Boolean functions and binary sequences are main tools used in cryptography. In this work, we introduce a new bijection between the set of Boolean functions and the set of binary sequences with period a power of two. We establish a connection between them which allows us to study some properties of Boolean functions through binary sequences and vice versa. Then, we define a new representation of sequences, based on Boolean functions and derived from the algebraic normal form, named reverse-ANF. Next, we study the relation between such a representation and other representations of Boolean functions as well as between such a representation and the binary sequences. Finally, we analyse the generalized self-shrinking sequences in terms of Boolean functions and some of their properties using the different representations.

翻译：布尔函数与二元序列是密码学中的核心工具。本研究在布尔函数集合与周期为2的幂的二元序列集合之间引入了一种新的双射映射。通过建立两者间的联系，我们可以借助二元序列研究布尔函数的某些性质，反之亦然。随后，我们基于布尔函数从代数标准型出发定义了一种新的序列表示方法，称之为逆代数标准型（reverse-ANF）。接着探讨了该表示与布尔函数其他表示之间以及该表示与二元序列之间的关系。最后，我们利用不同表示方法从布尔函数角度分析了广义自缩序列及其若干性质。