to restore the squared scaling factor $\Delta^2$ back to $\Delta$, and the other to convert a three-tuple ciphertext (decrypting under $(1, s, s^2)$) ba...

Table of Contents This is part of a tutorial series on the CKKS homomorphic encryption scheme. In the last article, we introduced symmetric and public-key encryption and decryption routines, and implemented modular polynomial arithmetic (using NTTs as a black box). This article covers the addition and multiplication operations performed on ciphertexts (without relinearization). ...

A quick update on our homomorphic encryption compiler HEIR: our partners at Belfort have a hotword detector in FHE that runs in 350ms. More specifically, they launched a live demo at hotword.belfortlabs.com, that has a little game inspired by the NY Times Connections puzzle. Instead of typing in your guess for the word that connects a group of clues, you say it out loud. Your au...

Table of Contents This is part of a tutorial series on the CKKS homomorphic encryption scheme. In the last article, we covered some groundwork about polynomials and the CKKS encoding method. This article covers the encryption and decryption routines. Notably, if you already know about CKKS, we will deviate from a usual treatment for explanatory purposes. In particular, we will f...