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fix: links fixed

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Sungchan Yi
2023-10-28 09:03:13 +09:00
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_posts/Lecture Notes/Internet Security/2023-09-11-symmetric-key-cryptography-1.md
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@@ -185,7 +185,7 @@ The case for $C = 1$ is similar.
### One-Time Pad (OTP) ### One-Time Pad (OTP)
![1. OTP, Stream Ciphers and PRGs > One-Time Pad (OTP)](2023-09-07-otp-stream-cipher-prgs.md#one-time-pad-otp) [1. OTP, Stream Ciphers and PRGs > One-Time Pad (OTP)](../../modern-cryptography/2023-09-07-otp-stream-cipher-prgs#one-time-pad-otp)
## Perfect Secrecy ## Perfect Secrecy

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_posts/Lecture Notes/Internet Security/2023-10-04-rsa-elgamal.md
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@@ -20,7 +20,7 @@ github_title: 2023-10-04-rsa-elgamal
Suppose we are given integers $a$ and $N$. For any integer $x$ that is relatively prime to $N$, we choose $b$ so that Suppose we are given integers $a$ and $N$. For any integer $x$ that is relatively prime to $N$, we choose $b$ so that
$$ $$
\tag{$*$} \tag{$*$}
ab \equiv 1 \pmod{\phi(N)}. ab \equiv 1 \pmod{\phi(N)}.
$$ $$
@@ -139,7 +139,7 @@ This is an inverse problem of exponentiation. The inverse of exponentials is log
Given $y \equiv g^x \pmod p$ for some prime $p$, we want to find $x = \log_g y$. We set $g$ to be a generator of the group $\mathbb{Z}_p$ or $\mathbb{Z}_p^*$, since if $g$ is the generator, a solution always exists. Given $y \equiv g^x \pmod p$ for some prime $p$, we want to find $x = \log_g y$. We set $g$ to be a generator of the group $\mathbb{Z}_p$ or $\mathbb{Z}_p^*$, since if $g$ is the generator, a solution always exists.
Read more in [discrete logarithm problem (Modern Cryptography)](2023-10-03-key-exchange.md#discrete-logarithm-problem-dl). Read more in [discrete logarithm problem (Modern Cryptography)](../../modern-cryptography/2023-10-03-key-exchange#discrete-logarithm-problem-dl).
## ElGamal Encryption ## ElGamal Encryption

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_posts/Lecture Notes/Internet Security/2023-10-09-public-key-cryptography.md
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@@ -14,7 +14,7 @@ date: 2023-10-09
github_title: 2023-10-09-public-key-cryptography github_title: 2023-10-09-public-key-cryptography
--- ---
In symmetric key cryptography, we have a problem with key sharing and management. More info in the first few paragraphs of [Key Exchange (Modern Cryptography)](2023-10-03-key-exchange.md#). In symmetric key cryptography, we have a problem with key sharing and management. More info in the first few paragraphs of [Key Exchange (Modern Cryptography)](../../modern-cryptography/2023-10-03-key-exchange).
## Public Key Cryptography ## Public Key Cryptography
@@ -31,7 +31,7 @@ These keys are created to be used in **trapdoor one-way functions**.
A **one-way function** is a function that is easy to compute, but hard to compute the pre-image of any output. Here are some common examples. A **one-way function** is a function that is easy to compute, but hard to compute the pre-image of any output. Here are some common examples.
- *Cryptographic hash functions*: [Hash Functions (Modern Cryptography)](2023-09-28-hash-functions.md#collision-resistance). - *Cryptographic hash functions*: [Hash Functions (Modern Cryptography)](../../modern-cryptography/2023-09-28-hash-functions#collision-resistance).
- *Factoring a large integer*: It is easy to multiply to integers even if they're large, but factoring is very hard. - *Factoring a large integer*: It is easy to multiply to integers even if they're large, but factoring is very hard.
- *Discrete logarithm problem*: It is easy to exponentiate a number, but it is hard to find the discrete logarithm. - *Discrete logarithm problem*: It is easy to exponentiate a number, but it is hard to find the discrete logarithm.
@@ -86,7 +86,7 @@ Choose a large prime $p$ and a generator $g$ of $\mathbb{Z}_p^{ * }$. The descri
> 3. Alice and Bob calculate $g^{xy} \bmod p$ separately. > 3. Alice and Bob calculate $g^{xy} \bmod p$ separately.
> 4. Eve can see $g^x \bmod p$, $g^y \bmod p$ but cannot calculate $g^{xy} \bmod p$. > 4. Eve can see $g^x \bmod p$, $g^y \bmod p$ but cannot calculate $g^{xy} \bmod p$.
Refer to [Diffie-Hellman Key Exchange (Modern Cryptography)](2023-10-03-key-exchange.md#diffie-hellman-key-exchange-dhke). Refer to [Diffie-Hellman Key Exchange (Modern Cryptography)](../../modern-cryptography/2023-10-03-key-exchange#diffie-hellman-key-exchange-dhke).
## Message Integrity ## Message Integrity