# homomorphic encryption Published articles for homomorphic encryption. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Updates on HEIR, the homomorphic encryption compiler project DevFeed: [Updates on HEIR, the homomorphic encryption compiler project]() Original publisher: [Read original article]() Published: 2026-09-04T18:53:40Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [homomorphic encryption](), [Compiler](), [Encryption](), [Cryptography](), [Machine learning](), [Inference](), [GitHub](), [bazel](), [Kaggle]() Tags: [bazel](), [ckks](), [compiler](), [cryptography](), [encryption](), [github](), [homomorphic-encryption](), [inference](), [kaggle](), [mathematics](), [ml](), [programming]() ### AI overview This companion article explains HEIR, a homomorphic encryption compiler that converts programs to operate directly on encrypted data. It discusses compiling pre-trained machine-learning models for private inference, describes the repository and setup, and reports an example involving encrypted credit-card fraud detection. ### Source excerpt 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 read the linked corporate blog post, HEIR is a compiler that converts an input program to a program that operates directly on encrypted data. ## CKKS -- Polynomials, the Canonical Embedding, and Encoding DevFeed: [CKKS -- Polynomials, the Canonical Embedding, and Encoding]() Original publisher: [Read original article]() Published: 2026-04-29T12:25:44Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [homomorphic encryption](), [Cryptography](), [Mathematics](), [Math and Logic]() Tags: [ckks](), [ckks-tutorial](), [cryptography](), [encoding](), [encryption](), [homomorphic-encryption](), [mathematics](), [neural-network](), [polynomial-ring](), [polynomials](), [programming](), [python](), [technical](), [tutorial]() ### AI overview This tutorial introduces the CKKS homomorphic encryption scheme and develops mathematical background on the polynomial ring used in its basic formulation and the canonical embedding used to encode cleartext messages as plaintexts. It also outlines CKKS's history, including its support for approximate arithmetic and later bootstrapping improvements. ### Source excerpt Table of Contents In this tutorial series, I will introduce the CKKS homomorphic encryption scheme from the ground up, in rather intricate detail. Each article in this series corresponds to a pull request on a GitHub repository. The code for this article is in this pull request. Follow along by cloning the repository and checking out the code at the relevant commit. This first article will cover some of the mathematical background necessary in the formulation of the CKKS encryption scheme, specifically the polynomial ring used in the most basic version of CKKS, and the canonical embedding used to encode cleartext messages as plaintexts. ## Deterministic Primality Testing for Limited Bit Width DevFeed: [Deterministic Primality Testing for Limited Bit Width]() Original publisher: [Read original article]() Published: 2026-04-07T13:00:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Algorithms](), [C++](), [Mathematics](), [Cryptography](), [homomorphic encryption]() Tags: [algorithm](), [c-plus-plus](), [code](), [cryptography](), [homomorphic-encryption](), [mathematics](), [miller-rabin](), [oeis](), [primes](), [programming](), [randomized-algorithm]() ### AI overview This article explains how to perform deterministic Miller-Rabin primality testing for 32-bit integers. It presents C++ code using the bases 2, 3, 5, and 7, which the article states is deterministic for all 32-bit inputs, and discusses strong pseudoprimes and related research. ### Source excerpt Problem: Determine if a 32-bit number is prime (deterministically) Solution: (in C++) // Bases to test. Using the first 4 prime bases makes the test deterministic // for all 32-bit integers. See https://oeis.org/A014233. int64_t bases[] = {2, 3, 5, 7}; inline int countTrailingZeros(uint64_t n) { if (n == 0) return 64; return __builtin_ctzll(n); } int64_t modularExponentiation(int64_t base, int64_t exponent, int64_t modulus) { int64_t res = 1; int64_t b = base % modulus; int64_t e = exponent; while (e > 0) { if (e & 1) { // Doesn't overflow because we assume 32-bit integer inputs res = (res * b) % modulus; } b = (b * b) % modulus; e >>= 1; } return res; } bool isPrime(int64_t n) { if (n < 2) return false; if (n < 4) return true; if (! ## Bicyclic Matrix-Matrix Multiplication in Fully Homomorphic Encryption DevFeed: [Bicyclic Matrix-Matrix Multiplication in Fully Homomorphic Encryption]() Original publisher: [Read original article]() Published: 2025-11-17T16:41:28Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [Encryption](), [Algorithm](), [Code](), [GitHub]() Tags: [algorithm](), [circuit](), [code](), [cryptography](), [encryption](), [fhe](), [github](), [homomorphic-encryption](), [linear-algebra](), [lwe](), [mathematics](), [programming](), [rlwe]() ### AI overview This article explains the bicyclic method for matrix-matrix multiplication in fully homomorphic encryption. It introduces the method's packing scheme, relates it to Halevi-Shoup diagonal packing, and discusses properties including multiplicative depth, layout invariance, and rotation complexity. The implementation is provided in a GitHub repository in a file named bicyclic.py. ### Source excerpt In an earlier article, I covered the basic technique for performing matrix-vector multiplication in fully homomorphic encryption (FHE), known as the Halevi-Shoup diagonal method. This article covers a more recent method for matrix-matrix multiplication known as the bicyclic method. The code implementing this method is in the same GitHub repository as the previous article, and the bicyclic method is in a file called bicyclic.py. The previous article linked above covers the general concepts behind "FHE packing," which I will assume as background knowledge for this article: ## FHE@PDX 2025 DevFeed: [FHE@PDX 2025]() Original publisher: [Read original article]() Published: 2025-07-25T16:56:45Z Content type: opinion Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [homomorphic encryption](), [Google](), [intel](), [Compiler](), [AdventureX 2025]() Tags: [2025](), [compiler](), [fhe](), [google](), [hackathon](), [homomorphic-encryption](), [intel](), [shortform]() ### AI overview The author describes hosting an informal mini-workshop on homomorphic encryption in Portland, Oregon, attended by about 18 people from the local community. The event included talks, discussion, a hackathon for the HEIR compiler, and plans for a possible repeat the following year. ### Source excerpt On Monday, July 14th 2025, I hosted a mini-workshop on homomorphic encryption at Google's Portland, Oregon office. Though Portland is a small city, it's becoming a hub for homomorphic encryption. Intel and Google both have a presence here, as well as the hardware startup Niobium, and a few individuals from other companies who happen to be based here. Since I had been having lunch with various subsets of the community, I figured it was about time to get us all in a room together. ## Frequently Asked Questions about FHE DevFeed: [Frequently Asked Questions about FHE]() Original publisher: [Read original article]() Published: 2025-07-18T17:31:49Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [homomorphic encryption](), [FHE](), [Cryptography](), [math](), [GPU](), [Facial recognition](), [Sorting]() Tags: [cryptography](), [encryption](), [facial-recognition](), [fhe](), [gpu](), [homomorphic-encryption](), [mathematics](), [programming]() ### AI overview A collection of short answers about fully homomorphic encryption (FHE), covering encrypted queries, computation on ciphertexts, sorting, performance, and security against quantum computers. The article explains that FHE can support operations on encrypted data without exposing the underlying plaintext, while computational overhead remains a key limitation. ### Source excerpt I work on homomorphic encryption (HE or FHE for "fully" homomorphic encryption) and I have written a lot about it on this blog (see the relevant tag). This article is a collection of short answers to questions I see on various threads and news aggregators discussing FHE. Facts If a service uses FHE and can respond to encrypted queries, can't the service see your query? How is it possible to operate on encrypted data without seeing it? ## Fully Homomorphic Encryption and the Public DevFeed: [Fully Homomorphic Encryption and the Public]() Original publisher: [Read original article]() Published: 2025-01-03T07:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [homomorphic encryption](), [Cryptography](), [Security]() Tags: [cryptography](), [fhe](), [homomorphic-encryption](), [privacy](), [security]() ### AI overview A living document records public reactions to homomorphic encryption, focusing on how journalists, bloggers, and social media participants perceive its risks and benefits. It includes discussion of Apple's use of homomorphic encryption in Enhanced Visual Search for Photos and related privacy concerns. ### Source excerpt In this living document, I will document reactions to uses of homomorphic encryption by members of the public. By "member of the public," I mean people who may be technical, but are not directly involved in the development or deployment of homomorphic encryption systems. This includes journalists, bloggers, aggregator comment threads, and social media posts. My main goal is to understand how the public perceives the risks and benefits of using homomorphic encryption. ## LWE Attack Benchmarking Project DevFeed: [LWE Attack Benchmarking Project]() Original publisher: [Read original article]() Published: 2024-10-15T22:43:03Z Content type: opinion Language: en Sources: [Jeremy Kun]() Topics: [benchmarking](), [FHE](), [homomorphic encryption](), [Security](), [Transformer]() Tags: [benchmark](), [benchmarking](), [fhe](), [homomorphic-encryption](), [research](), [security](), [shortform]() ### AI overview The article discusses a Facebook research project benchmarking attacks against learning with errors (LWE), motivated by the security implications of small, sparse secrets and errors in settings including Kyber and homomorphic encryption. It highlights a reported recovery of Hamming-weight-9 secrets in a specific homomorphic-encryption setting and notes that one attack is transformer-based. ### Source excerpt Kristin Lauter and her colleagues at Facebook research recently announced a project to benchmark attacks against LWE. The announcement was on the post-quanum crypto mailing list. They state: "Our approach is motivated by the need to study more carefully the effect on security of using small secrets and small error in standardized LWE settings like Kyber and Homomorphic Encryption. In addition, as sparse secrets have been used in Homomorphic Encryption for efficiency and functionality, it is important to study sparse secrets as well. ## Packing Matrix-Vector Multiplication in Fully Homomorphic Encryption DevFeed: [Packing Matrix-Vector Multiplication in Fully Homomorphic Encryption]() Original publisher: [Read original article]() Published: 2024-09-07T04:18:09Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [homomorphic encryption](), [FHE](), [Encryption](), [layout](), [parallel](), [Python]() Tags: [arithmetic](), [code](), [cryptography](), [data](), [encryption](), [fhe](), [github-repository](), [homomorphic-encryption](), [layout](), [linear-algebra](), [lwe](), [mathematics](), [packing](), [parallel](), [programming](), [python](), [rlwe](), [simd](), [strategies]() ### AI overview This article explains packing for SIMD-style fully homomorphic encryption. It describes how to arrange plaintext data in RLWE ciphertexts so matrix-vector multiplication requires fewer alignment multiplications and rotations, then introduces two basic packing techniques and a computational model. ### Source excerpt In my recent overview of homomorphic encryption, I underemphasized the importance of data layout when working with arithmetic (SIMD-style) homomorphic encryption schemes. In the FHE world, the name given to data layout strategies is called "packing," because it revolves around putting multiple plaintext data into RLWE ciphertexts in carefully-chosen ways that mesh well with the operations you'd like to perform. By "mesh well" I mean it reduces the number of extra multiplications and rotations required merely to align data elements properly, rather than doing the actual computation you care about. ## Converting Between Packings in SIMD-Style FHE DevFeed: [Converting Between Packings in SIMD-Style FHE]() Original publisher: [Read original article]() Published: 2024-09-02T21:01:03Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [homomorphic encryption](), [data](), [Code]() Tags: [compilers](), [encryption](), [fhe](), [github](), [graph-coloring](), [heir](), [homomorphic-encryption](), [mathematics](), [optimization](), [packing](), [permutation](), [programming](), [rlwe](), [simd]() ### AI overview This article explains packing in SIMD-style fully homomorphic encryption and focuses on converting between established packings. It introduces a computational model involving RLWE ciphertext vectors, elementwise operations, cyclic rotations, and differing operation costs. ### Source excerpt In my recent overview of homomorphic encryption, I underemphasized the importance of data layout when working with arithmetic (SIMD-style) homomorphic encryption schemes. In the FHE world, the name given to data layout strategies is called "packing," because it revolves around putting multiple plaintext data into RLWE ciphertexts in carefully-chosen ways that mesh well with the operations you'd like to perform. By "mesh well" I mean it reduces the number of extra multiplications and rotations required merely to align data elements properly, rather than doing the actual computation you care about. ## Fully Homomorphic Encryption in Production Systems DevFeed: [Fully Homomorphic Encryption in Production Systems]() Original publisher: [Read original article]() Published: 2024-07-31T07:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [homomorphic encryption](), [FHE](), [Encryption](), [Cryptography](), [Edge](), [Microsoft](), [iOS](), [Differential Privacy](), [Embeddings](), [clustering](), [Library]() Tags: [apple](), [clustering](), [cryptography](), [differential-privacy](), [embeddings](), [encryption](), [fhe](), [homomorphic-encryption](), [ios](), [library](), [mathematics](), [microsoft-edge](), [programming](), [systems]() ### AI overview A living document catalogs production systems known to use fully or somewhat homomorphic encryption. It describes deployments and techniques involving Microsoft Edge password checking, Apple's Live Caller ID Lookup, and Apple's private image search, while distinguishing FHE from SHE. ### Source excerpt In this living document, I will list all production systems I'm aware of that use fully homomorphic encryption (FHE). For background on FHE, see my overview of the field. If you have any information about production FHE systems not in this list, or corrections to information in this list, please send me an email with sufficient detail allow the claim to be publicly verified. For all production deployments, I will distinguish between cases where the deployed system does "fully" homomorphic encryption (with bootstrapping), aka FHE, and "somewhat" homomorphic encryption, aka SHE (avoiding bootstrapping). ## Remez and function approximations DevFeed: [Remez and function approximations]() Original publisher: [Read original article]() Published: 2024-05-06T17:18:29Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [homomorphic encryption](), [polynomials](), [Algorithm](), [Python]() Tags: [algorithm](), [approximation](), [article](), [fhe](), [homomorphic-encryption](), [how-to](), [library](), [optimization](), [polynomials](), [python](), [remez](), [shortform]() ### AI overview The article discusses approximating functions with low-degree polynomials for arithmetic fully homomorphic encryption. It examines lolremez, the Remez algorithm, Paterson-Stockmeyer evaluation, and a multi-interval Remez method for approximating discontinuous functions such as sign. ### Source excerpt I've been learning recently about how to approximate functions by low-degree polynomials. This is useful in fully homomorphic encryption (FHE) in the context of "arithmetic FHE" (see my FHE overview article), where the computational model makes low-degree polynomials cheap to evaluate and non-polynomial functions expensive or impossible. In browsing the state of the art I came across two interesting things. The first is the software package lolremez that implements polynomial (and rational polynomial $f(x) / g(x)$) function approximation using the so-called Remez algorithm. ## A High-Level Technical Overview of Fully Homomorphic Encryption DevFeed: [A High-Level Technical Overview of Fully Homomorphic Encryption]() Original publisher: [Read original article]() Published: 2024-05-04T15:30:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [homomorphic encryption](), [Encryption](), [Cryptography](), [toolchain](), [Compiler](), [Post-quantum cryptography]() Tags: [compiler](), [cryptography](), [encryption](), [fhe](), [google](), [homomorphic-encryption](), [linear-algebra](), [lwe](), [mathematics](), [post-quantum-cryptography](), [programming](), [rlwe](), [technical]() ### AI overview A technical, high-level survey of fully homomorphic encryption (FHE), explaining how programs can operate on encrypted data without decrypting it. The article discusses the field's current limitations, key techniques, and its relationship to the HEIR compiler toolchain. ### Source excerpt About two years ago, I switched teams at Google to focus on fully homomorphic encryption (abbreviated FHE, or sometimes HE). Since then I've got to work on a lot of interesting projects, learning along the way about post-quantum cryptography, compiler design, and the ins and outs of fully homomorphic encryption. If you've heard about FHE and you're a software person, you've probably heard two things: it lets you run programs directly on encrypted data without ever decrypting it; and it's still too slow to be useful for anything. ## Encoding Schemes in FHE DevFeed: [Encoding Schemes in FHE]() Original publisher: [Read original article]() Published: 2023-09-18T11:08:39Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Encoding](), [FHE](), [homomorphic encryption](), [Cryptography](), [Decoding]() Tags: [bits](), [complex-numbers](), [cryptography](), [decoding](), [encoding](), [fhe](), [homomorphic-encryption](), [learning-with-errors](), [lwe](), [mathematics](), [number-theory](), [programming](), [residue-number-system](), [rlwe](), [scaling](), [scheme]() ### AI overview This article explains how cleartexts are transformed into plaintexts through encoding, and reversed through decoding, in homomorphic encryption. It catalogs encoding approaches for different HE schemes, including bit-field encoding for LWE and considerations for noise, scaling, bit positions, and programmable bootstrapping in CGGI/TFHE. ### Source excerpt In cryptography, we need a distinction between a cleartext and a plaintext. A cleartext is a message in its natural form. A plaintext is a cleartext that is represented in a specific way to prepare it for encryption in a specific scheme. The process of taking a cleartext and turning it into a plaintext is called encoding, and the reverse is called decoding. In homomorphic encryption, the distinction matters. Cleartexts are generally all integers, though the bit width of allowed integers can be restricted (e. ## Google's Recent FHE work, and starting HEIR DevFeed: [Google's Recent FHE work, and starting HEIR]() Original publisher: [Read original article]() Published: 2023-08-10T12:22:29Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [homomorphic encryption](), [Google](), [Compiler](), [Machine learning]() Tags: [compiler](), [encryption](), [fhe](), [github](), [github-repository](), [google](), [hardware](), [homomorphic-encryption](), [mlir](), [models](), [repository]() ### AI overview A Google team reports recent work on fully homomorphic encryption, including video processing, machine-learning model compilation, TPU implementation, and compiler improvements. The article also introduces HEIR, an early project intended to provide a standardized foundation for FHE compilers using MLIR. ### Source excerpt Today my team at Google published an article on Google's Developers Blog with some updates on what we've been doing with fully homomorphic encryption (FHE). There's fun stuff in there, including work on video processing FHE, compiling ML models to FHE, an FHE implementation for TPUs, and improvements to the compiler I wrote about earlier this year. TODO: add mower gif video A simple object movement tracking algorithm in FHE, tracking a runaway lawn mower from a Nest camera. ## Sample Extraction from RLWE to LWE DevFeed: [Sample Extraction from RLWE to LWE]() Original publisher: [Read original article]() Published: 2023-02-27T08:00:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [Cryptography](), [Encryption]() Tags: [cryptography](), [encryption](), [fhe](), [homomorphic-encryption](), [linear-algebra](), [lwe](), [mathematics](), [programming](), [rlwe](), [scheme]() ### AI overview A tutorial deriving sample extraction, an FHE technique that partially converts a ciphertext from the Ring Learning With Errors (RLWE) scheme to the Learning With Errors (LWE) scheme. It introduces the relevant LWE and RLWE encryption constructions and explains the role of error terms. ### Source excerpt In this article I'll derive a trick used in FHE called sample extraction. In brief, it allows one to partially convert a ciphertext in the Ring Learning With Errors (RLWE) scheme to the Learning With Errors (LWE) scheme. Here are some other articles I've written about other FHE building blocks, though they are not prerequisites for this article. Modulus Switching in LWE Key Switching in LWE The Gadget Decomposition in FHE Negacyclic Polynomial Multiplication Estimating the Security of Ring Learning With Errors LWE and RLWE The first two articles in the list above define the Learning With Errors problem (LWE). ## Google's Fully Homomorphic Encryption Compiler -- A Primer DevFeed: [Google's Fully Homomorphic Encryption Compiler -- A Primer]() Original publisher: [Read original article]() Published: 2023-02-13T11:34:01Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [homomorphic encryption](), [FHE](), [C++](), [Compiler](), [Google](), [GitHub](), [Open Source](), [toolchain]() Tags: [c-plus-plus](), [circuit](), [compiler](), [encryption](), [fhe](), [github](), [google](), [homomorphic-encryption](), [how-to](), [open-source](), [toolchains]() ### AI overview This primer introduces Google's open-source fully homomorphic encryption compiler for C++. It explains how the compiler transforms supported plaintext C++ programs into programs that operate on encrypted data, and briefly discusses its internals, optimization passes, and circuit-based toolchain model. ### Source excerpt Back in May of 2022 I transferred teams at Google to work on Fully Homomorphic Encryption (newsletter announcement). Since then I've been working on a variety of projects in the space, including being the primary maintainer on github.com/google/fully-homomorphic-encryption, which is an open source FHE compiler for C++. This article will be an introduction to how to use it to compile programs to FHE, as well as a quick overview of its internals. ## Negacyclic Polynomial Multiplication DevFeed: [Negacyclic Polynomial Multiplication]() Original publisher: [Read original article]() Published: 2022-12-09T13:35:45Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [polynomials](), [Cryptography](), [homomorphic encryption](), [Encryption](), [Python](), [GitHub]() Tags: [article](), [complex-twist](), [cryptography](), [encryption](), [fourier-transform](), [github](), [homomorphic-encryption](), [mathematics](), [negacyclic](), [polynomial-ring](), [polynomials](), [programming](), [python]() ### AI overview This tutorial explains three techniques for computing negacyclic polynomial products, including the simpler cyclic product as a precursor. It places these operations in the context of lattice cryptography and fully homomorphic encryption and provides Python code on GitHub. ### Source excerpt In this article I'll cover three techniques to compute special types of polynomial products that show up in lattice cryptography and fully homomorphic encryption. Namely, the negacyclic polynomial product, which is the product of two polynomials in the quotient ring $\mathbb{Z}[x] / (x^N + 1)$. As a precursor to the negacyclic product, we'll cover the simpler cyclic product. All of the Python code written for this article is on GitHub. ## Key Switching in LWE DevFeed: [Key Switching in LWE]() Original publisher: [Read original article]() Published: 2022-08-29T08:00:00Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Encryption](), [Cryptography](), [scheme]() Tags: [cryptography](), [decrypt](), [encryption](), [gadget-decomposition](), [gaussian](), [homomorphic-encryption](), [learning-with-errors](), [mathematics](), [modulus-switching](), [real-analysis](), [secret]() ### AI overview This tutorial explains key switching in the LWE encryption scheme: transforming a ciphertext encrypted under one secret key into a ciphertext under another without knowing either key. It introduces the key-switching key, shows why the naïve approach causes excessive error growth, and explains how gadget decomposition reduces that error. ### Source excerpt Last time we covered an operation in the LWE encryption scheme called modulus switching, which allows one to switch from one modulus to another, at the cost of introducing a small amount of extra noise, roughly $\sqrt{n}$, where $n$ is the dimension of the LWE ciphertext. This time we'll cover a more sophisticated operation called key switching, which allows one to switch an LWE ciphertext from being encrypted under one secret key to another, without ever knowing either secret key. ## Modulus Switching in LWE DevFeed: [Modulus Switching in LWE]() Original publisher: [Read original article]() Published: 2022-07-16T14:39:56Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [homomorphic encryption](), [Cryptography](), [Encryption](), [Algorithms, Complexity]() Tags: [algorithms](), [cryptography](), [encryption](), [fhe](), [homomorphic-encryption](), [learning-with-errors](), [mathematics](), [modulus-switching](), [programming]() ### AI overview This tutorial explains modulus switching in Learning With Errors (LWE), a technique used in some fully homomorphic encryption schemes. It introduces an LWE encryption scheme and describes how ciphertexts can be converted to a smaller modulus while addressing the role of error in encryption and decryption. ### Source excerpt The Learning With Errors problem is the basis of a few cryptosystems, and a foundation for many fully homomorphic encryption (FHE) schemes. In this article I'll describe a technique used in some of these schemes called modulus switching. In brief, an LWE sample is a vector of values in $\mathbb{Z}/q\mathbb{Z}$ for some $q$, and in LWE cryptosystems an LWE sample can be modified so that it hides a secret message $m$. ## The Gadget Decomposition in FHE DevFeed: [The Gadget Decomposition in FHE]() Original publisher: [Read original article]() Published: 2021-12-11T13:57:25Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [FHE](), [homomorphic encryption](), [Cryptography](), [Computing](), [data](), [Code](), [GitHub]() Tags: [bootstrapping](), [core](), [encryption](), [fhe](), [gadget-decomposition](), [group-theory](), [homomorphic-encryption](), [learning-with-errors](), [linear-algebra](), [lwe](), [mathematics](), [matrix](), [number-theory](), [operations](), [programming](), [python]() ### AI overview A tutorial on gadget decomposition in fully homomorphic encryption (FHE). It explains how GSW and related schemes use random noise, how homomorphic operations increase that noise, why bootstrapping is needed, and how gadget decomposition helps limit noise growth. ### Source excerpt Lately I've been studying Fully Homomorphic Encryption, which is the miraculous ability to perform arbitrary computations on encrypted data without learning any information about the underlying message. It's the most comprehensive private computing solution that can exist (and it does exist!). The first FHE scheme by Craig Gentry was based on ideal lattices and was considered very complex (I never took the time to learn how it worked). Some later schemes (GSW = Gentry-Sahai-Waters) are based on matrix multiplication, and are conceptually much simpler. ## Why Theoretical Computer Scientists Aren't Worried About Privacy DevFeed: [Why Theoretical Computer Scientists Aren't Worried About Privacy]() Original publisher: [Read original article]() Published: 2013-06-10T09:51:27Z Content type: opinion Language: en Sources: [Jeremy Kun]() Topics: [online privacy](), [Security](), [national security](), [Computer science](), [Google](), [backdoor](), [Statistics](), [Databases](), [Users]() Tags: [backdoor](), [computer-science](), [cryptography](), [databases](), [differential-privacy](), [google](), [homomorphic-encryption](), [national-security](), [politics](), [privacy](), [security](), [statistics](), [users]() ### AI overview This opinion article discusses public concern about government surveillance and privacy, arguing that privacy, convenience, and security can be maintained together technologically. It also distinguishes the author's personal privacy preferences from opposition to privacy violations as policy. ### Source excerpt There has been a lot of news recently on government surveillance of its citizens. The biggest two that have pervaded my news feeds are the protests in Turkey, which in particular have resulted in particular oppression of social media users, and the recent light on the US National Security Agency's widespread "backdoor" in industry databases at Google, Verizon, Facebook, and others. It appears that the facts are in flux, as some companies have denied their involvement in this program, but regardless of the truth the eye of the public has landed firmly on questions of privacy.