# real analysis

Published articles for real analysis.

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.

## Big-O Notation--A Primer

DevFeed: [Big-O Notation--A Primer](<https://devfeed.tech/articles/big-o-notation-a-primer-40201.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2011/06/14/big-o-notation-a-primer/>)

Published: 2011-06-14T16:26:27Z

Content type: tutorial

Language: en

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

Topics: [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>), [Algorithms](<https://devfeed.tech/topics/algorithms.md>), [Mathematics](<https://devfeed.tech/topics/mathematics.md>)

Tags: [algorithm](<https://devfeed.tech/tags/algorithm.md>), [algorithms](<https://devfeed.tech/tags/algorithms.md>), [analysis](<https://devfeed.tech/tags/analysis.md>), [big-o-notation](<https://devfeed.tech/tags/big-o-notation.md>), [big-theta-notation](<https://devfeed.tech/tags/big-theta-notation.md>), [complexity](<https://devfeed.tech/tags/complexity.md>), [computational-complexity](<https://devfeed.tech/tags/computational-complexity.md>), [example](<https://devfeed.tech/tags/example.md>), [limits](<https://devfeed.tech/tags/limits.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [measurement](<https://devfeed.tech/tags/measurement.md>), [primer](<https://devfeed.tech/tags/primer.md>), [real-analysis](<https://devfeed.tech/tags/real-analysis.md>), [time](<https://devfeed.tech/tags/time.md>)

### AI overview

This primer introduces Big-O notation as a way to describe an algorithm's runtime growth. It defines the notation mathematically and illustrates it with a list-summing algorithm characterized as O(n), while also distinguishing Big-Theta notation.

### Source excerpt

The Quest to Capture Speed Companies and researchers spend hundreds of millions of dollars for the fruits of their algorithms. Whether one is indexing websites on the internet for search, folding proteins, or figuring out which warehouse is the most cost-effective to ship a product from, improvements in algorithm speed save immense amounts of money. It's no surprise then, that a similarly immense amount of money has gone into the mathematics behind algorithm analysis.