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Based on the ordering sequence of (1.7b), the bit expansion function of (1.6)becomes011 1 0 0 1 11 1 0 0 1 11 1 0 1 1 01 0 1 1 0 1E x ð jÞ ¼E f ½Rð jÞŠ ¼0 1 0 1 0 1ð1:8ÞB 0 1 0 0 0 0C@A0 0 1 1 1 11 1 0 1 1 0which equates to 48 bits, matching the number of bits of the key functionKð j þ 1Þ.SELECTION FUNCTION. For simplicity, consider an 8-bit selectionfunction S fj , where j ¼ 1; 2; ...; 8. Each function has l rows and (m þ 1)columns. The elements of selection function S fj have a specific arrangement ofany set of integers from 0 to m. From Example 1.1, each function S fj takes a 6-bit block as its input, S in , denoted byS in ¼ x 1 ; x 2 ; x 3 ; x 4 ; x 5 ; x 6ð1:9ÞSuppose r j and c j correspond to a particular row and column of selectionfunction S fj .Rowr j is determined by the first and last digits of S in ; that is, ðx 1 ,x 6 ). Since x 1 and x 6 are binary digits, it follows that there can be only fourpossible outcomes to indicate the four rows (l ¼ 4) of S fj while the other fourbinary digits (x 2 , x 3 , x 4 , x 5 ) will provide numbers between 0 and m, therebydetermining c j . The intersection of r j and c j in S fj produces a specific integerbetween 0 and m, which, when converted to its binary digits, gives the outputS op ¼ y 1 ; y 2 ; y 3 ; y 4ð1:10ÞIn practice, the elements of the selection functions S fj are tabulated like alookup table. In the case of DES, l ¼ 4 and m ¼ 15; these elements are shownin Table 1.1. As seen in Table 1.1, each selection function S fj has 4-bit output,giving a total of 32 bits for all selection functions. Example 1.2 demonstrateshow the selection function’s algorithm is implemented.Example 1.2: Take a row from (1.8), say the first row, as input data; that is,S in ¼ 110011. It follows that r j ¼ðx 1 ; x 6 Þ¼11 and c j ¼ 1001 ¼ 9. Our tasknow is to provide the output S op due to S in using the previous transformationprocess on the basis of the selection functions given by Table 1.1. If we letj ¼ 8, the element of S 8 in the 4th row and 9th column is 15, which equates tothe digital output S op ¼ y 1 , y 2 , y 3 , y 4 ¼ 1111.Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.