ENGG2013 Unit 10n × n determinant andan application to cryptographyFeb,2011
ENGG2013 Unit 10 n n determinant and an application to cryptography Feb, 2011
Yesterday - A formulafor matrix inverse using cofactorsa11a12a13A =a21a22a23a31a32a33cofactorsC11C31C211A-1C12 C22 C32det ACi3 C23 C33]UsuallycalledtheadjointofASupposethat det A is nonzero.Threestepsincomputingaboveformula1. fori,j = 1,2,3, replace each aij by cofactor Ci2.Take the transpose of the resulting matrix.3. divide bythedeterminantofA.kshumENGG2013
Yesterday – A formula for matrix inverse using cofactors kshum ENGG2013 Suppose that det A is nonzero. Three steps in computing above formula 1. for i,j = 1,2,3, replace each aij by cofactor Cij 2. Take the transpose of the resulting matrix. 3. divide by the determinant of A. Usually called the adjoint of A cofactors
Outlinenxn determinant Caesar CipherModulo arithmeticHill CipherkshumENGG2013
Outline • nxn determinant • Caesar Cipher • Modulo arithmetic • Hill Cipher kshum ENGG2013
DETERMINANTIN GENERALkshumENGG2013
DETERMINANT IN GENERAL kshum ENGG2013
A patterna11a12=a11a22—a12a21a21a22a11a12a13a21a22a23a31a32a33=a11a22a33—a11a23a32—a12a21a33+a12a23a31+a13a21a32—a13a22a31 Arrange the products so that the firstsubscripts are in ascending order. All possible orderings of the second subscriptsappear once and only once.ENGG2013kshum
A pattern • Arrange the products so that the first subscripts are in ascending order. • All possible orderings of the second subscripts appear once and only once. kshum ENGG2013