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

* PUSH NOTE : 1. OTP, Stream Ciphers and PRGs.md

* DELETE FILE : _posts/lecture-notes/internet-security/2023-09-07-otp-stream-cipher-prgs.md
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Sungchan Yi
2024-11-12 22:22:40 +09:00
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_posts/lecture-notes/internet-security/2023-09-11-symmetric-key-cryptography-1.md
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@@ -191,7 +191,7 @@ Let $m \in \left\lbrace 0, 1 \right\rbrace^n$ be the message to encrypt. Then ch
- Encryption: $E(k, m) = k \oplus m$. - Encryption: $E(k, m) = k \oplus m$.
- Decryption: $D(k, c) = k \oplus c$. - Decryption: $D(k, c) = k \oplus c$.
This scheme is **provably secure**. See also [[1. OTP, Stream Ciphers and PRGs#One-Time Pad (OTP)|one-time pad (Modern Cryptography)]]. This scheme is **provably secure**. See also [one-time pad (Modern Cryptography)](1.%20OTP,%20Stream%20Ciphers%20and%20PRGs.md#one-time-pad-(otp)).
## Perfect Secrecy ## Perfect Secrecy
@@ -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 $\lvert \mathcal{K} \rvert < \lvert \mathcal{M} \rvert$. *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 [[1. OTP, Stream Ciphers and PRGs#Shannon's Theorem|Shannon's Theorem (Modern Cryptography)]]. For the proof in detail, check [Shannon's Theorem (Modern Cryptography)](1.%20OTP,%20Stream%20Ciphers%20and%20PRGs.md#shannon's-theorem).
### Two-Time Pad is Insecure ### Two-Time Pad is Insecure