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* PUSH NOTE : You and Your Research, Richard Hamming.md

* PUSH NOTE : 18. Bootstrapping & CKKS.md

* PUSH NOTE : 17. BGV Scheme.md

* PUSH NOTE : 16. The GMW Protocol.md

* PUSH NOTE : 15. Garbled Circuits.md

* PUSH NOTE : 14. Secure Multiparty Computation.md

* PUSH NOTE : 13. Sigma Protocols.md

* PUSH NOTE : 05. Modular Arithmetic (2).md

* PUSH NOTE : 04. Modular Arithmetic (1).md

* PUSH NOTE : 02. Symmetric Key Cryptography (1).md

* PUSH NOTE : 랜덤 PS일지 (1).md
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Sungchan Yi
2024-11-12 19:52:52 +09:00
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_posts/Lecture Notes/Internet Security/2023-09-25-modular-arithmetic-1.md
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@@ -9,6 +9,7 @@ tags:
- lecture-note
- security
- cryptography
- number-theory
title: 04. Modular Arithmetic (1)
date: 2023-09-25
github_title: 2023-09-25-modular-arithmetic-1
@@ -169,7 +170,7 @@ The inverse exists if and only if $\gcd(a, n) = 1$.
> **Lemma**. For $n \geq 2$ and $a \in \mathbb{Z}$, its inverse $a^{-1} \in \mathbb{Z}_n$ exists if and only if $\gcd(a, n) = 1$.
*Proof*. We use the Extended Euclidean Algorithm. There exists $u, v \in \mathbb{Z}$ such that
*Proof*. We use the extended Euclidean algorithm. There exists $u, v \in \mathbb{Z}$ such that
$$
au + nv = \gcd(a, n).