cryptography

Cryptography? #

The methodology of concealing the content of messages. Originates from the Greek root word kryptos, which means hidden. The modern scientific study of crytography is sometimes referred to as cryptology¹.

Ciphers? #

A function that encrypts some plaintext into an unreadable ciphertext.

def cipher(plaintext) -> str:
    ...
    return ciphertext

Codebreaking? #

The analysis and attack of classical cryptosystems. In the context of modern cryptography, codebreaking refers to the exploitation of modern encryption systems.

Project progress #

(python only + no codebreaker required yet)

• Table substitution cipher
• Digraph substitution cipher
• Playfair cipher
• Shift cipher
• Vigenere cipher
• Affine cipher
• Steganography
• Xor
• One-time pad + proof of perfect secrecy
• Information theory: entropy analysis
• Information theory: wordle solver
• Block cipher
• Stream cipher
• Data encryption standard
• Padding oracle attack
• Hashing
• MACs
• Rainbow table attack
• RSA
• Diffie-Hellman key exchange
• ElGamal
• Complexity theory
• Abstract algebra review
• Factorization
• Discrete log
• Decisional Diffie-Hellman assumption
• Primality testing
• Elliptic-curve cryptography
• Lenstra’s elliptic-curve factorization
• Elliptic-curve digital signature algorithm
• RSA signature
• ElGamal signature
• Existential forgery
• Shortest Vector Problem (bounds)
• Fundamental domain of lattices
• Reduction of Closest Vector Problem to SVP
• Subset sum of cryptosystem
• NTRU encryption algorithm
• Ring Learning With Errors

The first third is mainly symmetric cryptography. The rest is assymetric cryptography.

Table substitution cipher #

This substitution cipher looks up each plaintext letter in an encryption table and writes the corresponding ciphertext letter in its place. Evidently, the decryption table is the inverse of the encryption table

decryption_table = {v: k for k, v in encryption_table.items()}

In a table substitution cipher, the ciphertext alphabet is a randomly chosen permutation of the 26 alphabet letters. The random permutation for this cipher is both lowercase and capital alphabet letters

Random permutation example: OaTyqwGerPSApdfghjXUIlzxcZLMVWKuZvbCRnmYNoQBkisFDtJH

plaintext to ciphertext values like O, a, and T are chosen randomly (or by using a generator).

Digraph substitution cipher #

Similar to the monoalphabetic table substitution cipher, this is another substitution cipher. Unlike the monoalphabetic table cipher, this cipher replaces every plaintext digraph with its corresponding ciphertext digraph instead of replacing every plaintext letter with its corresponding ciphertext letter. Each ciphertext digraph is located by position given a row index and column index determined by the plaintext digraph

shift_row = 4
shift_column = 17

alpha = "abcdefghijklmnopqrstuvwxyz"

# Shifts the alphabet over by `shift` amount. Loops overflow values to start.
def shift_alpha(alpha, shift) -> str:
    return alpha[shift:len(alpha)] + alpha[:shift]

sbox = [[shift_alpha(alpha, shift_column)[i] + (shift_alpha(alpha, shift_row)[j])
         for j in range(len(alpha))] for i in range(len(alpha))]

For an explanation of how plaintext turns into ciphertext, visit the title link.

Playfair cipher #

The playfair cipher! This one is sort of like the digraph substitution cipher in utilizing a table (this one’s is 5x5) and multiple digraph substitutions, but this cipher has a few more rules. Unlike the digraph substitution cipher mentioned above, this one does not have a ciphertext digraph intersection value based on two inputted label points from a plaintext digraph. The playfair cipher instead shifts isolated digraph characters up, down, or diagonally in the matrix according to the digraph classification.

Additionally, this cipher has a key! See more about keys and about the playfair encryption method at the title link.

key = "shadow"

Shift Cipher #

Otherwise known as a caesar cipher, the shift cipher takes each letter in a plaintext message and shifts it by n indexes in the looping alphabet.