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A method of constructing optical Hash function based on nonlinear cascaded Fourier transform is proposed. The proposed method consists of two single one-way encryption processes. In the first process, the digital information is divided to several data blocks with 512-bit each. The data blocks are encoded to 8 by 8 sub-images with 256 gray scales, creating information planes. Then take a nonlinear cascaded Fourier transform of sub-image to generate a data matrix through an optical/digital hybrid system. By extending the data matrix we get four information planes. Again, taking nonlinear cascaded Fourier transform to built information planes, we get a Hash value 64-bit long （hash1）. In the second process, we shift cydically every numerical value of the original information planes by 4-bit, constructing auxiliary information planes. Thereafter we take the same operations as we have done in the first process to the Hash value （hash2）. Once hash1 and hash2 obtained, they are combined to form a final Hash value 128-bit long （hash）. Furthermore, the avalanche effect coefficient （AEC） was also proposed to evaluate the performance of the optical Hash function. Theoretical analysis and simulation results are presented to show the effectiveness of optical Hash function constructed by our approach and the constructed optical Hash function has good performance of avalanche effect and collision resistance.
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Keywords:
- information optics /
- optical Hash function /
- nonlinear cascaded Fourier transform /
- avalanche effect
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[2] ［2］Yang Y G 2008 Chin. Phys. B 17 415
[3] ［3］Schneier B 1996 Applied Cryptography, second edition （John Wiley & Sons） p122—177
[4] ［4］Shimon E, Goldreich O, Micali S 1996 J. Cryptology 9 35
[5] ［5］Hu X D, Wei Q F 2005 Applied Cryptography tutorial （Beijing: Electronics industry Press） p122—177 （in Chinese）［胡向东、魏琴芳 应用密码学教程 2005 （北京:电子工业出版社） 第122页—177页］
[6] ［6］Rivest R L 1991 Lect. Notes. Comput. Sc. 537 303
[7] ［7］Rivest R L 1992 RFC 1321, MIT and RSA Data Security, Inc
[8] ［8］Wang X Y, Yu H B 2005 Lect. Notes. Comput. Sc. 3494 19
[9] ［9］Wang X Y, Yin Y L, Yu H B 2005 Lect. Notes. Comput. Sc. 3621 17
[10] ］Lin Q Q, Wang F Q, Mi J L, Liang R S, Liu S H 2007 Acta. Phys. Sin. 56 5796 （in Chinese）［林青群、王发强、米景隆、梁瑞生、刘颂豪 2007 56 5796］
[11] ］Cai J M, Liu D, Chen T M 2007 Comput. Appl. 27 219 （in Chinese）［蔡家楣、刘多、陈铁明 2007 计算机应用 27 219］
[12] ］Refregier P, Javidi B 1995 Opt. Lett. 20 767
[13] ］Liu G J, Shan L, Dai Y W, Sun J S, Wang Z Q 2006 Acta. Phys. Sin. 55 5688 （in Chinese）［刘光杰、单梁、戴跃伟、孙金生、王执铨 2006 55 5688］
[14] ］Wang J Z, Wang Y L, Wang M Q 2006 Acta. Phys. Sin. 55 5048 （in Chinese）［王继志、王应龙、王美琴 2006 55 5048］
[15] ］Peng X, Wei H Z, Zhang P 2006 Opt. Lett. 31 3579
[16] ］Yuan S, Zhou X, Alam M S, Lu X, Li X F 2009 Opt. Express 17 3270
[17] ］Peng X, Yu L F, Cai L L 2002 Opt. Express 10 41
[18] ］Peng X, Tang H Q, Tian J D 2007 Acta. Phys. Sin. 56 2629 （in Chinese）［彭翔、汤红乔、田劲东 2007 56 2629］
[19] ］Yi X 2005 IEEE T. Circuits. Syst. 52 354
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[1] ［1］Tsudik G 1992 Comput. Commun. Rev. 22 29
[2] ［2］Yang Y G 2008 Chin. Phys. B 17 415
[3] ［3］Schneier B 1996 Applied Cryptography, second edition （John Wiley & Sons） p122—177
[4] ［4］Shimon E, Goldreich O, Micali S 1996 J. Cryptology 9 35
[5] ［5］Hu X D, Wei Q F 2005 Applied Cryptography tutorial （Beijing: Electronics industry Press） p122—177 （in Chinese）［胡向东、魏琴芳 应用密码学教程 2005 （北京:电子工业出版社） 第122页—177页］
[6] ［6］Rivest R L 1991 Lect. Notes. Comput. Sc. 537 303
[7] ［7］Rivest R L 1992 RFC 1321, MIT and RSA Data Security, Inc
[8] ［8］Wang X Y, Yu H B 2005 Lect. Notes. Comput. Sc. 3494 19
[9] ［9］Wang X Y, Yin Y L, Yu H B 2005 Lect. Notes. Comput. Sc. 3621 17
[10] ］Lin Q Q, Wang F Q, Mi J L, Liang R S, Liu S H 2007 Acta. Phys. Sin. 56 5796 （in Chinese）［林青群、王发强、米景隆、梁瑞生、刘颂豪 2007 56 5796］
[11] ］Cai J M, Liu D, Chen T M 2007 Comput. Appl. 27 219 （in Chinese）［蔡家楣、刘多、陈铁明 2007 计算机应用 27 219］
[12] ］Refregier P, Javidi B 1995 Opt. Lett. 20 767
[13] ］Liu G J, Shan L, Dai Y W, Sun J S, Wang Z Q 2006 Acta. Phys. Sin. 55 5688 （in Chinese）［刘光杰、单梁、戴跃伟、孙金生、王执铨 2006 55 5688］
[14] ］Wang J Z, Wang Y L, Wang M Q 2006 Acta. Phys. Sin. 55 5048 （in Chinese）［王继志、王应龙、王美琴 2006 55 5048］
[15] ］Peng X, Wei H Z, Zhang P 2006 Opt. Lett. 31 3579
[16] ］Yuan S, Zhou X, Alam M S, Lu X, Li X F 2009 Opt. Express 17 3270
[17] ］Peng X, Yu L F, Cai L L 2002 Opt. Express 10 41
[18] ］Peng X, Tang H Q, Tian J D 2007 Acta. Phys. Sin. 56 2629 （in Chinese）［彭翔、汤红乔、田劲东 2007 56 2629］
[19] ］Yi X 2005 IEEE T. Circuits. Syst. 52 354
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