## AppendixGGlossary

Block Cipher

A block cipher repeatedly uses a single key in order to encipher successive pieces of plaintext.

Cipher

A cipher is a system by which a letter or block of letters in a message is replaced by another letter or block of letters in a systematic way.

Ciphertext

The ciphertext is the message you wish to transmit after it has been rewritten in order to hide its meaning.

Code

A code is a system by which words or phrses in a message are replaced by other words, phrases, or symbols in a systematic way.

Crib

In cryptology a crib is a known piece of plaintext which may be compared to as sample ciphertext in order to aid cryptanalysis.

Cryptoanalysis

Cryptoanalysis is an attempt to compute the key or determine the meaning of a message from the ciphertext.

Cryptography

Cryptography focuses on concealing the meaning of a message.

Cryptology

Cryptology is the science of maintaining secrets by either hiding the meaning or the existence of messages.

Decipher

Deciphering is the process by which blocks of ciphertext are replaced by plaintext.

Decrypt

Decrypting is the process by we discover the meaning of a ciphertext without the aid of a cipher key.

Encipher

Enciphering is the process by which blocks of plaintext are replaced by ciphertext.

Factorial

Given a counting number $n$ we define $n$-factorial as the number of ways in which we can arrange $n$ objects and we calculate it by taking the product of all the consecutive positive integers from $n$ down to 1, and we write:

\begin{equation*} n!=n(n-1)(n-2)\cdots 2 \cdot 1 \end{equation*}

Note that for a variety of reasons $0!=1\text{.}$

Frequency Analysis

Frequency analysis is the process of counting the characters, blocks of characters, or words in a text in order to determine how many of each there are relative to the entire length of the text.

Greatest Common Divisor

The greatest common divisor of two integers is the largest positive integer which divides both. For a variety of reasons it is important to know that it is also defined as the least positive linear combination of the two integers, i.e. 5 is the $gcd(15,35)$ because not larger positive integer divides both 15 and 35 and because $5=1\cdot (35) - 2\cdot(15)$ is the smallest possible positive combination of 15 and 35.

Homophonic Cipher

A homophonic cipher is a cipher in which a single plaintext letter may be replaced by multiple different ciphertext letters throughout a message.

Index of Coincidence

The index of coincidence for a block of text is the probability that two characters chosen at random are the same.

Modular Equivalence

Given a positive integer $n$ two integers are equivalent modulo $n$ if they have the same remainder when you divide them by $n\text{.}$ Equivalently, two integers $a$ and $b$ are equivalent modulo $n$ if $a-b$ is divisible by $n\text{.}$ When this is the case we write $a\equiv b\ \pmod{n}$

Monoalphabetic Substitution Cipher

A monoalphabetic substitution cipher is a cipher in which there is a one-to-one correspondence between plaintext letters and the cipher text so that a single plaintext letter is always replaced by the same letter, group of letters, or symbol and every letter, group of letters, or symbol in the ciphertext represents the same plaintext letter.

Multiplicative Identity

A number $a$ is the multiplicative identity if for all numbers $b\text{,}$

\begin{equation*} a\cdot b=b\cdot a = b. \end{equation*}
Multiplicative Inverse

See Reciprocal

N-Gram

An n-gram is a block of $n$ consecutive characters.

Nomenclator

A nomenclator is a system for disguising the meaning of a message which uses both cipher alphabets and a set of code words.

Null

A null is an extra character added to a cipher text to increase confusion. It may consist of extra characters added throughout the ciphertext designed to alter frequencies or characters added to the end of message to disguise the length of the message.

Pangrams

Pangrams are words or sentences containing every letter of the alphabet at least once.

Plaintext

The plaintext is the message you wish to transmit written in a readable form.

Polyalphabetic Substitution Cipher

A polyalphabetic substitution cipher is a cipher in which a single plaintext letter maybe replaced by several differnt ciphertext letters, groups of letters, or symbols and every letter, group of letters, or symbol in the ciphertext may represent more than one plain text letter.

Polygraphic Cipher

A polygraphic cipher is a cipher in which multiple plaintext characters are enciphered at a time so that how a character is enciphered depends on which other letters it is beside.

Polyphonic Cipher

A polyphonic cipher is a cipher in which a single ciphertext letter may be represent multiple different plaintext letters throughout a message.

Prime Number

A positive integer is prime if it has precisely two divisors, one and its self.

Reciprocal

The reciprocal (or multiplicative inverse) of a number $x$ is some number $y$ such that $x\cdot y=1\text{.}$

Relatively Prime Numbers

Two integers are relatively prime if there greatest common divisor is one. In this case we may say that one of the integers is prime to the other.

Shift cipher

Shift Cipher generally refers to a monoalphabetic cipher in which the order of letters is not changed in the ciphertext each letter is just replaced with a letter a fixed distance further along in the alphabet.

Steganography

Steganography focuses on concealing the existence of a message.

Stream Cipher

A stream cipher uses a sequence (or stream) of different keys in order to encipher successive pieces of plaintext.

Substitution Cipher

A substitution cipher changes individual characters or groups of characters, but does not change their position.

Transposition Cipher

A transposition cipher rearranges the positions of characters, but does not change the characters themselves.