# residue number system

Published articles for residue number system.

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## Encoding Schemes in FHE

DevFeed: [Encoding Schemes in FHE](<https://devfeed.tech/articles/encoding-schemes-in-fhe-40476.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2023/09/18/encoding-schemes-in-fhe/>)

Published: 2023-09-18T11:08:39Z

Content type: tutorial

Language: en

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

Topics: [Encoding](<https://devfeed.tech/topics/encoding.md>), [FHE](<https://devfeed.tech/topics/fhe.md>), [homomorphic encryption](<https://devfeed.tech/topics/homomorphic-encryption.md>), [Cryptography](<https://devfeed.tech/topics/cryptography.md>), [Decoding](<https://devfeed.tech/topics/decoding.md>)

Tags: [bits](<https://devfeed.tech/tags/bits.md>), [complex-numbers](<https://devfeed.tech/tags/complex-numbers.md>), [cryptography](<https://devfeed.tech/tags/cryptography.md>), [decoding](<https://devfeed.tech/tags/decoding.md>), [encoding](<https://devfeed.tech/tags/encoding.md>), [fhe](<https://devfeed.tech/tags/fhe.md>), [homomorphic-encryption](<https://devfeed.tech/tags/homomorphic-encryption.md>), [learning-with-errors](<https://devfeed.tech/tags/learning-with-errors.md>), [lwe](<https://devfeed.tech/tags/lwe.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [number-theory](<https://devfeed.tech/tags/number-theory.md>), [programming](<https://devfeed.tech/tags/programming.md>), [residue-number-system](<https://devfeed.tech/tags/residue-number-system.md>), [rlwe](<https://devfeed.tech/tags/rlwe.md>), [scaling](<https://devfeed.tech/tags/scaling.md>), [scheme](<https://devfeed.tech/tags/scheme.md>)

### 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.