Symmetric Cryptography

Goals and Terms

Cryptography: The practice of designing systems for secure communication in the presence of adversaries.
Cryptanalysis: Breaking cryptographic systems by recovering the message or key without being given the key.
Cryptology: The study of both cryptography and cryptanalysis.
Confidentiality: Keeping the contents of a message hidden from unauthorized readers.
Authentication: Verifying the origin of a message or the identity of a party.
Integrity: Ensuring that a message has not been modified.
Non-repudiation: Preventing a sender from later denying that they sent a message.
Plaintext: The original, readable message.
Ciphertext: The encrypted form of a message.
Encryption: Transforming plaintext into ciphertext.
Decryption: Recovering plaintext from ciphertext.
Cipher: The algorithm that transforms plaintext into ciphertext and back.
Key: The secret value that controls how a cipher transforms data.
Cryptosystem: A cipher together with its keys and the procedures for using them.
Symmetric encryption: Encryption in which the same key encrypts and decrypts.
Asymmetric encryption: Encryption in which different keys encrypt and decrypt.
Keyspace: The set of all possible keys for a cipher.
Brute-force attack: Trying every key until one produces readable plaintext.
Kerckhoffs’s Principle: A cryptosystem must remain secure when everything but the key is known.
Schneier’s Law: Anyone can design a cipher that they themselves cannot break.

Classical Ciphers

Classical cipher: A cipher designed to be operated by hand, before the twentieth century.
Substitution cipher: A cipher that replaces each symbol with another symbol.
Transposition cipher: A cipher that keeps the symbols but rearranges their order.
Caesar cipher: A substitution cipher that shifts every letter by a fixed amount.
Monoalphabetic substitution cipher: A cipher that maps each plaintext letter to one fixed ciphertext letter.
Bigram: A pair of adjacent letters, also called a digram.
Trigram: A sequence of three adjacent letters.
Frequency analysis: Breaking a cipher by matching symbol frequencies to a language’s letter frequencies.
Polyalphabetic cipher: A substitution cipher that changes its alphabet as it moves through the message.
Vigenère cipher: A polyalphabetic cipher in which a repeating keyword selects the shift for each letter.
Keystream: The sequence of key values applied one by one to successive units of plaintext.
Period: The number of letters before a keystream repeats.
Keyword: A repeated word whose letters select successive substitutions.
Kasiski attack: Finding a Vigenère keyword’s length from the distances between repeated ciphertext.
Columnar transposition: Writing a message in rows and reading the columns in keyword order.
Padding: Filler added so that a message fits a required size.
Playfair cipher: A nineteenth-century cipher that substituted pairs of letters instead of single letters.
ADFGVX cipher: A World War I German cipher that applied substitution and then transposition.

Rotor Machines

Rotor: A disk wired to perform a fixed substitution that changes as it turns.
Rotor machine: A cipher machine whose stacked rotors change the substitution with every letter.
Enigma: The German rotor machine of World War II, broken through its structural and procedural flaws.
Message key: The rotor starting positions chosen by an Enigma operator for one message.
Crib: A stretch of plaintext that an analyst can guess for a given ciphertext.
Bombe: The electromechanical machine that searched for Enigma settings consistent with a crib.
Stop: A bombe halt at a setting that produced no contradiction.
Traffic analysis: Learning who is communicating, when, and how much without reading the messages.
Stream cipher: A cipher that XORs the message with a generated sequence of key bits.

Information Theory and Perfect Secrecy

Entropy: The uncertainty in a random variable, measured in bits.
Redundancy: The portion of a message that a reader could have predicted.
Perfect secrecy: A cipher whose ciphertext reveals no information about the plaintext.
Exclusive-or (XOR): A bit operation that yields 1 when its inputs differ and 0 otherwise.
One-time pad: XORing the message with a random, never-reused key of the same length.
Computational security: Security that holds because breaking the cipher is infeasible, not impossible.
Bounded adversary: An attacker limited by time, computing power, money, and available ciphertext.
Computational indistinguishability: A feasible adversary cannot tell which of two chosen messages a ciphertext encrypts.
Ciphertext-only attack: An attack using intercepted ciphertext alone.
Known-plaintext attack: An attack using some plaintext together with its ciphertext.
Chosen-plaintext attack: An attack in which the adversary gets chosen messages encrypted.
Chosen-ciphertext attack: An attack in which the adversary gets chosen ciphertexts decrypted.
Confusion: Making the relationship between key and ciphertext too complex to express.
Diffusion: Spreading the influence of each plaintext bit across many ciphertext bits.
S-box: A small nonlinear lookup table that provides confusion.
Avalanche effect: A one-bit input change altering about half the output bits.
Round: One application of a cipher’s repeated sequence of operations.

Randomness

True random number: A value produced by an unpredictable physical process.
Pseudorandom number generator (PRNG): A deterministic algorithm that expands a seed into a long random-looking sequence.
Seed: The short secret value from which a pseudorandom generator starts.
Entropy source: A physical process whose measurements supply unpredictable bits.
Cryptographically secure pseudorandom number generator (CSPRNG): A generator whose output cannot be predicted or distinguished from true randomness.
Entropy pool: An operating system’s collection of unpredictable events used to seed its generator.

Block Ciphers

Block cipher: A cipher that encrypts fixed-size blocks of bits under a key.
State: The array of bytes a block cipher transforms during encryption.
Key schedule: The procedure that expands a key into separate round keys.
Round key: The key material mixed into the state during one round.
Substitution-permutation network (SPN): A block cipher structure alternating S-boxes, permutations, and key addition.
Feistel network: A block cipher structure that never needs to invert its round function.
Data Encryption Standard (DES): The 1977 Feistel cipher with a 56-bit key, now broken by brute force.
Triple DES (3DES): DES applied three times to extend its key length.
Meet-in-the-middle attack: Attacking double encryption from both ends to avoid searching both keys.
Birthday bound: The number of samples, about the square root of the possible values, after which repeats are likely.
Advanced Encryption Standard (AES): The 2001 standard block cipher, with a 128-bit block and 128- to 256-bit keys.
Rijndael: The cipher family from which AES was standardized.
AES-NI: Processor instructions that compute AES rounds in hardware.

Modes of Operation

Mode of operation: The method for applying a block cipher to messages longer than one block.
Electronic codebook (ECB): A mode that encrypts each block independently, exposing repeated blocks.
Cipher block chaining (CBC): A mode that XORs each plaintext block with the previous ciphertext block.
Padding oracle: An attack that decrypts ciphertext using a server’s reports of valid or invalid padding.
Initialization vector (IV): A random, non-secret block that starts CBC encryption of a message.
Counter (CTR) mode: A mode that encrypts counter values to produce a keystream.
Malleable: A property of ciphertext that lets an attacker make predictable changes to the plaintext.
Nonce: A number used once per message with a given key.
Galois/Counter mode (GCM): Counter mode with an authentication tag added.
Authenticated encryption with associated data (AEAD): Encryption that also produces a tag for detecting tampering.
Authentication tag: A short value that lets a receiver detect a modified ciphertext.
Associated data: Header information that an AEAD mode authenticates but does not encrypt.

Stream Ciphers

Keystream generator: A function that produces a keystream from a key and a nonce.
RC4: The biased stream cipher of the early Internet, now prohibited in TLS.
ChaCha20: The modern stream cipher built from additions, rotations, and XORs.
Poly1305: The authenticator paired with ChaCha20 in ChaCha20-Poly1305.

Cryptanalysis

Differential cryptanalysis: Tracing how plaintext differences propagate into ciphertext differences.
Linear cryptanalysis: Exploiting XOR relations among plaintext, ciphertext, and key bits that hold with bias.
Side-channel attack: Recovering secrets from an implementation’s timing, power, emissions, or faults.
Cache-timing attack: A side-channel attack that infers secrets from memory access patterns.
Power analysis: A side-channel attack that infers secrets from a device’s power consumption.
Fault injection: Inducing computation errors to reveal secrets from the faulty output.
Constant-time code: Code whose timing and memory accesses do not depend on secrets.
Masking: Randomizing intermediate values so that measurements do not correlate with secrets.
Bits of security: The exponent n when the best attack costs about 2^n operations.
Grover’s algorithm: A quantum search that halves the effective length of a symmetric key.