一种基于多重散射的光学Hash函数

何文奇; 陈嘉誉; 张莲彬; 卢大江; 廖美华; 彭翔

doi:10.7498/aps.70.20201492

摘要

本文提出了一种基于光与多重散射介质相互作用的光学Hash函数构造方法. 该方法创新性地利用多重散射介质对相干调制光的天然随机散射作用, 实现了对调制光的“混淆”和“扩散”, 从而满足了Hash函数的核心功能要求: 高安全强度的单向编码/加密. 所设计的光电混合系统能有效地模拟Hash函数中的“压缩函数”, 结合具有特征提取功能的Sobel滤波器, 能实现将任意长度的输入数据压缩并加密为固定长度为256 bit的输出(即Hash值). 一系列仿真结果表明: 该方法所构造的光学Hash函数具有良好的“雪崩效应”和“抗碰撞性”, 其安全性能可比拟当前最为广泛使用的传统Hash函数(MD5和SHA-1).

关键词:

Abstract

Hash functions, which can extract message digest from input messages as output, play an important role in digital signature and authentication. Meanwhile, Hash functions are essential in many cryptographic protocols and regimes. With the research becoming more and more in depth, a series of Hash functions is proposed, such as MD series and SHA series. At the same time, the security analysis and attacks against Hash functions are carried out. The security of Hash functions is threatened. In this case, how to improve the security of the Hash functions becomes the primary concern. In this paper, an optical Hash function based on the interaction between light and multiple scattering media is proposed. Unlike most of the traditional Hash functions which are based on mathematical transformations or complex logic operations, this method innovatively takes advantage of the natural random scattering effect of multiple scattering media on coherently modulated light, and realizes the “confusion” and “diffusion” of modulated light, which satisfies the core functional requirement of the Hash function: one-way encoding/encryption with strong security. The photoelectric hybrid system designed by this method can effectively simulate the "compression function" in the Hash function. Combined with the Sobel filter with feature extraction function, the input data of arbitrary length can be compressed and encrypted into the output with a fixed length of 256-bit (Hash value). The principle of the proposed optical Hash function can be described as follows. 1) Two 8-bit images with a size of 16×16 pixels are loaded in SLM₁ (amplitude-only spatial modulator) and SLM₂ (phase-only spatial modulator) respectively. 2) The coherent wavefront is modulated by SLM₁ and SLM₂, and then propagates on multiple scattering media. 3) A speckle pattern is recorded by CCD because of the confusion of multiple scattering media. 4) The features of the speckle pattern, which is extracted by Sobel filter, serve as the input of the next compression function. For the unpredicted and non-duplicated disorder multiple scattering media, it is tremendously difficult to determine the internal state of the multiple scattering media. Therefore, the proposed optical Hash function is considered to have a high security. A series of simulation results shows that the proposed optical Hash function has a good “avalanche effect” and “collision resistance”, and its security performance is comparable to that of the most widely used traditional Hash functions (MD5 and SHA-1).

Keywords:

作者及机构信息

深圳大学物理与光电工程学院，光电子器件与系统教育部/广东省重点实验室, 深圳　518060

通信作者: 廖美华, liaomeihua@outlook.com ; 彭翔, xpeng@szu.edu.cn

基金项目: 国家自然科学基金 (批准号: 61875129, 61705141, 61805152)、中德合作项目 (批准号: GZ1391, M-0044) 和广东省自然科学基金 (批准号: 2018A030310561)资助的课题

Authors and contacts

Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China

Corresponding author: Liao Mei-Hua, liaomeihua@outlook.com ; Peng Xiang, xpeng@szu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61875129, 61705141, 61805152), the Sino-German Center for Research Promotion (Grant Nos. GZ1391, M-0044), and the Natural Science Foundation of Guangdong Province, China (Grant No. 2018A030310561)

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参考文献

[1]	Schneier B, 1996 Government Information Quarterly 13 336
[2]	Refregier P, Javidi B 1995 Opt. Lett. 20 767 Google Scholar
[3]	刘福民, 翟宏琛, 杨晓苹 2003 52 2462 Google Scholar Liu F M, Zhai H C, Yang X P 2003 Acta Phys. Sin. 52 2462 Google Scholar
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[5]	Javidi B, Carnicer A, Yamaguchi M , Nomura T, Pérez-Cabré E 2016 J. Opt. 18 083001 Google Scholar
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[7]	Peng X, Zhang P, Wei H, Yu B 2006 Opt. Lett. 31 1044 Google Scholar
[8]	彭翔, 汤红乔, 田劲东 2007 56 2629 Google Scholar Peng X, Tang H Q, Tian J D 2007 Acta Phys. Sin. 56 2629 Google Scholar
[9]	Cheng X C, Cai L Z, Wang Y R, Meng X F, Zhang H, Xu X F, Shen X X, Dong G Y 2008 Opt. Lett. 33 1575 Google Scholar
[10]	Liao M H, He W Q, Lu D J, Wu J C, Peng X 2017 Opt. Laser. Eng. 98 34
[11]	Peng X, Wei H Z, Zhang P 2006 Opt. Lett. 31 3579 Google Scholar
[12]	Qin W, Peng X 2010 Opt. Lett. 35 118 Google Scholar
[13]	Cai J J, Shen X J, Lei M, Lin C, Dou S F 2015 Opt. Lett. 40 475 Google Scholar
[14]	Volodin B L, Kippelen B, Meerholz K, Javidi B, Peyghambarian N 1996 Nature 383 58 Google Scholar
[15]	Wang X G, Chen W, Mei S T, Chen X D 2015 Sci. Rep. 5 15668 Google Scholar
[16]	何江涛, 何文奇, 廖美华, 卢大江, 彭翔 2017 66 044202 Google Scholar He J T, He W Q, Liao M H, Lu D J, Peng X 2017 Acta Phys. Sin. 66 044202 Google Scholar
[17]	Rivest R L 1991 Lect. Notes. Comput. Sci. 537 303
[18]	Rivest R L https://www.rfc-editor.org/rfc/rfc1321 [2020-9-10]
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[20]	何文奇, 彭翔, 祁永坤, 孟祥锋, 秦琬, 高志 2010 59 1762 Google Scholar He W Q, Peng X, Qi Y K, Meng X F, Qin W, Gao Z 2010 Acta Phys. Sin. 59 1762 Google Scholar
[21]	Lai H, He W, Peng X 2013 Appl. Opt. 52 6213 Google Scholar
[22]	Webster A F, Tavares S E 1986 Lect. Notes. Comput. Sci. 218 523

施引文献

图 1 Hash函数的结构

Fig. 1. Schematic diagram of the Hash function.

下载: 全尺寸图片幻灯片

图 2 实现基于多重散射的光学压缩函数的光电系统结构示意图

Fig. 2. Schematic diagram of optoelectronic architecture for realizing the optical compression function based on multiple scattering.

下载: 全尺寸图片幻灯片

图 3 初始伪随机图像的生成

Fig. 3. Flowchart for creating initial pseudo-random image.

下载: 全尺寸图片幻灯片

图 4 级联压缩流程图

Fig. 4. Flowchart of cascade compression.

下载: 全尺寸图片幻灯片

图 5 级联压缩过程

Fig. 5. Procedure of cascaded compression.

下载: 全尺寸图片幻灯片

图 6 轻微修改原始消息的过程

Fig. 6. Flowchart of modifying the bit of message.

下载: 全尺寸图片幻灯片

图 7 多重散射介质仿真模型

Fig. 7. Simulation model of the MSM.

下载: 全尺寸图片幻灯片

图 8 10000次测试下的$ {\mathrm{A}\mathrm{E}\mathrm{C}} $分布, 消息长度为　(a) 10 kbit, (b) 100 kbit, (c) 1000 kbit

Fig. 8. Distribution of AEC values in tests for the messages with (a) 10 kbit, (b) 100 kbit, and (c) 1000 kbit.

下载: 全尺寸图片幻灯片

表 1 雪崩效应测试结果

Table 1. Results of testing avalanche effect.

10 kbit 100 kbit 1000 kbit 平均值

$ \overline{{\rm{AEC}}} $ 0.49 0.50 0.50 0.50
${\Delta }{B} $ 0.0770 0.0647 0.0636 0.0684

下载: 导出CSV

表 2 与MD5和SHA-1算法的比较

Table 2. Comparison with MD5 and SHA-1.

本方案 MD5 SHA-1

$ \overline{{\rm{AEC}}} $ 0.50 0.50 0.50
${\Delta }{B} $ 0.0684 0.0437 0.0392

下载: 导出CSV

map

[1]	Schneier B, 1996 Government Information Quarterly 13 336
[2]	Refregier P, Javidi B 1995 Opt. Lett. 20 767 Google Scholar
[3]	刘福民, 翟宏琛, 杨晓苹 2003 52 2462 Google Scholar Liu F M, Zhai H C, Yang X P 2003 Acta Phys. Sin. 52 2462 Google Scholar
[4]	Situ G H, Zhang J J 2004 Opt. Lett. 29 1584 Google Scholar
[5]	Javidi B, Carnicer A, Yamaguchi M , Nomura T, Pérez-Cabré E 2016 J. Opt. 18 083001 Google Scholar
[6]	Carnicer A, Montes-Usategui M, Arcos S, Juvells I 2005 Opt. Lett. 30 1644 Google Scholar
[7]	Peng X, Zhang P, Wei H, Yu B 2006 Opt. Lett. 31 1044 Google Scholar
[8]	彭翔, 汤红乔, 田劲东 2007 56 2629 Google Scholar Peng X, Tang H Q, Tian J D 2007 Acta Phys. Sin. 56 2629 Google Scholar
[9]	Cheng X C, Cai L Z, Wang Y R, Meng X F, Zhang H, Xu X F, Shen X X, Dong G Y 2008 Opt. Lett. 33 1575 Google Scholar
[10]	Liao M H, He W Q, Lu D J, Wu J C, Peng X 2017 Opt. Laser. Eng. 98 34
[11]	Peng X, Wei H Z, Zhang P 2006 Opt. Lett. 31 3579 Google Scholar
[12]	Qin W, Peng X 2010 Opt. Lett. 35 118 Google Scholar
[13]	Cai J J, Shen X J, Lei M, Lin C, Dou S F 2015 Opt. Lett. 40 475 Google Scholar
[14]	Volodin B L, Kippelen B, Meerholz K, Javidi B, Peyghambarian N 1996 Nature 383 58 Google Scholar
[15]	Wang X G, Chen W, Mei S T, Chen X D 2015 Sci. Rep. 5 15668 Google Scholar
[16]	何江涛, 何文奇, 廖美华, 卢大江, 彭翔 2017 66 044202 Google Scholar He J T, He W Q, Liao M H, Lu D J, Peng X 2017 Acta Phys. Sin. 66 044202 Google Scholar
[17]	Rivest R L 1991 Lect. Notes. Comput. Sci. 537 303
[18]	Rivest R L https://www.rfc-editor.org/rfc/rfc1321 [2020-9-10]
[19]	He W Q, Peng X, Qin W, Meng X F 2010 Opt. Commun. 283 2328 Google Scholar
[20]	何文奇, 彭翔, 祁永坤, 孟祥锋, 秦琬, 高志 2010 59 1762 Google Scholar He W Q, Peng X, Qi Y K, Meng X F, Qin W, Gao Z 2010 Acta Phys. Sin. 59 1762 Google Scholar
[21]	Lai H, He W, Peng X 2013 Appl. Opt. 52 6213 Google Scholar
[22]	Webster A F, Tavares S E 1986 Lect. Notes. Comput. Sci. 218 523

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一种基于多重散射的光学Hash函数