Design of a Robust Cryptosystem Algorithm for Non-Invertible Matrices Based on 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.