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A matrix approach for constructing quadratic APN functions

机译：构造二次APN函数的矩阵方法

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摘要

A one to one correspondence is given between quadratic homogeneous APN functions and a special kind of matrices which we call as QAM's. By modifying the elements of a known QAM, new quadratic APN functions can be constructed. Based on the nice mathematical structures of the QAM's, an efficient algorithm for constructing quadratic APN functions is proposed. On F_(2~7), we have found 471 new CCZ-inequivalent quadratic APN functions, which is 20 times more than the number of the previously known ones. Before this paper, It is only found 23 classes of CCZ-inequivalent APN functions on F_(2~8). With the method of this paper, we have found 2,252 new CCZ-inequivalent quadratic APN functions, and this number is still increasing.
机译：二次齐次APN函数与一种特殊的矩阵（我们称为QAM）之间存在一对一的对应关系。通过修改已知QAM的元素，可以构造新的二次APN函数。基于QAM的良好数学结构，提出了一种构造二次APN函数的有效算法。在F_（2〜7）上，我们发现了471个新的CCZ不等式二次APN函数，是以前已知函数的20倍。在此之前，在F_（2〜8）上仅发现23类CCZ不等价的APN函数。使用本文的方法，我们发现了2,252个新的CCZ不等式二次APN函数，并且这个数量还在不断增加。

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  • 来源
    《Designs, Codes and Crytography》 |2014年第2期|587-600|共14页
  • 作者

    Yuyin Yu; Mingsheng Wang; Yongqiang Li;

  • 作者单位

    The State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;

    The State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;

    The State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Quadratic functions; APN, EA-equivalence; CCZ-equivalence;

    机译：二次函数;APN;EA等效;CCZ等价;

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