基于 CSS类稳定子码的彩色与灰度图像水印算法

Color and grayscale image watermarking algorithm based on CSS class stable subcode

摘要

量子计算理论的研究成果预示着量子计算机有超高并行计算能力的优势，也为图像的安全保护带来了新的方向。回顾现有的研究结果，量子图像水印算法在嵌入量和鲁棒性方面仍然存在不足之处。几类不同的量子系统在运行过程中都不可避免地会受到环境的干扰，导致量子计算过程出错或信息丢失，含水印的载体图像遭遇噪声攻击后又会导致粒子发生量子比特翻转。因此，提出了基于CSS（calderbank-shor-steane）类稳定子码的彩色与灰度图像水印算法，保证纠错能力的同时降低了量子比特的消耗。将二值水印图像嵌入算法扩展到彩色与灰度图像的嵌入，使算法更具通用性。

Abstract

Quantum computing, with its ultra-high parallelism, offers new opportunities for image security, yet existing quantum image watermarking algorithms still suffer from limitations in embedding capacity and robustness. Environmental interference in quantum systems and noise attacks on watermarked carrier images can lead to quantum bit errors and information loss, further restricting the practical application of such algorithms. To address these challenges, this paper proposes a color and grayscale image watermarking algorithm based on calderbank-shor-steane (CSS) stabilizer codes, which achieves error correction capability while reducing qubit overhead. By extending binary watermark embedding to color and grayscale images, the algorithm gains improved versatility.

关键词

量子计算 / 量子图像处理 / 图像水印 / 量子图像水印 / 量子纠错码

Key words

quantum computing / quantum image processing / image watermark / quantum image watermarking / quantum error-correcting code

参考文献

[1] STINSON D R, PATERSON M B. Cryptography: Theory and practice[M]. 4th ed. Boca Raton: CRC Press, 2018.

[2] SCHNEIER B. Applied cryptography[M]. [S.l.]: Wiley, 2015.

[3] 章照止 . 现代密码学基础[M]. 北京: 北京邮电大学出版社, 2004.

[4] ZHANG Z Z. Fundamentals of modern cryptography[M]. Beijing: Beijing University of Posts and Telecommunications Press, 2004.

[5] KATZENBEISSER S, PETITOLAS F. Information hiding techniques for steganography and digital watermarking[J]. EDPACS the EDP Audit, Control and Security Newsletter, 1999, 28(6): 1-2.

[6] 汪小帆 . 信息隐藏技术: 方法与应用[M]. 北京: 机械工业出版社, 2001.

[7] WANG X F. Information hiding technology: Method and application[M]. Beijing: China Machine Press, 2001.

[8] 王丽娜, 张焕国, 叶登攀 . 信息隐藏技术与应用[M]. 2版. 武汉: 武汉大学出版社, 2009.

[9] WANG L N, ZHANG H G, YE D P. Information hiding technology and its application[M]. 2nd ed. Wuhan: Wuhan University Press, 2009.

[10] PARNAS D L. On the criteria to be used in decomposing systems into modules[J]. Communications of the ACM, 1972, 15(12): 1053-1058.

[11] JOHNSON N F, JAJODIA S. Exploring steganography: Seeing the unseen[J]. Computer, 31(2): 26-34.

[12] 孙圣和, 陆哲明 . 数字水印处理技术[J]. 电子学报, 2000, 28(8): 85-90.

[13] SUN S H, LU Z M. Digital watermark processing technology[J]. Electronic Journal, 2000, 28(8): 85-90.

[14] 王炳锡, 陈琦, 邓峰森 . 数字水印技术[M]. 西安: 西安电子科技大学出版, 2003.

[15] WANG B X, CHEN Q, DENG F S. Digital watermarking technology[M]. Xi'an: Xi'an University of Electronic Science and Technology Press, 2003.

[16] VENEGAS—ANDRACA S E, BOSE S. Storing, processing, and retrieving an image using quantum mechanics[C]// Proceedings of the Quantum Information and Computation. [S.l.]: SPIE, 2003: 137-147.

[17] LATORRE J I. Image compression and entanglement[EB/OL]. [2025—01—12]. https://arxiv.org/pdf/quant—ph/0510031.

[18] VENEGAS—ANDRACA S E, BALL J L. Processing images in entangled quantum systems[J]. Quantum Information Processing, 2010, 9(1): 1-11.

[19] JIANG N, WANG L. Quantum image scaling using nearest neighbor interpolation[J]. Quantum Information Processing, 2015, 14(5): 1559-1571.

[20] LI P, XIAO H, LI B. Quantum representation and watermark strategy for color images based on the controlled rotation of qubits[J]. Quantum Information Processing, 2016, 15(11): 4415-4440.

[21] NASERI M, HEIDARI S, BAGHFALAKI M, et al. A new secure quantum watermarking scheme[J]. Optik, 2017, 139: 77-86.

[22] LI H S, CHEN X, XIA H Y, et al. A quantum image representation based on bitplanes[J]. IEEE Access, 2018, 6: 62396-62404.

[23] WANG L, RAN Q W, MA J, et al. QRCI: A new quantum representation model of color digital images[J]. Optics Communications, 2019, 438: 147-158.

[24] GRIGORYAN A M, AGAIAN S S. New look on quantum representation of images: Fourier transform representation[J]. Quantum Information Processing, 2020, 19(5): 148.

[25] WANG L, RAN Q W, MA J. Double quantum color images encryption scheme based on DQRCI[J]. Multimedia Tools and Applications, 2020, 79(9): 6661-6687.

[26] TUDORACHE A G, MANTA V, CARAIMAN S. Quantum steganography using two hidden thresholds[J]. Advances in Electrical and Computer Engineering, 2021, 21(4): 79-88.

[27] ABDOLMALEKY M, NASERI M, BATLE J, et al. Red—green—blue multi—channel quantum representation of digital images[J]. Optik, 2017, 128: 121-132.

[28] SANG J Z, WANG S, LI Q. A novel quantum representation of color digital images[J]. Quantum Information Processing, 2016, 16(2): 42.

[29] TIRKEL A Z, RANKIN G A, VAN S R M, et al. Electronic watermark[J]. Digital Image Computing, Technology and Applications, 1993: 666-673.

[30] JIANG N, WU W Y, WANG L. The quantum realization of Arnold and Fibonacci image scrambling[J]. Quantum Information Processing, 2014, 13(5): 1223-1236.

[31] WU L L, ZHANG J W, DENG W T, et al. Arnold transformation algorithm and anti—Arnold transformation algorithm[C]// Proceedings of the 1st International Conference on Information Science and Engineering. [S.l.]: IEEE, 2009: 1164-1167.

[32] HUYNH—THU Q, GHANBARI M. Scope of validity of PSNR in image/video quality assessment[J]. Electronics Letters, 2008, 44(13): 800.

[33] POLLET T, VAN B M, MOENECLAEY M. BER sensitivity of OFDM systems to carrier frequency offset and Wiener phase noise[J]. IEEE Transactions on Communications, 43(2/3/4): 191-193.

[34] HORE A, ZIOU D. Image quality metrics: PSNR vs. SSIM[C]// Proceedings of the 20th International Conference on Pattern Recognition. [S.l.]: IEEE, 2010: 2366-2369.

[35] CHAN R H, CHUNG W A, NIKOLOVA M. Salt—and—pepper noise removal by Median—type noise detectors and detail—preserving regularization[J]. IEEE Transactions on Image Processing, 14(10): 1479-1485.

基金资助

国家自然科学基金(61772295)

重庆市自然科学基金创新发展联合基金重点项目(CSTB2023NSCQ-LZX0139)

重庆市教育委员会科学技术重大项目(KJZD-M202000501)