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* PUSH NOTE : 09. Transport Layer Security.md

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* PUSH NOTE : 08. Public Key Infrastructure.md

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* PUSH NOTE : 07. Public Key Cryptography.md

* PUSH NOTE : 06. RSA and ElGamal Encryption.md

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

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

* PUSH NOTE : 03. Symmetric Key Cryptography (2).md

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

* PUSH NOTE : 01. Security Introduction.md

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* PUSH NOTE : 9. Public Key Encryption.md

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* PUSH NOTE : 7. Key Exchange.md

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* PUSH NOTE : 6. Hash Functions.md

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* PUSH NOTE : 5. CCA-Security and Authenticated Encryption.md

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* PUSH NOTE : 4. Message Authentication Codes.md

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* PUSH NOTE : 2. PRFs, PRPs and Block Ciphers.md

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* PUSH NOTE : 16. The GMW Protocol.md

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* PUSH NOTE : 13. Sigma Protocols.md

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* PUSH NOTE : 12. Zero-Knowledge Proofs (Introduction).md

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* PUSH NOTE : 10. Digital Signatures.md

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

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Sungchan Yi
2024-11-12 20:54:38 +09:00
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10
_posts/lecture-notes/modern-cryptography/2023-10-26-digital-signatures.md
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@@ -14,9 +14,9 @@ title: 10. Digital Signatures
date: 2023-10-26
github_title: 2023-10-26-digital-signatures
image:
path: assets/img/posts/Lecture Notes/Modern Cryptography/mc-10-dsig-security.png
path: assets/img/posts/lecture-notes/modern-cryptography/mc-10-dsig-security.png
attachment:
folder: assets/img/posts/Lecture Notes/Modern Cryptography
folder: assets/img/posts/lecture-notes/modern-cryptography
---
## Digital Signatures
@@ -57,7 +57,7 @@ $$
The definition is similar to the [secure MAC](./2023-09-21-macs.md#secure-mac-unforgeability). The adversary can perform a **chosen message attack**, but cannot create an **existential forgery**.
![mc-10-dsig-security.png](../../../assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-10-dsig-security.png)
![mc-10-dsig-security.png](../../../assets/img/posts/lecture-notes/modern-cryptography/mc-10-dsig-security.png)
> **Definition.** Let $\mc{S} = (G, S, V)$ be a signature scheme defined over $(\mc{M}, \Sigma)$. Given an adversary $\mc{A}$, the game goes as follows.
>
@@ -184,7 +184,7 @@ This scheme is originally from the **Schnorr identification protocol**.
Let $G = \left\langle g \right\rangle$ be a cyclic group of prime order $q$. We consider an interaction between two parties, prover $P$ and a verifier $V$. The prover has a secret $\alpha \in \Z_q$ and the verification key is $u = g^\alpha$. **$P$ wants to convince $V$ that he knows $\alpha$, but does not want to reveal $\alpha$**.
![mc-10-schnorr-identification.png](../../../assets/img/posts/Lecture%20Notes/Modern%20Cryptography/mc-10-schnorr-identification.png)
![mc-10-schnorr-identification.png](../../../assets/img/posts/lecture-notes/modern-cryptography/mc-10-schnorr-identification.png)
The protocol $\mc{I}_\rm{sch} = (G, P, V)$ works as follows.
@@ -239,7 +239,7 @@ Schnorr's scheme was protected by a patent, so NIST opted for a ad-hoc signature
How would you trust public keys? We introduce **digital certificates** for this.
Read in [public key infrastructure (Internet Security)](../../Lecture%20Notes/Internet%20Security/2023-10-16-pki.md).
Read in [public key infrastructure (Internet Security)](../internet-security/2023-10-16-pki.md).
[^1]: A Graduate Course in Applied Cryptography
[^2]: By using the [Fiat-Shamir transform](./2023-11-07-sigma-protocols.md#the-fiat-shamir-transform).