Abstract

This paper deals with a novel and secure method of encryption using matrices and public key cryptography algorithm. Matrices have a very well-known property of invertibility i. e. if AX=B then X=A-1B[1]. This paper exploits this property to achieve encryption of plain text into cipher text. The idea is simple and intriguing. A non-singular integer valued square matrix Ai. e. det|A| ? 0 is taken so that A is invertible and it is possible to obtain A-1. This matrix A serves as the encryption matrix. The plain text to be encrypted is taken and ASCII values of each character is obtained and matrix X is formed such that Aq x q xD7 Xq x r= Bq x r. Before performing the multiplication of A and X to obtain cipher text ASCII value matrix B, circular shift operation is performed on rows and/ or columns of A. A single operation is stored as a string of 4 values viz. R32L9 or C8D61. The first character tells whether the circular shift operation is to be done on a row or a column. Second value tells the row or column number. Third character tells whether row is to be shifted left or right or if column is to be shifted then either up or down. The last value tells the number of times shift operation has to be performed. Successive operations are concatenated with a hyphen viz. R2R45-C6U8-C32D9 and encryption matrix A' is obtained. This key along with the matrix B' (=A'xD7X) is encrypted using RSA algorithm and sent to the other user who has the original matrix A. Receiver decrypts the message using private key, performs shift operation, finds the inverse of matrix A' as A' -1and finds A' -1xD7 B' to eventually obtain X and hence the original plain text message.

References

Keywords

Encryption, matrices,circular shift, RSA