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“Residue matrices”, of which all elements are included in Zn, where n represents a prime, are commonly used in cryptography. Modular arithmetic is used to perform all matrix transformations on residue matrices. The properties of “residue matrices” are identical to those of “general matrices”.

Figure 4.1 Complex plane Z(n).

A matrix is defined in computing science by a set in two dimensions including p × q elements, where p represents the number of rows and q represents the number of columns (cols). A matrix is typically represented by a capital character like M. The element mij is assigned in the place which meets at the ith row and the jth col [5].

A matrix with p = 1 is referred to as a row matrix, while one with q = 1 is referred to as “a column matrix”. A matrix with p = q is referred to as “a square matrix” and its elements m₁₁, m₂₂, ----, mqq is referred to as “a main diagonal”. A matrix having all rows and cols which put to 0’s is referred as “an additive identity matrix” and the letter 0 is used to represent it. A square one having 1’s on “the main diagonal” and 0’s somewhere else is referred to as “an identity matrix” and the letter I is used to represent it [5].

If two matrices have the identical number of rows and columns and their corresponding elements are identical, then they are identical. In terms of representation of letters, M = N if they have mij = nij for all i’s and j’s [5].