Abstract: With the development of quantum computing technology, traditional image encryption algorithms are facing the challenge of insufficient quantum attack resistance, while existing quantum image encryption algorithms have problems such as high quantum bit consumption and limited parameter space of chaotic systems. To address the above unsolved problems, this paper proposes a dual-quantum image encryption algorithm based on a chaotic system, aiming to achieve a balance between low resource consumption and high security. Firstly, a dual-bit-plane quantum image representation model (DBRQI) is proposed, which only requires 2n+4 quantum bits to store a grayscale image, reducing quantum bit consumption by 50% compared with the BRQI model. Secondly, a 3D hyperchaotic system (3D-CHCMM) is constructed: the parameter space of its 4 control parameters is increased by 33% compared with existing systems, and its 3 Lyapunov exponents are all positive. Moreover, the system has passed 15 NIST tests, enabling it to generate pseudorandom sequences with high randomness. The algorithm maps quantum states through DBRQI, scrambles pixel information via odd-even bit-plane scrambling and random row-column scrambling, and then performs an XOR operation with the pseudorandom sequences to generate ciphertext. Experimental results show that the horizontal correlation of the encrypted image is as low as 0.0041, the information entropy reaches 7.9993, and the NPCR is 99.6251%, indicating that the algorithm’s attack resistance and anti-interference capability are significantly enhanced. The algorithm in this paper provides an efficient solution for image encryption in current scenarios with limited quantum hardware.

摘要： 随着量子计算技术的发展，传统图像加密算法面临抗量子攻击能力不足的挑战，而现有量子图像加密算法存在量子比特消耗大、混沌系统参数空间有限等问题。针对上述待解问题，本文提出一种基于混沌系统的双量子图像加密算法，以实现低资源消耗与高安全性的平衡。首先，提出双位平面量子图像表示模型（DBRQI），仅需 个量子比特存储 灰度图像，较 BRQI 模型减少50%量子比特消耗，其次，构建三维超混沌系统（3D-CHCMM），4个控制参数的参数空间较现有系统提升33%，3个李雅普诺夫指数均为正值且通过15项NIST测试，可生成高随机性伪随机序列。算法通过DBRQI映射量子态，经奇偶位平面置乱与行列随机置乱打乱像素信息，再与伪随机序列执行异或操作生成密文。实验结果表明：加密图像水平相关性低至0.0041、信息熵达7.9993、NPCR为99.6251%，抗攻击与抗干扰能力显著增强。本文算法为当前量子硬件受限场景下的图像加密提供了高效解决方案。