From f394e395b0780cb7287b5a36cf57505894657b99 Mon Sep 17 00:00:00 2001 From: Sungchan Yi Date: Tue, 12 Nov 2024 21:43:41 +0900 Subject: [PATCH] [PUBLISHER] upload files #163 * PUSH NOTE : 02. Symmetric Key Cryptography (1).md * PUSH NOTE : 1. OTP, Stream Ciphers and PRGs.md * DELETE FILE : _posts/lecture-notes/internet-security/2023-09-11-symmetric-key-cryptography-1.md * DELETE FILE : _posts/lecture-notes/internet-security/2023-09-11-symmetric-key-cryptography-1/2023-09-07-otp-stream-cipher-prgs.md --- .../2023-09-11-symmetric-key-cryptography-1.md | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) rename _posts/lecture-notes/internet-security/{ => 2023-09-11-symmetric-key-cryptography-1}/2023-09-11-symmetric-key-cryptography-1.md (97%) diff --git a/_posts/lecture-notes/internet-security/2023-09-11-symmetric-key-cryptography-1.md b/_posts/lecture-notes/internet-security/2023-09-11-symmetric-key-cryptography-1/2023-09-11-symmetric-key-cryptography-1.md similarity index 97% rename from _posts/lecture-notes/internet-security/2023-09-11-symmetric-key-cryptography-1.md rename to _posts/lecture-notes/internet-security/2023-09-11-symmetric-key-cryptography-1/2023-09-11-symmetric-key-cryptography-1.md index 460444b..fa42e78 100644 --- a/_posts/lecture-notes/internet-security/2023-09-11-symmetric-key-cryptography-1.md +++ b/_posts/lecture-notes/internet-security/2023-09-11-symmetric-key-cryptography-1/2023-09-11-symmetric-key-cryptography-1.md @@ -5,7 +5,7 @@ math: true categories: - Lecture Notes - Internet Security -path: _posts/lecture-notes/internet-security +path: _posts/lecture-notes/internet-security/2023-09-11-symmetric-key-cryptography-1 tags: - security - lecture-note @@ -191,22 +191,22 @@ Let $m \in \left\lbrace 0, 1 \right\rbrace^n$ be the message to encrypt. Then ch - Encryption: $E(k, m) = k \oplus m$. - Decryption: $D(k, c) = k \oplus c$. -This scheme is **provably secure**. See also [one-time pad (Modern Cryptography)](../modern-cryptography/2023-09-07-otp-stream-cipher-prgs.md#one-time-pad-(otp)). +This scheme is **provably secure**. See also [one-time pad (Modern Cryptography)](../../modern-cryptography/2023-09-07-otp-stream-cipher-prgs/2023-09-07-otp-stream-cipher-prgs.md#one-time-pad-(otp)). ## Perfect Secrecy > **Definition.** Let $(E, D)$ be a cipher defined over $(\mathcal{K}, \mathcal{M}, \mathcal{C})$. We assume that $\lvert \mathcal{K} \rvert = \lvert \mathcal{M} \rvert = \lvert \mathcal{C} \rvert$. The cipher is **perfectly secure** if for all $m \in \mathcal{M}$ and $c \in \mathcal{C}$, -> +> > $$ > \Pr[\mathcal{M} = m \mid \mathcal{C} = c] = \Pr[\mathcal{M} = m]. > $$ -> +> > Or equivalently, for all $m_0, m_1 \in \mathcal{M}$, $c \in \mathcal{C}$, -> +> > $$ > \Pr[E(k, m _ 0) = c] = \Pr[E(k, m _ 1) = c] > $$ -> +> > where $k$ is chosen uniformly in $\mathcal{K}$. In other words, the adversary learns nothing from the ciphertext. @@ -225,7 +225,7 @@ since for each $m$ and $c$, $k$ is determined uniquely. *Proof*. Assume not, then we can find some message $m_0 \in \mathcal{M}$ such that $m_0$ is not a decryption of some $c \in \mathcal{C}$. This is because the decryption algorithm $D$ is deterministic and $\lvert \mathcal{K} \rvert < \lvert \mathcal{M} \rvert$. -For the proof in detail, check [Shannon's Theorem (Modern Cryptography)](../modern-cryptography/2023-09-07-otp-stream-cipher-prgs.md#shannon's-theorem). +For the proof in detail, check [Shannon's Theorem (Modern Cryptography)](../../modern-cryptography/2023-09-07-otp-stream-cipher-prgs/2023-09-07-otp-stream-cipher-prgs.md#shannon's-theorem). ### Two-Time Pad is Insecure