Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Constructions of vectorial Boolean functions with good cryptographic properties

具有良好密码学性质的向量布尔函数的构造

创新点

作为传统流密码系统中的重要非线性部件,向量布尔函数的密码学性质极大的影响着整个流密码系统的安全性。为了抵抗各种已知的攻击,一般要求所选用的布尔函数具有平衡性,高的非线性度,一定的相关免疫阶及高的代数次数等。在本文中,我们给出一种新的构造向量布尔函数的方法,得到了一大类具有严格几乎最优非线性度的平衡向量布尔函数。我们还构造出了具有最高非线性度的一阶相关免疫向量布尔函数。最后,我们证明了这些函数还具有较高的代数次数。

This is a preview of subscription content, log in to check access.

References

  1. 1

    Siegenthaler T. Correalation immunity of nonlinear combining functions for cryptographic applications. IEEE Trans Inf Theory, 1984, 30: 776–780

  2. 2

    Nyberg K. Perfect nonlinear S-boxes. In: Advances in Cryptology—EUROCRYPT. Berlin: Springer-Verlag, 1991. 547: 378–386

  3. 3

    Zhang M., Zheng Y L. Cryptographically resilient functions. IEEE Trans Inf Theory, 1997, 43: 1740–1747

  4. 4

    Chen L. Fu F W. On the construction of new resilient functions from old ones. IEEE Trans Inf Theory, 1999, 45: 2077–2082

  5. 5

    Johansson T. Pasalic E. A construction of resilient functions with high nonlinearity. IEEE Trans Inf Theory, 2003, 49: 494–501

  6. 6

    Zhang. G, Pasalic E. Constructions of resilient S-boxes with strictly almost optimal nonlinearity through disjoint linear codes. IEEE Trans Inf Theory, 2014, 60: 1638–1651

  7. 7

    Zhang. G, Pasalic E. Highly nonlinear balanced Sboxes with good differential properties. IEEE Trans Inf Theory, 2014, 60: 7970–7979

  8. 8

    Maitra S. Pasalic E. Further constructions of resilient Boolean functions with very high nonlinearity. IEEE Trans Inf Theory, 2002, 48: 1825–1834

Download references

Author information

Correspondence to Weiguo Zhang.

Electronic supplementary material

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, L., Zhang, W. Constructions of vectorial Boolean functions with good cryptographic properties. Sci. China Inf. Sci. 59, 119103 (2016). https://doi.org/10.1007/s11432-015-0863-3

Download citation

关键词

  • 向量布尔函数
  • 流密码
  • 非线性度
  • b平衡性
  • 相关免疫
  • 代数次数
  • 119103