CN111460488A - 基于预存储和n维Arnold变换的多图像快速加密方法 - Google Patents

基于预存储和n维Arnold变换的多图像快速加密方法 Download PDF

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CN111460488A
CN111460488A CN202010364034.4A CN202010364034A CN111460488A CN 111460488 A CN111460488 A CN 111460488A CN 202010364034 A CN202010364034 A CN 202010364034A CN 111460488 A CN111460488 A CN 111460488A
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CN111460488B (zh
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张晓强
孙志康
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China University of Mining and Technology CUMT
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Abstract

针对图像加密方法效率低和加密容量有限的问题,受著名的外部设备联机并行操作(Simultaneous Peripheral Operations On‑Line,Spooling)系统启发,采取空间换取时间的思想,设计了一种基于预存储和n维Arnold变换的多图像快速加密方法。在加密前,预计算周期T个新变换矩阵,并将其分别保存到T个文本文件中。在加密时,从第t∈[1,T‑1]个文本文件中读取对应的新变换矩阵,并对原始图像进行一次新n维Arnold变换,等价于t次传统n维Arnold变换迭代,可得加密图像。实验表明:该方法操作简单,可明显提高图像加密效率,能够同时保护多幅图像内容的安全。

Description

基于预存储和n维Arnold变换的多图像快速加密方法
技术领域
本发明涉及图像加密领域,具体涉及一种基于预存储和n维Arnold变换的多图像快速加密方法。
背景技术
随着信息化程度的不断提高和互联网的广泛使用,在政治、经济和军事等多个领域中,无时无刻都会产生大量的重要图像信息。因此,信息的泄露、篡改等问题不容忽视,研究高效、安全的图像加密方法意义重大。
大数据时代下,信息传输能力不断增强 ,单图像加密传输已经不能满足人们的需求。目前,多图像加密方法大多基于多种加密技术的结合,操作复杂。因此,有必要研究操作容易并且加密效果良好的多图像加密方法。
图像加密方法通常对算法效率要求较高,而对存储空间开销即占用的存储空间大小要求不高。
Arnold变换是一种常用的图像加密方法,具有周期性。然而,它计算量大,特别是当选取迭代次数较大时,会导致加密效率很低。基于此,受著名的外部设备联机并行操作(Simultaneous Peripheral Operations On-Line,Spooling)系统启发,考虑利用空间换取时间的思路来提高Arnold变换的效率。
发明内容
本发明的目的:针对图像加密方法效率低和加密容量有限的问题,提出一种基于预存储和n维Arnold变换的多图像快速加密方法。
本发明的技术方案:为实现上述发明目的,采用的技术方案为一种基于预存储和n维Arnold变换的多图像快速加密方法,图像加密步骤详述如下:
1. 基于预存储和n维Arnold变换多图像快速加密方法,其特征在于,加密过程步骤如下:
步骤1:计算变换周期:令原始图像为n幅大小为m×m的灰色图像I 1, I 2, …, I n ,计算:
Figure 956140DEST_PATH_IMAGE001
, (1)
其中,
Figure 190812DEST_PATH_IMAGE002
为变换矩阵,像素值x 1 0I 1, x 2 0I 2, …, x n 0I n x 1 1,x 2 1, …, x n 1表示变换后n幅图像的像素值;从集合{0, 1, …, 255}中任取n个数分别作为x 1 0, x 2 0, …, x n 0的值,利用公式(1)反复迭代数次,当迭代结果与x 1 0, x 2 0, …, x n 0的值完全相同时,此迭代次数即为n维Arnold变换的周期T
步骤2:计算新变换矩阵:
B k =A k mod 256,k=1, 2, …, T, (2)
可得T个新变换矩阵B 1, B 2, …, B T
步骤3:存储新变换矩阵:将B 1, B 2, …, B T 的元素值分别保存到T个文本文件中;
步骤4:选取迭代次数:随机选取任一整数t∈[1, T-1]作为此次加密的迭代次数;
步骤5:图像扩散:从第t个文本文件中读取新变换矩阵B t ,对I 1, I 2,…, I n 进行一次新n维Arnold变换,可得n幅加密图像J 1, J 2,…, J n
进一步地,所述步骤5中,新n维Arnold变换指:
Figure 454172DEST_PATH_IMAGE003
, (3)。
进一步地,利用数学归纳法,公式(3)的推导为:
证明:当n=1时,由公式(1)和(2)可知,显然成立;
假设n=t时成立,则有
Figure 661162DEST_PATH_IMAGE003
n=t+1时,根据n维Arnold变换定义得:
Figure 368087DEST_PATH_IMAGE004
因为
Figure 762159DEST_PATH_IMAGE003
所以
Figure 330675DEST_PATH_IMAGE005
根据公式(2)可得:A=B
Figure 188910DEST_PATH_IMAGE006
所以当n=t+1时,公式(3)成立;
因此,根据数学归纳法,可知公式(3)等价为tn维Arnold变换成立。
附图说明
图1:基于预存储和n维Arnold变换的多图像快速加密流程图;
图2:原始图像;
图3:加密图像。
具体实施方式
下面结合具体附图和实例对本发明的实施过程进一步详细说明。
图1是本方法的加密流程图。
采用的编程软件为Matlab R2017b,选取图2所示的4幅256×256的灰色图像作为原始图像,对其进行四维(即n=4)Arnold变换。采用本方法,对4幅原始图像加密的详细过程描述如下:
步骤1:计算变换周期:选取x 1 0, x 2 0, x 3 0, x 4 0的值分别为1, 1, 0, 4,根据公式(1),可得四维Arnold变换的周期T=448;
步骤2:计算新变换矩阵:根据公式(2),可得448个新变换矩阵B 1, B 2, …, B 448
步骤3:存储新变换矩阵:将448个新变换矩阵B 1, B 2, …, B 448的元素值分别保存到448个文本文件中;
步骤4:选取迭代次数:选取t=292作为此次加密的迭代次数;
步骤5:图像扩散:从第292个文本文件中读取新变换矩阵B 292,对原始图像I 1, I 2, I 3, I 4进行一次新四维Arnold变换(即公式(3)中n=4时),可得4幅加密图像J 1, J 2, J 3, J 4,如图3所示。

Claims (2)

1.基于预存储和n维Arnold变换的多图像快速加密方法,其特征在于,加密过程步骤如下:
步骤1:计算变换周期:令原始图像为n幅大小为m×m的灰色图像I 1, I 2, …, I n ,计算:
Figure 622125DEST_PATH_IMAGE001
, (1)
其中,
Figure 96969DEST_PATH_IMAGE002
为变换矩阵,像素值x 1 0I 1, x 2 0I 2, …, x n 0I n x 1 1,x 2 1, …, x n 1表示变换后n幅图像的像素值;从集合{0, 1, …, 255}中任取n个数分别作为x 1 0, x 2 0, …, x n 0的值,利用公式(1)反复迭代数次,当迭代结果与x 1 0, x 2 0, …, x n 0的值完全相同时,此迭代次数即为n维Arnold变换的周期T
步骤2:计算新变换矩阵:
B k =A k mod 256,k=1, 2, …, T, (2)
可得T个新变换矩阵B 1, B 2, …, B T
步骤3:存储新变换矩阵:将B 1, B 2, …, B T 的元素值分别保存到T个文本文件中;
步骤4:选取迭代次数:随机选取任一整数t∈[1, T-1]作为此次加密的迭代次数;
步骤5:图像扩散:从第t个文本文件中读取新变换矩阵B t ,对I 1, I 2, …, I n 进行一次新n维Arnold变换,可得n幅加密图像J 1, J 2, …, J n
2.根据权利要求1所述的方法,其特征在于:所述步骤5中,新n维Arnold变换指:
Figure 593809DEST_PATH_IMAGE003
。 (3)。
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CN111881438A (zh) * 2020-08-14 2020-11-03 支付宝(杭州)信息技术有限公司 基于隐私保护进行生物特征识别的方法、装置及电子设备

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CN103455971A (zh) * 2013-09-04 2013-12-18 上海理工大学 三维Arnold变换和混沌序列结合的图像加密方法
CN107169911A (zh) * 2016-11-28 2017-09-15 黄宗美 一种基于二维Arnold变换的图像加密方法

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CN103455971A (zh) * 2013-09-04 2013-12-18 上海理工大学 三维Arnold变换和混沌序列结合的图像加密方法
CN107169911A (zh) * 2016-11-28 2017-09-15 黄宗美 一种基于二维Arnold变换的图像加密方法

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CN111881438A (zh) * 2020-08-14 2020-11-03 支付宝(杭州)信息技术有限公司 基于隐私保护进行生物特征识别的方法、装置及电子设备
CN111881438B (zh) * 2020-08-14 2024-02-02 支付宝(杭州)信息技术有限公司 基于隐私保护进行生物特征识别的方法、装置及电子设备

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