Math ∩ Programming
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CKKS — Key Switching and Relinearization
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 $\Delta^2$…
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CKKS — Addition and Multiplication
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…
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Hotword detection in FHE on GPU in 350ms
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.…
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CKKS — Encryption and Decryption
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…
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Updates on HEIR, the homomorphic encryption compiler project
On 2026-08-14 I published an article on the Google Security blog with an update on HEIR, our homomorphic encryption (HE) compiler. This is a companion article, in which I have no limits on word count or jargon, and I can feel free to be honest. So strap in. Assuming you won’t…