# Modern Cryptography Notes (To be continued…)

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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