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Hacker Professional Ebook part 157

Tham khảo tài liệu 'hacker professional ebook part 157', công nghệ thông tin, kỹ thuật lập trình phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The base-10 logarithm of the ratio of two power values which is also the same as the difference between the log of each power value . The basis for the more-common term decibel One bel equals 10 decibels. Bent Function A bent function is a Boolean function whose fast Walsh transform has the same absolute value in each term except possibly the zeroth . This means that the bent function has the same distance from every possible affine Boolean function. We can do FWT s in the bottom panel at the end of Active Boolean Function Nonlinearity Measurement in JavaScript page of the Ciphers By Ritter JavaScript computation pages. Here is every bent sequence of length 4 first in 0 1 notation then in 1 1 notation with their FWT results bent 0 1 FWT bent 1 -1 FWT 0 0 0 1 1 -1 -1 1 1 1 1 -1 2 2 2 -2 0 0 1 0 1 1 -1 -1 1 1 -1 1 2 -2 2 2 0 1 0 0 1 -1 1 -1 1 -1 1 1 2 2 -2 2 1 0 0 0 1 1 1 1 -1 1 1 1 2 -2 -2 -2 1 1 1 0 3 1 1 -1 -1 -1 -1 1 -2 -2 -2 2 1 1 0 1 3 -11 1 -1 -1 1 -1 -2 2 -2 2 1 0 11 3 1 -1 1 -1 1 -1 -1 -2 -2 2 -2 0 1 1 1 3 -1 -1 -1 1 -1 -1 -1 -2 2 2 2 These sequences like all true bent sequences are not balanced and the zeroth element of the 0 1 FWT is the number of 1 s in the sequence. Here are some bent sequences of length 16 bent 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 FWT 6 -2 2 -2 2 -2 2 2 -2 -2 2 -2 -2 2 -2 -2 bent 1 -1 1 -1 1 1 1 -1 1 1 -1 -1 1 -1 1 1 -1 1 FWT 4 4 -4 4 -4 4 -4 -4 4 4 -4 4 4 -4 4 4 bent 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 1 1 0 FWT 6 2 2 -2 -2 2 -2 2 -2 -2 -2 -2 2 2 -2 -2 bent 1 -1 1 1 -1 1 1 -1 1 1 -1 1 1 1 -1 -1 -1 1 FWT 4 -4 -4 4 4 -4 4 -4 4 4 4 4 -4 -4 4 4 Bent sequences are said to have the highest possible uniform nonlinearity. But to put this in perspective recall that we expect a random sequence of 16 bits to have 8 bits different from any particular sequence linear or otherwise. That is also the maximum possible nonlinearity and here we actually get a nonlinearity of 6. There are various more or less complex constructions for these sequences. In most .