k-bent functions: from coding theory to cryptology

N. Tokareva
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Abstract

In this paper we would like to give a new example of the fact that ideas of coding theory sometimes find unexpected applications in cryptology. Our example is based on new notions of k-Walsh-Hadamard transform for a Boolean function and k-bent function (here k is integer, 1 les k les m/2, m is an even number of variables), which we introduce. These notions appeared at first as geometric images of coding theory. But soon they found applications in cryptanalysis. Using these notions we study special quadratic approximations in block ciphers and prove that by using k-bent functions in a cipher it is possible to make it resistant to these approximations.
k弯曲函数:从编码理论到密码学
在本文中,我们想给出一个新的例子,证明编码理论的思想有时会在密码学中找到意想不到的应用。我们的例子是基于布尔函数和k-弯曲函数的k- walsh - hadamard变换的新概念(这里k是整数,1乘以k乘以m/2, m是偶数变量),我们引入了它。这些概念最初是作为编码理论的几何图像出现的。但很快他们就在密码分析中找到了应用。利用这些概念,我们研究了分组密码中的特殊二次逼近,并证明了在密码中使用k-弯曲函数可以使密码抵抗这些逼近。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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