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