### 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. Distribution of the Walsh-Hadamard spectra for Boolean functions of n variables.

"... In PAGE 3: ... Each of them has different and unique spectra. Table1 shows distribution of spectral coefficients for some Boolean functions of n -variables. Table 1.... In PAGE 6: ... Mentioned functions are balanced. It is possible to construct of Boolean functions of n 3 = variables with eight nonzero spectral coefficients but such functions are not balanced ( Table1 and Table 2). For and , it is possible to construct balanced Boolean functions f with algebraic degree .... ..."

Cited by 1

### Table 2: Distribution of Boolean functions satisfying the SAC n 2 3 4

1991

"... In PAGE 6: ... Boolean functions satisfying the 2-nd order SAC 4. Bent functions[2] By computer search, we give the distribution of Boolean functions of satisfying any order SAC in Table2 . Since the function satisfying the 1-st order SAC always satis es the 0-th order SAC, we did not count twice a function satisfying a higher order SAC in Table 2.... ..."

Cited by 9

### 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. Distribution of the 65536 four-bit Boolean functions by gate complexity and the results of d-monomial tests on Boolean functions of given gate complexity.

2006

"... In PAGE 6: ... The maximum gate complexity turned out to be 7 (see Figure 2). Table1 gives the distribution of functions by gate complexity. In it, Gi is the number of functions of gate complexity i.... In PAGE 6: ... The table contains the bias fraction qi,d = gi,d/(Gi parenleftbig4 d parenrightbig). Note how in Table1 the d-Monomial bias qi,d tends to be strongly increasing as the gate complexity i grows (apart for anomaly at q6,4). This is clear evidence of a correlation between the complexity of a Boolean circuit and the d-monomial test.... ..."

Cited by 2

### 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 5.1: Basic functionality annotations for naming concept responsibilities

### Table 7: Larger Boolean functions

1993

"... In PAGE 1: ...the number of i/o-pairs in the truth table (A), the number of variables (vars) and clauses of the Satis ability problem and the number of iterations and CPU time for the interior point algorithm to produce the Boolean function. Finally, in Table7 , we summarize results for three larger Boolean functions. In addition to the parameters shown in Table 6, this table gives the number of input variables (n) of the instance.... ..."

Cited by 13