AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Tsinghua Science and Technology Article
PDF (8.3 MB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Open Access

Evolutionary Cryptography Theory-Based Generating Method for Secure ECs

Chao Wang, Feng Hu( ), Huanguo Zhang, Jie Wu
Key Laboratory of Specialty Fiber Optics and Optical Access Networks, School of Communication and Information Engineering, Shanghai University, Shanghai 200072, China.
Department of Computer and Information Sciences, Temple University, Philadelphia, PA 19122, USA.
Key Lab of Aerospace Information Security and Trusted Computing, Wuhan University, Wuhan 430072, China.
Show Author Information

Abstract

Ant Colony Optimization (ACO) has the character of positive feedback, distributed searching, and greedy searching. It is applicable to optimization grouping problems. Traditional cryptographic research is mainly based on pure mathematical methods which have complicated theories and algorithm. It seems that there is no relationship between cryptography and ACO. Actually, some problems in cryptography are due to optimization grouping problems that could be improved using an evolutionary algorithm. Therefore, this paper presents a new method of solving secure curve selection problems using ACO. We improved Complex Multiplication (CM) by combining Evolutionary Cryptography Theory with Weber polynomial solutions. We found that ACO makes full use of valid information generated from factorization and allocates computing resource reasonably. It greatly increases the performance of Weber polynomial solutions. Compared with traditional CM, which can only search one root once time, our new method searches all roots of the polynomial once, and the average time needed to search for one root reduces rapidly. The more roots are searched, the more ECs are obtained.

Keywords

ECsWeber polynomialevolutionary algorithmant algorithmcomplex multiplication

References

[1]
Zhang H. G., Feng X. T., Tan Z. P., and Liu Y. Z., Evolutionary cryptosystems and evolutionary design for DES, (in Chinese), Journal of China Institute of Communications, vol. 23, no. 5, pp. 57-64, 2002.
Google Scholar
[2]
Zhang H. G. and Tan Z. P., Evolutionary Cryptosystem, (in Chinese). Wuhan University Press, 2011.
[3]
Pontie S., Maistri P., and Leveugle R., An elliptic curve crypto-processor secured by randomized windows, in Proc. 17th Euromicro Conf. on Digital System Design (DSD), Verona, Italy, 2014, pp. 535-542.
Crossref
[4]
He D. and Zeadally S., An analysis of RFID authentication schemes for internet of things in healthcare environment using elliptic curve cryptography, IEEE Internet of Things Journal, vol. 2, no. 1, pp. 72-83, 2015.
Crossref Google Scholar
[5]
Thiranant N., Lee Y. S., and Lee H., Performance comparison between RSA and elliptic Curve cryptography-based QR code authentication, presented at the IEEE, International Conference on Advanced Information NETWORKING and Applications Workshops IEEE, Gwangiu, South Korea, 2015.
Crossref
[6]
Xu J. W., Wang K. D., Wang C., Hu F., Zhang Z. H., Xu S. Y., and Wu J., Byzantine fault-tolerant routing for large-scale wireless sensor networks based on fast ECDSA, Tsinghua Science and Technology, vol. 20, no. 6, pp. 627-633, 2015.
Crossref Google Scholar
[7]
Jia H., Wang C., and Gu J., Error bit correction of ECC attack based on grover quantum intermediate encounter search algorithm, Netinfo Security, vol. 2, no. 6, pp. 28-34, 2016.
Google Scholar
[8]
Chen Y. H., Jia H. H., and Jiang L. Y., ECC scanning attack based on grover algorithm, Netinfo Security, vol. 2, pp. 28-32, 2016.
Google Scholar
[9]
Wang C., Zhang H. G., and Liu L. L., The experiment of Koblitz elliptic curves generating based on evolutionary cryptography theory and verifying the parameters recommended by NIST, China Communications, vol.8 , no. 4, pp. 41-49, 2016.
Google Scholar
[10]
Wang C., Zhang H. G., and Liu L. L., Evolutionary cryptography theory based generating method for secure Kobtliz EC and its improvement by HMM, Science China Information Sciences, vol. 55 , no. 4, pp. 911-920, 2012.
Crossref Google Scholar
[11]
Atkin A. O. L. and Morain F., Elliptic curves and primality proving, Mathematics of Computation, vol. 61, no. 203, pp. 29-68, 1993.
Crossref Google Scholar
[12]
Spallek A. M., Konstruktion einer elliptischen Kurve uber einem endlichen Korper zu gegebener Punktegruppe, Master Thesis, Universitat GH Essen, Diman, the Netherland, 1992.
[13]
Lay G. J. and Zimmer H., Constructing elliptic curves with given group order over large finite fields, Lecture Notes in Computer Science, vol. 887, pp. 250-263, 1994.
Crossref Google Scholar
[14]
Cornacchia G., u di un metodo per la risoluzone in numeri interi dell equazione, Giornale di Matermatiche di Battaglini, vol. 46, no. 1, pp. 33-90. 1980.
Google Scholar
[15]
IEEE P1363/D13, Standard specifications for public key cryptography, ballot draft, http://www.grouper.ieee.org/groups/1363/tradPK/draft.html, 1999.
[16]
Harald B., Efficient algorithms for generating elliptic curves over finite fields suitable for use in crytography, Ph.D. Dissertation, Dept. of Computer Science, Technical Univ. of Darmstadt, Darmstadt, German, 2002.
[17]
Joachim V., Zur G., and Daniel P., Factoring polynomials over finite fields: A survey, Journal of Symbolic Computation, vol. 31, nos. 1&2, pp. 3-17, 2001.
Crossref Google Scholar
[18]
Pohlig S. C. and Hellman M. E., An improved algorithm for computing logarithms over GF(P) and the cryptographic significance, IEEE Transactions on Information Theory, vol. 24, no. 1, pp. 106-110, 1978.
Crossref Google Scholar
[19]
Oorschot P. and Wiener M. J., Parallel collision search with cryptanalytic applications, Journal of Cryptology, vol. 12, no. 1, pp. 1-28, 1999.
Crossref Google Scholar
[20]
Menezes A. T., Okamoto T., and A Vanstone S., Reducing elliptic curve logarithms in a finite field, IEEE Transactions on Information Theory, vol. 39, no. 5, pp. 1639-1646, 1993.
Crossref Google Scholar
[21]
Shu Q., Zhang H. G., and Wang Z. Y., Evolutionary design for Bent function, Journal of Electronics, vol. 32, no. 11, pp. 1901-1903, 2004.
Google Scholar
[22]
Song J., Zhang H. G., and Meng Q. S., Cryptoanalysis of four-round DES based on genetic algorithm, presented at the Proceedings of the International Conference on Wireless Communications, Networking and Mobile Computing, Shanghai, China, 2007.
Crossref
[23]
Yang F., Song J., and Zhang H., Quantitative cryptanalysis of six-round DES using evolutionary algorithms, presented at the Proceedings of the International Symposium on Intelligence Computation and Applications, Wuhan, China, 2008.
Crossref
[24]
Clark J. A., Jacob J. L., and Stepney S., The design of Sboxes by simulated annealing, New Generation Computing, vol. 23, no. 5, pp. 219-231, 2005.
Crossref Google Scholar
[25]
Clark J. A., Jacob J. L., Stepney S., Maritra S., and Willan W., Evolving Boolean functions satisfying multiple criteria, Lecture Notes in Computer Science, vol. 2551, pp. 246-259, 2002.
Crossref Google Scholar
[26]
Clark A. and Dawson E., A parallel genetic algorithm for cryptanalysis of the polyalphabetic substitution cipher, Cryptologia, vol. 21, no. 2, pp. 129-138, 1997.
Crossref Google Scholar
[27]
Gambardella L. M. and Dorigo M., Solving symmetric and asymmetric TSPs by ant colonie, in Proceedings of the IEEE Conference on Evolutionary Coomputation, Nagoya, Japan, 1996.
[28]
Gambardella L. M. and Dorigo M., Ant-Q: A reinforcement learning approach to the traveling salesman problem, in Proceedings of the ML-95, the 12th International Conference on Machine Learning, Tahoe City, CA, America, 1995.
Crossref
[29]
Stutzle, T and Hoos H. H., MAX-MIN ant system, Future Generation Computer Systems Journal, vol. 16, no. 8, pp. 889-914, 2000.
Crossref Google Scholar
[30]
Cordon O., Viana I. D., Herrera F., and Moreno L., A new ACO model integrating evolutionary computation concepts: The best-worst ant system, presented at the ANTS2000-From Ant Colonies to Artificial Ants, Brussels, Belgium, 2000.
Tsinghua Science and Technology
Volume 22 Issue 5,
October 2017
Pages 499-510
DOI: 10.23919/TST.2017.8030539
Cite this article:
Wang C, Hu F, Zhang H, et al. Evolutionary Cryptography Theory-Based Generating Method for Secure ECs. Tsinghua Science and Technology, 2017, 22(5): 499-510. https://doi.org/10.23919/TST.2017.8030539

585

Views

30

Downloads

0

Crossref

N/A

Web of Science

6

Scopus

1

CSCD

Altmetrics
Received: 14 November 2016
Accepted: 06 February 2017
Published: 11 September 2017
© The author(s) 2017
Return