基于混沌与不可约多项式的动态 S 盒构造及其在图像加密中的应用

摘要

S 盒（替换盒）是现代对称密码体制的核心组件，其非线性度、差分均匀性和不可预测性直接决定了密码算法的安全性。然而，静态 S 盒一旦结构固定，就容易受到代数攻击与侧信道攻击。本文提出了一种动态 S 盒构造方案，结合二维混沌映射与上的不可约多项式：混沌映射提供密钥敏感性与巨大参数空间，使不同密钥生成不同 S 盒；不可约多项式则提供代数结构以约束最坏情况下的密码学指标。

消融实验在非线性度、严格雪崩准则（SAC）、比特独立准则（BIC）、差分/线性逼近概率以及生成效率等标准密码学指标上系统评估所生成的 S 盒，结果均满足或优于密码学使用要求。

我们进一步将动态 S 盒集成到分组密码图像加密流程中，在标准测试图像上验证其加密效果：像素级扰乱与扩散效果显著，密文直方图接近均匀分布，NPCR / UACI 分数高，能有效抵抗差分攻击、统计攻击与暴力破解。

@article{luo2024dynamic, title={Constructing Dynamic S-boxes Based on Chaos and Irreducible Polynomials for Image Encryption}, author={Luo, Chunlei and Wang, Yong and Fu, Yongji and others}, journal={Nonlinear Dynamics}, year={2024}, publisher={Springer} }

Background

Symmetric ciphers rely on S-boxes to provide the confusion layer that resists linear and differential cryptanalysis. A static, key-independent S-box leaks the same algebraic structure across every ciphertext it produces, so once the structure is known it becomes the natural attack surface.

What this paper proposes

Chaos-driven keying. A 2-D chaotic map is used to produce, for every key, a fresh S-box. Sensitivity to initial conditions means a small change in the key yields a structurally different S-box.
Algebraic anchoring in . Candidate S-boxes are built from irreducible polynomials over , which bounds the worst-case nonlinearity and differential uniformity so that every instance meets the cryptographic criteria.
Standard-battery evaluation. Ablations on nonlinearity, SAC, BIC, and differential/linear approximation probability, plus generation-cost measurements.
Image-encryption pipeline. The dynamic S-box is dropped into a block-cipher image encryptor and evaluated on standard test images: near-uniform histograms, high NPCR/UACI, and resistance to differential / statistical / brute-force attacks.

Figure

Dynamic S-box construction