论文标题
通过其差异光谱的两类功率功能的双向光谱
Boomerang Spectra of Two Classes of Power Functions via Their Differential Spectra
论文作者
论文摘要
在2018年Eurocrypt中，CID $ et \; al。$在S-Boxes的加密属性上介绍了一个新概念，以评估Boomerang风格的攻击的微妙之处。这个概念被称为Boomerang连接表（简称BCT）。对于功率函数，BCT的分布可以由其回旋镖光谱直接确定。在本文中，我们通过其差分光谱研究了两个类别功能在特征有限场上的动力功能的回旋镖光谱。 The boomerang spectrum of the power function $ {x^{2^{m+1} - 1}} $ over $ {\mathbb{F}_{2^{2m}}} $ is determined, where $2^{m+1}-1$ is a kind of Niho exponent.还确定了黄金函数$ g（x）= x^{2^t+1} $ of $ {\ mathbb {f} _ {2^n}} $上的Boomerang频谱。结果表明，黄金函数具有两个值的回旋镖光谱。
In EUROCRYPT 2018, Cid $et\;al.$ introduced a new concept on the cryptographic property of S-boxes to evaluate the subtleties of boomerang-style attacks. This concept was named as boomerang connectivity table (BCT for short) . For a power function, the distribution of BCT can be directly determined by its boomerang spectrum. In this paper, we investigate the boomerang spectra of two classes power functions over even characteristic finite fields via their differential spectra. The boomerang spectrum of the power function $ {x^{2^{m+1} - 1}} $ over $ {\mathbb{F}_{2^{2m}}} $ is determined, where $2^{m+1}-1$ is a kind of Niho exponent. The boomerang spectrum of the Gold function $G(x)=x^{2^t+1}$ over $ {\mathbb{F}_{2^n}} $ is also determined. It is shown that the Gold function has two-valued boomerang spectrum.
