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In the mathematical field of combinatorics, a bent function is a special type of Boolean function. This means it takes several inputs and gives one output, each of which has two possible values (such as ''0'' and ''1'', or ''true'' and ''false''). The name is figurative. Bent functions are so called because they are as different as possible from all linear and affine functions, the simplest or "straight" functions. This makes the bent functions naturally hard to approximate. Bent functions were defined and named in the 1960s by Oscar Rothaus in research not published until 1976.〔 They have been extensively studied for their applications in cryptography, but have also been applied to spread spectrum, coding theory, and combinatorial design. The definition can be extended in several ways, leading to different classes of generalized bent functions that share many of the useful properties of the original. == Walsh transform == Bent functions are defined in terms of the Walsh transform. The Walsh transform of a Boolean function is the function given by : where is the dot product in Z.〔 Alternatively, let and . Then and hence : For any Boolean function ''ƒ'' and the transform lies in the range : Moreover, the linear function and the affine function correspond to the two extreme cases, since : Thus, for each the value of characterizes where the function ''ƒ''(''x'') lies in the range from ''ƒ''0(''x'') to ''ƒ''1(''x''). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「bent function」の詳細全文を読む スポンサード リンク
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