### Table 1: Nonlinearity of symmetric Boolean functions on even number of variables by Construction 3 and maximum nonlinearity by exhaustive search.

2005

Cited by 10

### Table 2 Relation of Higher Order Nonlinearity, Partial Higher Order Nonlinearity, Algebraic Immunity and Degree for Some Balanced Boolean Function f of 6 Arguments

### Table 1. The number of terms of nonlinear order i,0#14 i #14 8, in the boolean functions corresponding to the eight output bits of the exponential mapping 45#28:#29.

"... In PAGE 7: ... Table1 shows the number of terms of each nonlinear order i that appear in the boolean function for the j-th output bit in the function 45#28:#29 where j =1 and j = 8 denote the most signi#0Ccant and least signi#0Ccant bits of the output, respectively, for i =1; 2; .... ..."

### Table 2. The number of terms of nonlinear order i,0#14 i #14 8, in the boolean functions corresponding to the eight output bits of the logarithmic mapping log45#28:#29.

"... In PAGE 7: ... One sees immediately that, in each output bit position j, the number of terms appearing is remarkably close to the mean number ,8 i #01=2 for a randomly chosen function. Table2 is a similar table for the function log45#28:#29 and again the agreement is remarkably close. Table 2.... ..."

### Table 4: Average nonlinearity for combination of PJ PDBF and greedy algorithms.

"... In PAGE 8: ...alues f0; 1g are allowed. Thus the resulting function can have less unde ned values (i.e. ?) than starting function. PJ PDBF(size) choose random PDBF f of given size while (f is a new one) compute (any) permutation m satisfying (1) nd a pair (x; v) 2 M such that D is maximum f f[x 7! v] g return f attaining the highest nonlinearity The following Table4 presents an average nonlinearity of Boolean functions obtained by combination of PJ PDBF and greedy algorithm. Since we tried to maximize nonlinearity, the property P in greedy algorithm was nonlinearity.... ..."

### Table 2: Average nonlinearity and pcdev(1) for randomized algorithms.

"... In PAGE 6: ... We did not consider this additional \feature quot; because the same process can be applied to resulting functions from our algorithms. Therefore we compare only results from the rst column of Table2 (with property P1 { nonlinearity). Average nonlinearity of generated Boolean functions by the PJ method is 475:38.... ..."

### Table 1: Nonlinearity of S-boxes DES s2DES s3DES s5DES

1995

"... In PAGE 6: ... In this Section, we compare the quantitative characteristics of S-boxes in DES and siDES in various points of cryptographic view and evaluate the goodness-of- t of them. We checked the nonlinearity of 4 Boolean functions: Z6 2 ! Z2 consisting of an S-box as shown in Table1 . In the output bit column of this table, 4 denotes the most signi cant location of an output vector and 1 denotes the least signi cant location of an output vector.... ..."

Cited by 1

### Table 2. Bit-Wise Nonlinear Boolean Operations Used in P1, P2, P3 and P4

"... In PAGE 3: ... Four Internal Passes As can be seen from Figure 2, the four internal passes Pi, i = 1; 2; 3; 4, all operate in a similar fashion, although each pass employs a different sub-key, as well as a different nonlinear function for bit-wise Boolean operations. The four nonlinear bit-wise operations are shown in Table2 in the form of logic sum (XOR) of product (AND) . 1 See also a recent report by Blaze et al [2] which suggests that the length of a key for a private key cipher should be at least 75 to provide adequate security for critical... In PAGE 4: ... Bit-Wise Nonlinear Boolean Operations Used in P1, P2, P3 and P4 The input data (a string of 8 words) to Pi is processed in r 4 consecutive rounds, each involving the corresponding word in the sub-key Ki, where i = 1; 2; 3; 4. In the first round (round 0), the first 7 words in the input are bit-wise processed according to Fi which is shown in Table2 . The result of this operation is then cyclically shifted to right.... ..."

### Table 1: Nonlinearity of S-boxes DES s2DES s3DES s5DES Box output bit output bit output bit output bit

1995

"... In PAGE 8: ...Local Properties We compare the quantitative characteristics of S-boxes in DES and siDES in various points of crypto- graphic view and evaluate the goodness-of- t of them. We checked the nonlinearity of 4 Boolean functions: Z6 2 ! Z2 consisting of an S-box as shown in Table1 . In the output bit column of this table, 4 denotes the most signi cant location of an output vector and 1 denotes the least signi cant location of an output vector.... ..."

Cited by 4

### Table 1: Nonlinearity of S-boxes in DES, s2DES and s3DES DES s2DES s3DES Box output bit output bit output bit

"... In PAGE 7: ... Comparison In this Section, we compare the quantitative characteristics of S-boxes in DES, s2DES and s3DES in various points of cryptographic view and evaluate the goodness-of- t of them. First we checked the nonlinearity of 4 Boolean functions: Z6 2 ! Z2 consisting of an S-box as shown in Table1 . In the output bit column of this table, 4 denotes the most signi cant location of an output vector and 1 denotes the least signi cant location of an output vector.... ..."