Cryptography

main resource Introduction_to_Modern_Cryptography.pdf

Chapter 1: Introduction and classical ciphers

Setting of Private-key encryption

• setting in which communicating parties share some secret information in advance is private-key (or symmetric-key) setting

The syntax of encryption Private-key encryption scheme

• key-generation algorithm: Gen is a probabilistic algorithm that outputs a key k chosen according to some distribution
• encryption algorithm: Enc take as a input a key k and a plantext m and outputs a ciphertext c → $En{c}_k(m)$
• decryption algorithm: Dec takes input a key k and ciphertext c and outputs a plaintext m → $De{c}_k(c)$

Generating keys defines a key space $\mathcal{K}$ (i.e. set of all possible keys), and encryption scheme is defined over some set of possible plaintext messages denoted $\mathcal{M}$

Basic correct requirement of any encryption scheme is that for every key k by Gen and every plaintext messagr $m\in \mathcal{M}$, it holds that $De{c}_k(En{c}_k(m))=m$

In words, an encryption scheme must have the property that decrypting a ciphertext (with the appropriate key) yields the original message that was encrypted.

Keys and Kerckoff’s principle If adversary knows the algorithm Dec as well as the key k shared by two communicating parties, then that adversary will be able to decrypt all communication between these parties.

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.

Historical Ciphers and their crpytoanalysis

• Caesar’s cipher
• Mono-alphabetic substition
• The Vigenère (poly-alphabetic shift) cipher