Reference Guide

Cryptography Glossary

Selected terms for exploring cryptography

A B C D E F GH IJ K L M N O P QR S T UV WX YZ

58 terms

A

Algorithm

Mathematics

A precise, step-by-step procedure. Cryptographic algorithms include encryption, decryption, signing, verification, hashing and key agreement. Their designs can be public; a secure system must not depend on keeping its algorithm secret.

Asymmetric Encryption

Modern Cryptography · 1976

Encryption using a mathematically related public key and private key. A sender encrypts with the recipient’s public key; decryption requires the private key under the scheme’s security assumptions. RSA supports public-key encryption when used with an appropriate encoding scheme. Diffie–Hellman instead establishes shared key material; it does not itself encrypt messages.

Avalanche Effect

Horst Feistel · 1973

The tendency of a small input change to alter many output bits. For a well-designed cipher, flipping one input bit should change about half the output bits on average over suitable inputs. This is a statistical property, not a promise that every individual change flips exactly half, and it is not by itself proof of security.

B

Bilinear Pairing

Modern Cryptography

A map e(P,Q) with the property e(aP,bQ) = e(P,Q)^ab. Carefully chosen pairings let protocols test relations between hidden scalars. They support some zk-SNARKs, identity-based encryption and signatures; other proof systems use different constructions. Interactive: Bilinear Pairings (§156).

Block Cipher

Modern Cryptography

A cipher that operates on fixed-size groups (blocks) of bits. AES uses 128-bit blocks. For each key, the primitive is a deterministic permutation of blocks. Modes such as CBC and GCM construct message-encryption schemes around that primitive, using additional inputs such as IVs or nonces; they do not change the underlying permutation.

See also: Stream Cipher, Mode of Operation

Brute Force Attack

Cryptanalysis

Testing candidate keys until one satisfies the available evidence. A uniformly chosen n-bit key has 2ⁿ possibilities; classical exhaustive search takes about half that many trials on average. Recognizing the right key requires enough known structure or other verification. Algorithmic attacks can be much faster than exhaustive search.

C

Cipher

Arabic: sifr (zero) · Latin: cifra

An algorithm for performing encryption or decryption — a system of rules for transforming readable text (plaintext) into an unreadable form (ciphertext) and back. In historical terminology, codebooks often replace words or phrases. A cipher is not limited to individual letters: modern schemes operate on bits or bytes.

Ciphertext

Core Concept

The encrypted output of an encryption scheme. A secure scheme should conceal the protected plaintext under its stated attack model. Ciphertexts can still expose length, public headers or formatting; not every secure format is indistinguishable from uniform random bytes.

Confusion

Claude Shannon · 1949

Shannon’s design idea of making the relationship between ciphertext statistics and the key difficult to exploit. Nonlinear substitutions such as AES S-boxes contribute to confusion. Paired with diffusion, this is a design principle, not a numerical security measure or proof.

Crib

Bletchley Park · WWII

A known or guessed piece of plaintext used to help analyze a cipher. Predictable weather-report language supplied cribs against Enigma. A guessed crib must be tested; a known-plaintext attack instead assumes that matching plaintext and ciphertext are already available.

Cryptanalysis

Greek: kryptós (hidden) + analysis

The study of attacks on cryptographic security goals, including recovering plaintext or keys, forging authentication, and finding hash collisions. Methods include frequency analysis, differential cryptanalysis and side-channel analysis; not every successful attack recovers a full message or key.

Cryptography

Greek: kryptós (hidden) + graphein (to write)

The practice and study of techniques for securing communication in the presence of adversaries. Encompasses encryption, authentication, integrity verification, and non-repudiation. Cryptology is the umbrella field covering both cryptography and cryptanalysis.

D

Decryption

Core Concept

The reverse of encryption: transforming ciphertext back into readable plaintext using the correct key. In symmetric ciphers, the same key encrypts and decrypts. In asymmetric ciphers, the private key decrypts what the public key encrypted.

Diffusion

Claude Shannon · 1949

Shannon’s design idea of spreading plaintext statistical structure across the ciphertext. In modern block ciphers, mixing such as AES MixColumns helps spread dependencies. A permutation alone only moves positions; it does not make one changed symbol affect many output symbols. Confusion and diffusion are design concepts, not proofs of security.

Digraph

Linguistics / Cryptography

A pair of letters treated as a single unit. The Playfair cipher encrypts digraphs rather than individual letters, which disrupts single-letter frequency analysis. Common English digraphs: TH, HE, IN, ER, AN.

E

Elliptic Curve

Mathematics

For a nonsingular short-Weierstrass curve, the points satisfying y² = x³ + ax + b, together with a point at infinity, form a group. Over the reals, a line-and-reflection construction illustrates addition; over finite fields, modular formulas define it. Addition is efficient. Security in suitable ECDH and ECDSA groups relies on the difficulty of recovering a scalar k from P and kP. Interactives: the group law (§150) and finite fields (§142).

Encryption

Core Concept

The process of converting plaintext into ciphertext using a cipher and a key. Its intended security is confidentiality under a stated attack model; weak schemes can still be broken. Encryption protects confidentiality — one of the three pillars of information security (CIA triad).

Entropy

Information Theory · Claude Shannon · 1948

A measure of uncertainty in a probability distribution. A uniformly sampled n-bit key has n bits of Shannon entropy, but n bits of entropy does not in general imply exactly 2ⁿ equally likely outcomes. Entropy belongs to a generation process, not to a string merely because it looks complicated; min-entropy is useful when bounding the most likely guess.

F

Finite Field

Mathematics

A finite set with field arithmetic: addition, subtraction, multiplication and division by any nonzero element. Integers modulo a prime p form a field. AES uses GF(2⁸); its S-box combines field inversion (with a special rule at zero) and an affine transformation. Interactive: Finite Fields (§142).

Fractionation

19th Century · Delastelle

A technique that breaks each plaintext letter into multiple components (e.g., coordinates on a grid), manipulates the components separately, then recombines them. Used in Bifid, Trifid, and ADFGVX ciphers. It provides a useful comparison with modern diffusion, without establishing a direct design lineage.

Frequency Analysis

Al-Kindi · Baghdad · ~850 AD

Comparing symbol and symbol-sequence frequencies with expected language patterns. Monoalphabetic substitution preserves frequency counts while relabeling the symbols. Those counts suggest mappings; short samples, unusual vocabulary and ambiguity prevent them from guaranteeing a key. Al-Kindi’s surviving treatise is an early systematic account.

H

Hash Function

Modern Cryptography

A function mapping messages to fixed-size digests, within its defined input limits. Cryptographic hashes aim for computational resistance to preimage, second-preimage and collision attacks. Collisions necessarily exist; security concerns the difficulty of finding them. SHA-256 produces a 256-bit digest, and a plain unkeyed hash does not authenticate a message.

Homophonic Substitution

15th–16th Century

A substitution cipher where each plaintext letter can map to multiple different ciphertext symbols, roughly proportional to the letter's frequency. E might map to 13 different symbols, Z to 1. This flattens frequency distributions, making frequency analysis much harder — but not impossible.

I

Index of Coincidence (IC)

William Friedman · 1922

The probability that two distinct positions sampled without replacement from a text contain the same letter. For N letters with counts nᵢ, IC = Σ nᵢ(nᵢ−1) / [N(N−1)]. Typical long English samples are near 0.066; uniform A–Z samples approach 1/26 ≈ 0.0385. Values depend on language, text length and preprocessing, and provide clues rather than certain cipher identification.

Initialization Vector (IV)

Modern Cryptography

A public input to a cipher mode whose requirements depend on that mode. CBC encryption needs an unpredictable IV; uniqueness alone is insufficient. GCM requires nonce/IV uniqueness for each key, with careful limits when values are generated randomly. An IV need not be secret, and it does not replace authentication. See NIST SP 800-38A and SP 800-38D.

K

Kasiski Examination

Friedrich Kasiski · 1863

A way to propose repeating-key periods. Measure the distances between repeated ciphertext fragments and examine common factors. Repetitions can be accidental, and useful distances may reflect multiples of the true period. Check proposed periods with additional statistical evidence rather than treating their greatest common divisor as proof.

Kerckhoffs's Principle

Auguste Kerckhoffs · 1883

A cryptosystem should remain secure when its design is known to an adversary. Published algorithms still need appropriate keys, parameters, protocols and implementations. Unkeyed hashes such as SHA-256 have no secret key; their security goals depend on the difficulty of specified attacks.

Key

Core Concept

A value that selects an operation within a cryptographic scheme. Symmetric and private keys are secret; public keys are intentionally shared. An unrestricted n-bit key space contains 2ⁿ values, but effective security also depends on the sampling process and attacks against the scheme.

Key Pair

Asymmetric Cryptography · 1976

A related public key and private key used by an asymmetric scheme. The public key is shared and the private key kept secret. Encryption, signatures and key agreement are different operations: signatures are not generally encryption run backwards. Examples include RSA encryption, ECDSA signatures and Diffie–Hellman key agreement.

Keyspace

Cryptanalysis

The set of permitted keys. Caesar has 26 shifts if the identity shift is included, or 25 nonidentity shifts. A substitution permutation has 26! possibilities; AES-256 has 2²⁵⁶ keys. Large keyspaces alone do not guarantee security: attacks may exploit structure without testing every key.

L

Lattice

Post-Quantum Cryptography

The set of integer combinations of independent basis vectors. Certain high-dimensional lattice problems are believed hard for classical and quantum computers. ML-KEM and ML-DSA use structured module-lattice assumptions; they do not rely on every lattice instance being difficult. Interactive: Lattices & the SVP (§147).

Learning With Errors (LWE)

Post-Quantum Cryptography

Distinguishing or recovering a secret from noisy linear relations, under a specified distribution of matrices, secrets and errors. ML-KEM uses Module-LWE: its public key encodes a noisy matrix–secret-vector product, and decapsulation uses the short secret vector to cancel a shared term before decoding. The plain LWE and module variants are related but distinct assumptions. Interactive: Learning With Errors (§157); the geometry of decoding (§152).

M

Mode of Operation

Modern Block Ciphers

A method for applying a block cipher to messages longer than one block. ECB (Electronic Codebook) encrypts each block independently — insecure because identical blocks produce identical ciphertext. CBC (Cipher Block Chaining) XORs each plaintext block with the previous ciphertext block before encryption, using an IV for the first block. GCM provides authenticated encryption when its nonce and usage requirements are met.

Modular Arithmetic

Mathematics

Arithmetic with residues: 9 + 5 ≡ 2 (mod 12). Classical finite-field Diffie–Hellman uses a suitable subgroup modulo a prime. RSA uses arithmetic modulo a composite number n, normally the product of two primes. Interactive: Modular Arithmetic (§143).

Monoalphabetic Cipher

Ancient

A substitution cipher using a single fixed alphabet mapping. Each plaintext letter always maps to the same ciphertext letter. Caesar, Atbash, and keyword substitution are all monoalphabetic. Vulnerable to frequency analysis because letter frequencies are preserved exactly.

N

Nonce

Number used once

A value required to be unique within the context specified by a protocol, often for each encryption key. Reusing an AES-GCM nonce repeats its counter-mode keystream, revealing the XOR of equal-length plaintext portions, and can enable authentication forgeries. Nonces may be counters or carefully generated random values; requirements are scheme-specific.

Nomenclator

Renaissance · 15th–18th Century

A hybrid system combining a simple substitution alphabet with a codebook of common words and names. Used extensively in diplomatic correspondence for centuries. Security varies with the key, code list and traffic. Substitution analysis can expose useful clues without automatically reconstructing the whole vocabulary.

O

One-Time Pad (OTP)

Gilbert Vernam · 1917 / Claude Shannon · 1949

Encryption with uniformly random secret key material independent of the message, at least as long as the message, and never reused. Under those conditions it provides perfect secrecy for fixed-length messages. Other constructions can also provide perfect secrecy. The pad does not hide length or authenticate ciphertext, and secure key distribution remains essential.

One-Way Function

Modern Cryptography

A function that is efficient to compute but conjectured hard to invert on inputs sampled from a specified distribution. No general existence proof is known. Multiplication of suitably sampled primes illustrates a candidate based on factoring, whose difficulty depends on size and structure. Interactive: The One-Way Function (§146).

P

Plaintext

Core Concept

The original data before encryption, whether text or other information. Denoted P or M in formulas. The goal of encryption is to protect plaintext from unauthorized readers. Recovering plaintext is one possible goal of cryptanalysis.

Polyalphabetic Cipher

Leon Battista Alberti · 1467

A cipher that uses multiple substitution alphabets, switching between them according to a key. The Vigenère cipher is the classic example: each key letter selects a different Caesar shift. For repeating-key constructions, periodic patterns may support Kasiski or coincidence analysis. Not every polyalphabetic construction has a fixed repeating keyword.

Polybius Square

Polybius · ~150 BC

A modern Latin-alphabet version uses a 5×5 grid with I/J sharing a cell. Polybius’s ancient account describes arranging the Greek alphabet on five tablets for coordinate signaling. Bifid and ADFGX use square coordinates in fractionation. Trifid uses three coordinates from a cube; the additive Nihilist cipher instead adds numerical coordinate pairs.

Polynomial Ring

Post-Quantum Cryptography

A ring of polynomials with coefficient addition and multiplication. ML-KEM and ML-DSA use a particular quotient ring, R_q = ℤ_q[X]/(Xⁿ+1): coefficients are reduced modulo q and Xⁿ is replaced by −1. Their module operations use vectors and matrices over this ring. Interactive: Polynomial Rings (§153).

Public Key

Diffie-Hellman · 1976

The publicly shared key of an asymmetric key pair. Its purpose depends on the scheme: encryption, signature verification or key agreement. The related private key must remain infeasible to recover under the scheme’s assumptions, and users also need a way to authenticate whose public key they received.

R

Random Oracle

Modern Cryptography

An ideal function that assigns independent uniform outputs to distinct inputs and answers repeated queries consistently. Some proofs assume access to this oracle. Replacing it with a concrete hash is an additional design step, not a proof that SHA-256 is an oracle. Fiat–Shamir can transform suitable interactive protocols into noninteractive proofs or signatures under specified assumptions. Interactive: The Random Oracle (§154).

Rotor

Enigma Machine · 1920s

A wired wheel that maps input contacts to output contacts. In Enigma, several rotors and a reflector produce a changing substitution; the stepping mechanism advances before the electrical transformation. Three 26-position rotors have 17,576 displayed starting positions for a fixed order, while ring settings, plugboard choices and stepping behavior are separate parts of the configuration.

Round

Modern Block Ciphers

One complete iteration of a cipher's internal transformation. AES uses 10, 12, or 14 rounds depending on key size. Each AES round applies SubBytes, ShiftRows, MixColumns, and AddRoundKey — except the final round, which skips MixColumns. More rounds usually cost more computation; their security effect depends on the construction and attack. Repeating an operation does not automatically strengthen it.

S

S-box (Substitution Box)

Modern Block Ciphers

A lookup table that performs nonlinear substitution in block ciphers. In AES, each byte of state is replaced via a 256-entry S-box derived from finite field inversion. Its nonlinear structure contributes to confusion. Resistance to linear and differential attacks depends on the complete cipher, including its diffusion and round count.

Secret Sharing (Shamir's)

Modern Cryptography

Represent a secret as the constant coefficient of a polynomial of degree at most k−1 over a finite field. Sample the other coefficients independently and uniformly. Any k distinct nonzero share positions reconstruct the secret; fewer than k reveal no information under this model. Ordinary Shamir sharing does not detect forged shares. Interactive: Polynomial Interpolation (§155).

Shortest Vector Problem (SVP)

Post-Quantum Cryptography

Given a basis of a lattice, find a shortest nonzero vector. Difficulty depends on dimension, the lattice family and whether an exact or approximate answer is required. Lattice cryptography uses carefully specified related assumptions, and is only one family of post-quantum cryptography. Interactive: Lattices & the SVP (§147).

Steganography

Greek: steganos (covered) + graphein (to write)

Hiding the existence of a message, rather than hiding its meaning. Invisible ink, microdots, messages hidden in image pixels. Complementary to cryptography: steganography conceals the fact that communication is happening; cryptography protects the content if it's discovered.

Stream Cipher

Modern Cryptography

A cipher that combines a message with a generated keystream. Modern binary examples such as ChaCha20 use XOR and derive the stream from a secret key, nonce and counter. Performance depends on the platform; block-cipher counter modes also generate streams. Encryption alone does not provide message authentication.

Substitution Cipher

Ancient

Any cipher that replaces each element of the plaintext with another element. Monoalphabetic substitution uses one mapping; polyalphabetic uses multiple. Homophonic maps each letter to several possible symbols. Substitution may act on individual symbols or on larger blocks.

Symmetric Encryption

Secret-key cryptography · Modern: AES

A system where the same key is used for both encryption and decryption. Many historical keyed systems are symmetric. Unkeyed encodings displayed in the museum are not secret-key encryption. Modern examples: AES, ChaCha20. The key must be shared securely between parties — the fundamental key distribution problem that asymmetric cryptography was invented to solve.

T

Tabula Recta

Johannes Trithemius · published 1518

In the modern A–Z version, a 26×26 grid where each successive row is shifted by one position. The foundational tool for Vigenère-type ciphers: find the plaintext letter's column, the key letter's row, and the intersection is the ciphertext letter. Also called a Vigenère square.

Transposition Cipher

Ancient / Military

A cipher that permutes plaintext positions. Rail Fence, Columnar and Route ciphers preserve each symbol’s frequency, apart from any added padding. Frequency analysis can therefore suggest the language or cipher family, but cannot by itself recover the permutation. Anagramming, structural clues and language scoring help reconstruct the order.

V

Vigenère Cipher

Giovan Battista Bellaso · 1553 (misattributed to Vigenère)

A polyalphabetic substitution cipher using a repeating keyword. Each key letter selects a different Caesar shift. The repeating-key form is associated with Babbage’s mid-nineteenth-century work and Kasiski’s published 1863 method. A claim of three centuries of universal unbreakability obscures earlier variants, attacks and operational differences.

X

XOR (Exclusive OR)

Boolean Logic / Cryptography

The binary operation 0⊕0=0, 0⊕1=1, 1⊕0=1, 1⊕1=0. It is self-inverse: A⊕B⊕B=A. XOR with an independent uniform bit produces a uniform output; XOR alone does not create randomness from arbitrary inputs. Binary one-time pads and modern binary stream ciphers use it; alphabetic additive ciphers may use modular addition instead.

Reading

Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, Handbook of Applied Cryptography (1997 edition), chapters 1 and 7; Joshua Holden, The Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital Encryption (2017 edition), chapters 2 and 4–5; Claude E. Shannon, “Communication Theory of Secrecy Systems” (1949), §§10 and 23. Modern implementation requirements depend on the relevant protocol or standard.