Modern Cryptography Notes (To be continued…)

虽然课上完了，但是由于本人精力有限，暂且无限期鸽鸽本文。。。

Cryptography course notes taking from Introduction to Modern Cryptography.

Intro

What make Modern Crypto Modern?

• The central role of definitions
• The importance of formal and precise assumptions
• The possibility of proof of security

Scenarios

• Secure Communication Through Space ($A -> B$, E)
• Secure Communication Through Time ($A_{past} -> A_{future}$, E)

Encryption Scheme Syntax

• $\mathcal{M}$: message space
• $\mathsf{Gen}$: procedure for generating keys
• $\mathsf{Enc}$: procedure for encrypting
• $\mathsf{Dec}$: procedure for decrypting
• Satisfy: $\mathsf{Dec}_k (\mathsf{Enc}_k (m)) = m$

Steps

Encryption scheme: tuple $(\mathsf{Gen}, \mathsf{Enc}, \mathsf{Dec})$

1. $k \leftarrow \mathsf{Gen}(1^n)$
2. $c \leftarrow \mathsf{Enc}_k (m)$
3. $m \coloneqq \mathsf{Dec}_k(c)$

Historic Cipher

• Shift Cipher
• Permutation Cipher
• Vigen`ere Cipher

Attacks

• Frequency Analysis
• Index of Coincidence

Kerckhoffs’ Principle

The cipher method must not be required to be secret, and it must be able to fall into the hands of the enemy without inconvenience.

Formal Definition

learn no additional information about the plaintext, regardless of any prior information an attacker has learned

Threat Models

• Ciphertext-only attack
• Known-plaintext attack
• Chosen-plaintext attack
• Chosen-ciphertext attack