Scholarlink

<p>To determine the Carlet–Charpin–Zinoviev equivalence (CCZ-equivalence) between known infinite families of almost perfect nonlinear (APN) functions is an important problem on cryptographic functions. In 2022, Göloǧlu (IEEE Trans Inf Theory 68(7):4750–4760, 2022) introduced the concept of biprojective APN functions. Later, Göloǧlu and Kölsch (Equivalences of biprojective almost perfect nonlinear functions. <a href="http://arxiv.org/abs/2111.04197">arXiv:2111.04197</a>, 2022) obtained the inequivalence results of biprojective functions. In this paper, we study the natural triprojective case by using the method that Göloǧlu and Kölsch adopted in (Equivalences of biprojective almost perfect nonlinear functions. <a href="http://arxiv.org/abs/2111.04197">arXiv:2111.04197</a>, 2022) and (Trans Am Math Soc 376(3):1683–1716, 2023). Very recently, Li and Kaleyski (IEEE Trans Inf Theory 70(2):1436–1452, 2024) constructed two new APN functions in trivariate form. They observed that the orthoderivative differential spectra of the two families of functions are the same in small dimensions and, hence, the functions may be equivalent. We confirm this observation by showing the EL-equivalence between the two newly constructed families of APN functions theoretically. Finally, we determine the number of CCZ-inequivalent functions in that two new families of trivariate APN functions. This is the first time that the CCZ-equivalence between two trivariate form APN functions is studied.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On CCZ-equivalence of two new APN functions in trivariate form

  • 期刊论文

  • 发表日期：

    2025年7月21日

查看全文
  • Chenmiao Shi,
  • Jie Peng,
  • Haibin Kan,
  • Jinjie Gao

摘要

To determine the Carlet–Charpin–Zinoviev equivalence (CCZ-equivalence) between known infinite families of almost perfect nonlinear (APN) functions is an important problem on cryptographic functions. In 2022, Göloǧlu (IEEE Trans Inf Theory 68(7):4750–4760, 2022) introduced the concept of biprojective APN functions. Later, Göloǧlu and Kölsch (Equivalences of biprojective almost perfect nonlinear functions. arXiv:2111.04197, 2022) obtained the inequivalence results of biprojective functions. In this paper, we study the natural triprojective case by using the method that Göloǧlu and Kölsch adopted in (Equivalences of biprojective almost perfect nonlinear functions. arXiv:2111.04197, 2022) and (Trans Am Math Soc 376(3):1683–1716, 2023). Very recently, Li and Kaleyski (IEEE Trans Inf Theory 70(2):1436–1452, 2024) constructed two new APN functions in trivariate form. They observed that the orthoderivative differential spectra of the two families of functions are the same in small dimensions and, hence, the functions may be equivalent. We confirm this observation by showing the EL-equivalence between the two newly constructed families of APN functions theoretically. Finally, we determine the number of CCZ-inequivalent functions in that two new families of trivariate APN functions. This is the first time that the CCZ-equivalence between two trivariate form APN functions is studied.