Foundational#

Cryptography is the practice and study of techniques for securing communication in the presence of adversaries. The primary goal is to conceal a message so that only intended recipients can understand it.

On Security#

The principles of information security provide a framework for protecting data. Confidentiality ensures that information is only accessible to authorized users, for example, encrypting emails so only the intended recipient can read them. Integrity guarantees that data is accurate and unaltered, such as using a checksum to verify a downloaded file has not been tampered with. Availability ensures that information and systems are accessible when needed, like maintaining redundant servers so a website remains online during outages. Authentication confirms the identity of users or systems, for instance, requiring a username and password before accessing an account. Non-repudiation prevents parties from denying their actions, such as using digital signatures to prove the sender authored a document.

Concealing a Message#

There are three historically distinct approaches:

  1. Hiding the existence of the message
  2. Obscuring the structure of the message
  3. Transforming the message into an unreadable form

Steganography#

Steganography is the practice of hiding a message so that its existence is concealed.

  • The message is hidden within another medium (text, image, object).
  • If discovered, the message may be readable immediately.
  • Security relies on secrecy of the method, not strong mathematics.

Historical examples:

  • Writing a message on a person’s shaved scalp and allowing hair to regrow over it (Herodotus).
  • Scraping wax off wooden tablets, writing the message underneath, then recoating with wax.
  • Invisible inks, microdots, digital image steganography.

Key idea: The attacker should not even suspect a message exists.

Transposition#

A transposition cipher rearranges the characters of a message according to a fixed system.

  • The letters themselves are unchanged.
  • Only their positions are permuted.
  • Common types include columnar transposition and route ciphers.

Example 1: Columnar Transposition#

PLAINTEXT:  ATTACKATDAWN
TRANSPOSED: TTAWACDATKAN

Example 2: Scytale (Ancient Greek military)#

  • A scytale is a cylinder around which a strip of parchment is wound.
  • The message is written along the length of the cylinder.
  • When unwound, the letters appear scrambled. Only a cylinder of the same diameter can read it correctly.
PLAINTEXT:  ATTACKATDAWN
SCYTALE STRIP (scrambled when flat):
A C A
T K T
T A D
A W N
  • Reading column-wise along the cylinder reconstructs the original message.

Properties:

  • Preserves letter frequency.
  • Vulnerable to statistical analysis if used alone.
  • Often combined with substitution for added security.

Encryption#

Encryption is the process of transforming plaintext into ciphertext using an algorithm and a key.

  • Comes from the Greek kryptós (hidden or secret).
  • Assumes the attacker knows the algorithm but not the key (Kerckhoffs’s Principle).
  • Modern cryptography relies on computational hardness, not obscurity.

Cipher#

A cipher is a specific algorithm for performing encryption or decryption.

  • Operates at the level of letters, bits, or symbols
  • Uses a key to control the transformation

Ciphers can be classified as:

  • Substitution ciphers (replace symbols)
  • Transposition ciphers (reorder symbols)
  • Product ciphers (combine both)

Code#

A code replaces entire words or phrases with symbols or numbers.

  • Operates at the semantic level (words/phrases), not letters.
  • Requires a codebook.
  • Example: “Attack at dawn” → “4729”

Differences from ciphers:

  • Codes are language-dependent.
  • Codebooks are bulky and hard to distribute securely.
  • Historically used in diplomacy and military communication.

Cryptanalysis#

Cryptanalysis is the study of methods for breaking cryptographic systems—recovering the plaintext or key without authorization.

Determining the Secret Key#

The primary goal of cryptanalysis is to determine the secret key or otherwise recover plaintext.

Attack models include:

  • Ciphertext-only attack
  • Known-plaintext attack
  • Chosen-plaintext attack
  • Brute-force attack

Decryption#

Decryption is the process of converting ciphertext back into plaintext.

  • From the Greek kryptós (hidden) + lýein (to loosen or release).
  • Normally requires the secret key.
  • Cryptanalysis seeks to decrypt without the key.

Crib#

A known piece of plaintext appearing within a piece of ciphertext. Turing used a crib when cracking the Enigma machine, knowing that at 06:05 each day the German’s transmitted a weather report containing the plaintext “wetter” (German for weather).

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