两类幂函数的Boomerang谱及其微分谱
Boomerang Spectra of Two Classes of Power Functions via Their Differential Spectra
摘要：
在2018年的EUROCITY PT上，Cid $et\;al.$引入了一个关于S盒加密属性的新概念，以评估回飞棒式攻击的微妙之处。这一概念被命名为回飞棒连通表（Boomerang Connectivity Table，简称BCT）。对于幂函数，BCT的分布可以直接由其回飞棒谱确定。本文利用偶特征有限域上两类幂函数的微分谱，研究了它们的回旋谱。确定了$ {\mathbb{F}_{2^{2m}}} $上的幂函数$ {x^{2^{m+1} - 1}} $的回飞式谱，其中$2^{m+1}-1$是一种Niho指数.还确定了Gold函数$G(x)=x^{2^t+1}$在$ {\mathbb{F}_{2^n}} $上的回飞棒谱。证明了Gold函数具有二值Boomerang谱。
英文摘要：
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.
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