Inverse Of Nonsingular Matrix Research Articles

Security Enhancement of Text Message Based on Matrix Approach Using Elliptical Curve Cryptosystem

The cryptosystem nowadays based on Elliptic Curve Cryptography (ECC) is becoming the trend in public key cryptography. Elliptic Curve Cryptography (ECC) was introduced by Victor Miller and Neil Kolbitz in 1986 is fast replacing the public key cryptosystem such as RSA, ElGamal Cryptosystems, etc., as ECC is more complex and thus it provides greater security and more efficient performance This paper presents the FPGA implementation of ECC by transforming the text message into an affine point called Pm(x, y) on the Elliptic Curve (EC), over the finite field GF (p). Each character in the text message is represented by its ASCII value. The ASCII value is mapped to the affine point. These affine points are later mapped again using Matrix Mapping method. Later these points are encoded using ElGamal encryption method. And the encoded message can be decrypted by ElGamal decryption technique and to get back the original message. The matrix obtained by ElGamal decryption is multiplied with the inverse of non-singular matrix, and de-mapping performed to get back the original ASCII Character and this ASCII character is converted back to the text message. The entire design is simulated, synthesized and implemented on FPGA.

A Computer Program for Calculating the Moore Penrose Generalized Inverse of a Rectangular or Singular Matrix

The inverse of a nonsingular matrix is often used to solve the system of simultaneous equations when the number of equations are the same as the number of unknowns. The inverse of a singular or rectangular matrix can also be defined such that is can be used to solve the system of equations when the number of equations are not equal to the number of unknowns. This paper deals with some of the results of the above inverse and a computer program to calculate the same.