# gadget decomposition

Published articles for gadget decomposition.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## Key Switching in LWE

DevFeed: [Key Switching in LWE](<https://devfeed.tech/articles/key-switching-in-lwe-40456.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2022/08/29/key-switching-in-lwe/>)

Published: 2022-08-29T08:00:00Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Encryption](<https://devfeed.tech/topics/encryption.md>), [Cryptography](<https://devfeed.tech/topics/cryptography.md>), [scheme](<https://devfeed.tech/topics/scheme.md>)

Tags: [cryptography](<https://devfeed.tech/tags/cryptography.md>), [decrypt](<https://devfeed.tech/tags/decrypt.md>), [encryption](<https://devfeed.tech/tags/encryption.md>), [gadget-decomposition](<https://devfeed.tech/tags/gadget-decomposition.md>), [gaussian](<https://devfeed.tech/tags/gaussian.md>), [homomorphic-encryption](<https://devfeed.tech/tags/homomorphic-encryption.md>), [learning-with-errors](<https://devfeed.tech/tags/learning-with-errors.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [modulus-switching](<https://devfeed.tech/tags/modulus-switching.md>), [real-analysis](<https://devfeed.tech/tags/real-analysis.md>), [secret](<https://devfeed.tech/tags/secret.md>)

### 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.

## The Gadget Decomposition in FHE

DevFeed: [The Gadget Decomposition in FHE](<https://devfeed.tech/articles/the-gadget-decomposition-in-fhe-40450.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2021/12/11/the-gadget-decomposition-in-fhe/>)

Published: 2021-12-11T13:57:25Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [FHE](<https://devfeed.tech/topics/fhe.md>), [homomorphic encryption](<https://devfeed.tech/topics/homomorphic-encryption.md>), [Cryptography](<https://devfeed.tech/topics/cryptography.md>), [Computing](<https://devfeed.tech/topics/computing.md>), [data](<https://devfeed.tech/topics/data.md>), [Code](<https://devfeed.tech/topics/code.md>), [GitHub](<https://devfeed.tech/topics/github.md>)

Tags: [bootstrapping](<https://devfeed.tech/tags/bootstrapping.md>), [core](<https://devfeed.tech/tags/core.md>), [encryption](<https://devfeed.tech/tags/encryption.md>), [fhe](<https://devfeed.tech/tags/fhe.md>), [gadget-decomposition](<https://devfeed.tech/tags/gadget-decomposition.md>), [group-theory](<https://devfeed.tech/tags/group-theory.md>), [homomorphic-encryption](<https://devfeed.tech/tags/homomorphic-encryption.md>), [learning-with-errors](<https://devfeed.tech/tags/learning-with-errors.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [lwe](<https://devfeed.tech/tags/lwe.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [matrix](<https://devfeed.tech/tags/matrix.md>), [number-theory](<https://devfeed.tech/tags/number-theory.md>), [operations](<https://devfeed.tech/tags/operations.md>), [programming](<https://devfeed.tech/tags/programming.md>), [python](<https://devfeed.tech/tags/python.md>)

### 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.