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基于LFSR高次剩余問題構(gòu)造公鑰密碼體制的研究

姜正濤,  柳毅,  王育民

姜正濤, 柳毅, 王育民. 基于LFSR高次剩余問題構(gòu)造公鑰密碼體制的研究[J]. 電子與信息學(xué)報, 2006, 28(3): 542-545.
引用本文: 姜正濤, 柳毅, 王育民. 基于LFSR高次剩余問題構(gòu)造公鑰密碼體制的研究[J]. 電子與信息學(xué)報, 2006, 28(3): 542-545.
Jiang Zheng-tao, Liu Yi, Wang Yu-min. Research on the Construction of Public-Key Cryptosystems Based on LFSR Residuosity Problem[J]. Journal of Electronics & Information Technology, 2006, 28(3): 542-545.
Citation: Jiang Zheng-tao, Liu Yi, Wang Yu-min. Research on the Construction of Public-Key Cryptosystems Based on LFSR Residuosity Problem[J]. Journal of Electronics & Information Technology, 2006, 28(3): 542-545.

基于LFSR高次剩余問題構(gòu)造公鑰密碼體制的研究

Research on the Construction of Public-Key Cryptosystems Based on LFSR Residuosity Problem

  • 摘要: 該文對用線性反饋移位寄存器(LFSR)構(gòu)造公鑰密碼體制做了進(jìn)一步的研究，定義了LFSR的高次(非)剩余問題，基于新的困難問題探討了構(gòu)造一種加解密不同于GH的密碼原型，并給出了具體的加解密過程，證明了它的可行性；在此基礎(chǔ)上，進(jìn)一步把該體制改進(jìn)為概率加密體制，克服了GH加密確定性的缺點，同時對體制的安全性和效率做了初步分析，具有單向性和語意安全性，最后證明了該體制的單向性等價于LFSR高次剩余問題，語意安全性等價于LFSR判斷高次剩余問題。
    Abstract: Further research on the construction of public-key cryptosystem based on Linear Feedback Shift Register (LFSR) is provided, and the LFSR higher (non) residuosity problem is defined. Based on new intractability problems a new public-key encryption primitive with encryption/decryption procedures differ from GH is investigated. The encryption and decryption procedures are specified. It is further improved to be a probabilistic encryption scheme. Efficiency and security analysis of the proposed encryption scheme is provided. It has properties of one-wayness and semantic security. The one-wayness and semantic security are equivalent to higher LFSR residuosity and decisional LFSR residuosity problems respectively.
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  • Diffie W, Hellman M E. New directions in cryptography[J]. IEEETrans. on oflnformation Theory, 1976, IT-22 (6): 644 - 654.[2]Rivest R, Shamir A, Adleman L. A method for abstaining digitalsignatures and public-key cryptosystems[J].Comm. of the ACM.1978,21(2):120-[3]Rabin M 0 . Digital signatures and public key functions asintractable as factorization[R]. Cambridge: MITILCSITR-212,1979.[4]Williams H C. An M3 public-key encryption scheme[A].Advances in Cryptology-CRYPT0'85[C]. Berlin: Springer-Verlag, 1986: 358 - 368.[5]Paillier P. Public-key cryptosystems based on composite degreeresiduosity classes. Advances in Cryptology- EUROCRYPT'99[C], Berlin: Springer-Verlag, 1999, LNCS 1592: 223 - 238.[6]Smith P, Lennon M. LUC: A new public-key system[A].Proceeding of IFIP/Sec'93[C], Elsevier Science Publications,1994: 97- 111.[7]Gong G, Ham L. Public-key cryptosystems based on cubic finitefield extensions[J]. IEEE Trans. on Information Theory, 1999, IT-45(7): 2601 - 2605.[8]Gong G, Ham L, Wu H P. The GH public-key cryptosystem[A].Selected areas in cryptography[C]. SAC, Toronto, 2001: 284 -300.[9]Jiang Z T, Hao Y H, Wang Y M. A new public-key encryptionscheme based on lucas sequence[J]. Journal of Electronics-(China). 2005,22(5):490 - 497.[10]Paillier P, Pointcheval D. Efticient public-key cryptosystemprovably secure against active adversaries[A]. Advances inCryptology-ASIACRYPT'99[C], Berlin: Springer-Verlag, 1999,LNCS 1716: 163 - 179.[11]Catalano D, Gennaro R, Graham N H. The bit security ofPaillier's encryption scheme and its applications[A]. Advances inCryptology-EUROCRYPTO'O I [C], Berlin: Springer-Verlag,200 1, LNCS 2045: 229 - 243.[12]Damgard I, Jurik M. A generalization, a simplification and someapplication of Paillier's probabilistic public-key system[A].Advances in Cryptology-PKC'99[C], Berlin: Springer-Verlag,200 1, LNCS 1992: 1 19 - 136.[13]姜正濤, 龐遼軍, 王育民. 一種高效的可選擇驗證完整性和消息源的加密體制[J].電子與信息學(xué)報.2005, 27(4):621-624瀏覽
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出版歷程
  • 收稿日期:  2004-09-09
  • 修回日期:  2005-04-21
  • 刊出日期:  2006-03-19

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