The Hill cipher is a classical symmetric encryption algorithm that succumbs to the know-plaintext attack. Although its vulnerability to cryptanalysis has rendered it unusable in practice, it still serves an important pedagogical role in cryptology and linear algebra. In this paper, a variant of the Hill cipher is introduced that makes the Hill cipher secure while it retains the efficiency. The proposed scheme includes a ciphering core for which a cryptographic protocol is introduced.

A secure variant of the Hill Cipher

In 2000, Saeednia proposed a new scheme to make the Hill cipher secure. The author makes use of permutations of columns and rows of a matrix to get a different key for encrypting each message. This paper shows that the cipher key Ht can be obtained by parameter u. Besides, the Saeednia's scheme costs a lot of time in matrix computation. To overcome the drawbacks of Saeednia's scheme, a more secure cryptosystem with a one‐way hash function is proposed.

https://ir.nctu.edu.tw:443/bitstream/11536/26412/1/000223895700013.pdf

Comments on Saeednia's Improved Scheme for the Hill Cipher

Summary Information security is an important issue. Hill Cipher is one of the most famous symmetric cryptosystem that can be used to protect information from unauthorized access.Hill cipher is a polygraph substitution cipher based on linear algebra. Invented by Lester S. Hill in 1929, it was the first polygraph cipher which was practical to operate on more than three symbols at once, Hill Cipher has many advantages in data encryption. First, it is resistant to the frequency letter analysis. It's also very simple since it uses matrix multiplication. Finally, it has high speed and high throughput [1,13,14], However, noninvertible key matrix over is the main disadvantage of Hill Cipher, because few of the matrices have inverses over . This means that the encrypted text can't be decrypted [2]. This paper suggests a new technique in Hill Cipher algorithm to overcome its major problemnoninvertible key matrix. also our paper suggest enhancement the security of Hill Cipher against known plaintext attack because all steps in Hill Cipher depend on linear algebra calculation This is possible by using public key idea and key generating depending on various options and without linear algebra steps. Therefore, it will be difficult for the attacker to get the key. Finally, our paper will present a proper solution for the problem of sending secret key ( ) for the first time. Our idea is using a public key public ( ) that doesn't sent but generated in the encryption and decryption sides.

http://paper.ijcsns.org/07_book/200905/20090502.pdf

Design of a robust cryptosystem algorithm for non-invertible matrices based on hill cipher

A Modified Hill Cipher Based on Circulant Matrices

The Hill cipher is a famous symmetric cryptosystem that have several advantages in data encryption. However, the Hill cipher algorithm cannot encrypt images that contain large areas of a single color. Thus, it does not hide all features of the image which reveals patterns in the plaintext. Moreover, it can be easily broken with a known plaintext attack revealing weak security. In this paper, novel cryptosystem is used to encrypt image that overcomes these disadvantages. The novel cryptosystem uses randomly generated self-invertible matrix as an encryption key for each block encryption and also this method eliminates the computational complexity involved in finding inverse of the matrix while decryption. The proposed variant yields higher security and significantly superior encryption quality compared to the original one.

/pdf/image-encryption-by-novel-cryptosystem-using-matrix-3i0ryjuyd8.pdf

Image Encryption by Novel Cryptosystem Using Matrix Transformation

An improvement of the Hill cipher is proposed. In the Hill cipher, a randomly generated nonsingular matrix is used as an encryption key, and the inverse of the matrix is used as the decryption key. The weakness of Hill cipher is that the matrix may be revealed under known-plaintext attack. In the proposed cryptosystem a plaintext message is first partitioned into some suitable length of blocks and each block b concatenates with a random string r and a special control symbol c as r.//c//.b The new string is converted to a vector. The components of the vector are positive integers. To overcome the drawbacks of the Hill cipher, a more secure number system with different bases and an enforced transformation of the enciphering matrix are provided. >

A new cryptosystem using matrix transformation

Proposes a private key cryptosystem in which a specially designed permutation table is used as an enciphering/deciphering key. By the permutation table, an enforced random substitution scheme substitutes the characters in a plaintext message. It is hard to guess the correct plaintext characters from known ciphertext characters. The secure measurement and some possible attacks on the proposed cryptosystem are also discussed. >

Y.-S. Yeh

Papers

A new cryptosystem using matrix transformation

A private key cryptosystem based upon enforced random substitution scheme