Hill cipher

A Hill cipher of dimension 6 was once implemented mechanically.

Early encryption techniques such as the Hill cipher also used matrices.

Since this has no common factors with 26, this matrix can be used for the Hill cipher.

Fortunately, matrices which satisfy the conditions to be used in the Hill cipher are fairly common.

Among his notable contributions was the Hill cipher.

The net effect is that the effective keyspace of a basic Hill cipher is about .

Unfortunately, the basic Hill cipher is vulnerable to a known-plaintext attack because it is completely linear.

In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra.

Consequently a useful variant of the Hill cipher adds 3 extra symbols (such as a space, a period and a question mark) to increase the modulus to 29.

In 1929, Lester S. Hill developed the Hill cipher, which uses matrix algebra to encrypt blocks of any desired length.

The Hill cipher, invented in 1929 by Lester S. Hill, is a polygraphic substitution which can combine much larger groups of letters simultaneously using linear algebra.

The Hill cipher is vulnerable to a known-plaintext attack because it is completely linear, so it must be combined with some non-linear step to defeat this attack.

The Hill cipher has achieved Shannon's diffusion, and an n-dimensional Hill cipher can diffuse fully across n symbols at once.

There are matrices of dimension n x n. Thus or about is an upper bound on the key size of the Hill cipher using n x n matrices.

If the determinant is 0, or has common factors with the modular base, then the matrix cannot be used in the Hill cipher, and another matrix must be chosen (otherwise it will not be possible to decrypt).

When operating on 2 symbols at once, a Hill cipher offers no particular advantage over Playfair or the bifid cipher, and in fact is weaker than either, and slightly more laborious to operate by pencil-and-paper.

Mohsen Toorani, and Abolfazl Falahati, A Secure Variant of the Hill Cipher, Proceedings of the 14th IEEE Symposium on Computers and Communications (ISCC'09), pp.

In the later stages of the competition, the ADFGVX cipher, the Solitaire cipher, the Double Playfair cipher, the Hill cipher, the Book cipher and versions of the Enigma and Fialka cipher machines have all been used.

The combination of wider and wider weak, linear diffusive steps like a Hill cipher, with non-linear substitution steps, ultimately leads to a substitution-permutation network (e.g. a Feistel cipher), so it is possible - from this extreme perspective - to consider modern block ciphers as a type of polygraphic substitution.