Getting Ready for Hill Ciphers and Operations on Matrices

Flashcards covering key concepts related to Hill Ciphers and operations on matrices.

Commutative Property

A property that states that the order of operations does not change the result, e.g., a + b = b + a.

Multiplicative Identity

The number that, when multiplied by any number, returns that same number, typically represented as 1.

Additive Identity

The number that, when added to any number, returns that same number, typically represented as 0.

Additive Inverse

A number that, when added to a given number, results in the additive identity, e.g., a + (-a) = 0.

Multiplicative Inverse

A number that, when multiplied by a given number, results in the multiplicative identity, e.g., a × (1/a) = 1.

Matrix Multiplication

A method of multiplying two matrices that involves taking the dot product of rows and columns.

Identity Matrix

A square matrix that, when multiplied by another matrix, does not change the other matrix, typically denoted as I.

Hill Cipher

An encryption method using matrix multiplication to encode messages, invented by Lester S. Hill in 1929.

Caesar Cipher

A type of substitution cipher where each letter in the plaintext is 'shifted' a certain number of places down or up the alphabet.

Encryption Matrix

A matrix used in the Hill Cipher to transform plaintext into ciphertext by matrix multiplication.

Deciphering Code

The process of converting encoded messages back into their original form, often using the multiplicative inverse matrix.