多输出bent函数的优化设计

An Optimized Method for Multiple Output Bent Functions

本文运用密码函数输入变元的复合可逆变换 ,对文 [1,2 ]的多输出bent函数进行优化设计 ,结果获得了更为丰富的新的多输出bent函数簇 :(1)有很大一部分不属于Maiorana- McFarland型bent函数 ;(2 )同样可以获得最大的代数次数和最大的输出维数 ;(3)具有良好的构造计数等 .此外 ,本文也说明了密码函数输入变元的复合可逆变换 ,为构造具有良好密码学性质的函数 ,提供了一种简洁、且易于实现的方法 .

Kaisa Nyberg and Takashi Satoh gave some methods for constructing multiple ou tput bent functions in paper[1,2] respectively,while these bent functions belo ng to Maiorana-McFarland bent functions.In this paper,an optimizing method for multiple output bent functions in paper[1,2] is presented by using Cryptograph ic functions` input-variety compounding reversible transform.As a result,many n ew multiple output bent functions were obtained,and these functions have followi ng properties:(1)they do not belong to Maiorana-McFarland bent functions;(2)the y have highest algebraic degree and maximal number of output bits;(3)they also h ave good construction number.Moreover,it also means that compounding reversible transform is very useful for constructing good Cryptographic functions and the m ethod is concise and easily implemented.