Abstract
Investigated the properties of LUCas sequence(LUC), the paper proposed a new variant of (probabilistic) public-key encryption scheme. Security analysis of the proposed encryption schemes shows that its one-wayness is equivalent to partial LUC discrete logarithm problem in Z N, and for the proposed probabilistic encryption scheme, its semantic security is equivalent to decisional LUC Diffie-Hellman problem in Z N. At last, the efficiency of the proposed schemes is briefly analyzed.
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References
W. Diffie, M. E. Hellman, New directions in cryptography, IEEE Trans. on Information Theory, IT-22(1976)6, 644–654.
R. Rivest, A. Shamir, et al., A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, 21(1978)2, 120–126.
P. Smith, M. Lennon, LUC: A new public-key system, Proceedings of the IFIP TC11, Ninth International Conference on Information Security: Computer Security, Toronto, May 12–14, 1993, 103–117.
D. Bleichenbacher, W. Bosma, et al., Some remarks on Lucas-based cryptosystems, Advances in Cryptology-CRYPTO’95, LNCS 963, Berlin, Springer-Verlag, 1995, 386–396.
M. Adleman, J. DeMarrais, A subexponential algorithm over all finite fields, Advances in Cryptology-CRYPTO’93, LNCS 773, Berlin, Springer-Verlag, 1993, 147–158.
A. E. Brouwer, R. Pellikaan, et al., Doing more with fewer bits, Advances in Cryptology-ASIACRYPT’99, LNCS 1716, Berlin, Springer-Verlag, 1999, 321–332.
P. Paillier, Efficient public-key cryptosystem provably secure against active adversaries, Advances in Cryptology-ASIACRYPT’99, LNCS 1716, Springer-Verlag, 1999, 159–179.
I. B. Damgard, M. J. Jurik, Efficient protocols based on probabilistic encryption using composite degree residue classes, http://www.brics.dk/RS/00/5/BRICS-RS-00-5.pdf.
S. J. Li, X. Q. Mou, et al., Problems with a probabilistic encryption scheme based on chaotic systems, International Journal of Bifurcation and Chaos, 13(2003)10, 3063–3077.
D. Boneh, The decision Diffie-Hellman problem, Third Algorithmic Number Theory Symposium, LNCS 1423, Berlin, Springer-Verlag, 1998, 48–63.
S. M. Yen, C. S. Laih, Common-multiplicand multiplication and its applications to public key cryptography, Electronics Letters, 29(1993)17, 1583–1584.
S. M. Yen, C. S. Laih, Fast algorithms for LUC digital signature computation, IEE Proceeding of Computers and Digital Techniques, 142(1995)2, 165–169.
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Supported by the 973 State Key Project of China (No.G1999035803) and the National Natural Science Foundation of China (No.69931010).
Communication author: Jiang Zhengtao, born in 1976, male, Ph.D. candidate. National Key Lab of Integrated Service Networks, Xidian University, Xi’an 710071, China.
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Jiang, Z., Hao, Y. & Wang, Y. A new public-key encryption scheme based on LUCas sequence. J. of Electron.(China) 22, 490–497 (2005). https://doi.org/10.1007/BF03037006
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DOI: https://doi.org/10.1007/BF03037006