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Cipher is a first polygraphic substitution cipher that works on digraphs, trigraphs (3 letter squares) or hypothetically blocks of any magnitude. The Hill Cipher utilizes a region of science called Linear Algebra, and specifically requires the client to have a rudimentary knowledge of matrices. It additionally makes utilization of Modulo Arithmetic (like the Affine Cipher). To perform decryption, the hill cipher requires the inverse of the key matrix. This is the major shortcoming of Hill cipher since every key matrix is not invertible. We will propose a new variant of hill cipher, which will find the decryption of the cipher text even when the key matrix is non invertible.

The Hill cipher, also known as matrix encryption, is a polygraphic substitution cipher, developed by the mathematician Lester S. Hill in 1929. While various attacks had been known on the Hill cipher, the ciphertext-only attack without assumptions about the encryption matrix or probable plaintext words was introduced only recently by Bauer and Millward. They obtained high efficiency of attack by recovering the decryption matrix row by row rather than all rows at once. In this paper, we extend their ciphertext-only attack in two ways. First, we present a better scoring system for cryptanalysis based on the goodness-of-fit statistics. Specifically, we reduce the average number of candidate rows from 24.83 to 7.00 for 3 × 3 matrix and from 4027.78 to 1220.38 for 4 × 4 matrix. Second, we show how to apply our attacks to the Hill cipher without knowing the numeric equivalents of the letters of the plaintexts.

The Hill Cypher was Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once. As stated before, the Hill Cipher is an encryption algorithm that uses polygraphic substitution ciphers based on linear algebra concepts. Each letter is encoded as a number. In the case of the English alphabet, letters are usually represented by the following scheme: A =0, B=1, C=2 Z=25. The message that is to be encrypted/decrypted will be held in a block of n letters and multiplied by a square matrix using modulo of the amount of letters in the alphabet in use. In this research project, the main goal is to recreate this cipher using the values of the ASCII table. Since the Hill Cipher works by assigning a numeric value to the characters that are to be used, using the ASCII table seems like a perfect fit for this application.

This paper presents a non-numerical polygraphic substitution cipher which appears more efficient than Hill's algebraic system. For instance, by using the same number of “operations” per message as a 6-graphic algebraic substitution cipher, the present cipher can achieve 4096-graphic substitution. Less dramatically, a 16-graphic application of the present cipher requires only one-eighth as many operations as a 16-graphic algebraic cipher. The source of the greater efficiency of the proposed cipher is that the number of letters which can be jointly enciphered is exponential, rather than linear, with respect to the number of operations performed.