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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).
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Keywords:
- optical information security /
- optical Hash function /
- multiple scattering media /
- avalanche effect
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[22] Webster A F, Tavares S E 1986
Lect. Notes. Comput. Sci. 218 523 -
图 1 Hash函数的结构
Figure 1. Schematic diagram of the Hash function.
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
Figure 2. Schematic diagram of optoelectronic architecture for realizing the optical compression function based on multiple scattering.
图 3 初始伪随机图像的生成
Figure 3. Flowchart for creating initial pseudo-random image.
图 4 级联压缩流程图
Figure 4. Flowchart of cascade compression.
图 5 级联压缩过程
Figure 5. Procedure of cascaded compression.
图 6 轻微修改原始消息的过程
Figure 6. Flowchart of modifying the bit of message.
图 7 多重散射介质仿真模型
Figure 7. Simulation model of the MSM.
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 kbitFigure 8. Distribution of AEC values in tests for the messages with (a) 10 kbit, (b) 100 kbit, and (c) 1000 kbit.
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 
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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
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[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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