Encryption Technique using Matrix Representation of Linear Transformation

Abstract

In this paper a different cryptographic algorithm is developed by using linear transformation on vector space
with dimension . Each character of the message is converted to number and then transformed to another
number. This transformation is different for each character of message depending upon the position of
character in the sequence. Uniqueness of the transformation is that if any character appearing twice will have
different encryption. Modular arithmetic is also applied to reduce big numbers to small numbers. Key K is
symmetric and has two components (

)

consists the dimension of vector space and
coefficients of linear transformation,

is the basis set in which all the n vectors are linearly independent
and can generate the vector space. Since basis set in not unique and it will increases the security level of
symmetric key. Afterwards linear transformation defined will be represented by the matrix relative to the
basis set. This process can be iterated number of times for encryption of text data