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 .
