Hill

The Hill cipher is a polygraphic substitution cipher that operates on groups of letters in a plaintext message, transforming them using matrix multiplication.

Preserve Capitals

Preserve Symbols

Preserve Whitespace

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Input Message

Output Message

Explanation

The Hill cipher is a type of polygraphic substitution cipher based on linear algebra and is one of the earliest known examples of a block cipher. The Hill cipher operates on blocks of plaintext letters and uses matrix multiplication to encrypt and decrypt messages.

The encryption key in the Hill cipher is a square matrix called the encryption matrix. The size of the matrix (i.e., the number of rows and columns) depends on the key length and the block size of the plaintext. The determinant of the encryption matrix must be relatively prime to the size of the alphabet used (typically 26 for English text) to ensure that the encryption matrix is invertible.

To encrypt a message, the plaintext is divided into blocks of letters, each block matching the size of the encryption matrix. Each block is then represented as a column vector, with each element of the vector representing the numerical value of a letter in the plaintext. The encryption matrix is multiplied by each column vector of plaintext letters modulo the size of the alphabet. The resulting matrix of encrypted numerical values is then converted back into ciphertext letters.

Decryption is performed by multiplying the ciphertext column vectors by the inverse of the encryption matrix modulo the size of the alphabet. The resulting numerical values are converted back into plaintext letters.

The Hill cipher offers a higher level of security compared to simple substitution ciphers because it operates on blocks of letters rather than individual letters, making it resistant to frequency analysis. However, it is vulnerable to known plaintext attacks if the attacker can obtain enough ciphertext and corresponding plaintext pairs to deduce the encryption matrix.

One limitation of the Hill cipher is that it requires the plaintext to be divided into blocks of fixed length, which can result in padding if the plaintext length is not a multiple of the block size. Additionally, the size of the encryption matrix and the choice of plaintext block size can impact the complexity and security of the cipher.

Facts

It was invented by Lester S. Hill in 1929.

It is one of the earliest examples of a block cipher.