matrix_inverse.sh

#!/bin/bash

function printMatrix {
	A=( $@ )
	for j in {0..1}
	do
		i=$j
		echo -n "|"
		while [ $i -lt ${#A[@]} ] ; do
			printf " %2d " ${A[$i]}
			i=$(($i+2))
		done
		echo "|"
	done
}

#Let the key = FIRD
K=( 5 8 17 3 )

function matrixInverse {
	#Evaluating the determinant

	#          |         |             |             |
	#          |  A   C  |             |  K[0]  K[2] |
	# det K =  |         | = AD - BC = |             |
	#          |  B   D  |             |  K[1]  K[3] |
	#          |         |             |             |


	det=$(( ${K[0]} * ${K[3]} - ${K[1]} * ${K[2]} ))

	#Negative modulo correction
	
	#                 All    -ve    +ve
	#                  |      |      |
	#                  |      |      |
	#                  V      V      V

	det=$(( ( ( $det % 26 ) + 26 ) % 26 ))

	echo 1/det = 1/$det

	if [[ $(( $det % 2 )) == 0 || $(( $det % 13 )) == 0 ]]
	then
		echo "Decryption not possible"
		exit 1
	fi
	
	#Finding   1/$det mod 26 = x
	#Therefore $det * x = 1 mod 26
	
	rem=0
	x=-1

	while [ $rem != 1 ] ; do
		x=$(($x+2))
		rem=$(( $(( $det * $x )) % 26 ))
	done

	#				    ^
	#                                   |
	#                                   |
	#                              Always +ve

	echo 1/$det mod 26 = $x

	##### K = ( ${K[3]} -${K[1]} -${K[2]} ${K[0]} )

	K=( $((( ${K[3]} * $x )%26)) $((((( -${K[1]} * $x )%26)+26)%26 )) $((((( -${K[2]} * $x )%26)+26)%26 )) $((( ${K[0]} * $x )%26)) )

}

echo Original Key: FIRD
echo

printMatrix ${K[@]}
echo

matrixInverse
echo

echo Inverse Key
echo
printMatrix ${K[@]}