信息安全研究2026，Vol.12Issue(6)：517-525,9.DOI:10.12379/j.issn.2096-1057.2026.06.04
基于新型组合混沌系统和分数数论变换的图像加密方法
Image Encryption Method Based on Novel Combined Chaotic System and Fractional Number Theory Transformation
摘要
Abstract
Aiming at addressing existing issues in current image encryption technologies regarding encryption speed,security,and sensitivity,this paper proposes a novel image encryption method based on a combined chaotic system and fractional number-theoretic transform.First,a new chaotic structure is proposed by combining two traditional one-dimensional mappings to create a fully chaotic mapping.Metrics such as bifurcation diagrams,Lyapunov exponents,and information entropy demonstrate that the proposed chaotic structure exhibits excellent chaotic performance,large parameter space,strong sensitivity,and high randomness.Subsequently,a new image encryption method is developed based on this chaotic mapping and multi-parameter fractional number theoretic transform.The hash value of the plaintext image is linked with the parameters of the chaotic system to generate initial chaotic keys and scrambling parameters.A multi-parameter fractional number theoretic transform is defined by constructing a number theoretic transform feature vector.The plaintext image undergoes one round of number theoretic transform to obtain an intermediate image,followed by Arnold scrambling to disrupt the image.Finally,another round of number-theoretic transformation is applied to generate the ciphertext image.Experimental results indicate that the algorithm achieves excellent encryption performance:the pixel change rate(NPCR)and unified average changing intensity(UACI)closely approach their ideal values;the average correlation coefficient of ciphertext images is 0.001 8,approaching zero;the normalized entropy of ciphertext images reaches 0.999 4,nearing the maximum value of 1.With an average encryption time of 0.273s and decryption time of 0.324s,the method outperforms other comparative schemes in efficiency.It demonstrates robust resistance against common attacks including chosen-plaintext attacks,differential attacks,and exhaustive attacks,exhibiting high security and promising application prospects in multimedia security fields.关键词
图像加密/混沌系统/数论变换/多参数变换/鲁棒性Key words
image encryption/chaotic system/number theoretic transform/multiple-parameter transform/robustness分类
信息技术与安全科学引用本文复制引用
梅锦程,张平,赖富豪,吴礼发..基于新型组合混沌系统和分数数论变换的图像加密方法[J].信息安全研究,2026,12(6):517-525,9.基金项目
国家自然科学基金联合重点项目(U23B2002) （U23B2002）
国家自然科学基金面上项目(62272238) （62272238）
国家自然科学基金青年科学基金(C类)项目(61902195) （C类）
