Abstract
Elliptic curve cryptography (ECC) is one of public key cryptography suitable for the limited storages and low power devices. The reason is that ECC has the same security level with other public key cryptographies, although bits length is very small. However, ECC is based on Elliptic Curve Discrete Logarithm Problem (ECDLP) that is very difficult to be solved. At present, many algorithms were introduced to solve the problem. Nevertheless, the efficiency of each algorithm is based on the characteristic of k, Q = kP, when Q and P are known points on the curve, and type of curve. Deeply, brute force attack is one of techniques to solve ECDLP. This algorithm has very high performance when k is small. However, to find k, 2P, 3P, 4P, ···, (k − 1)P and kP must be computed. Thus, numbers of inversion process are k − 1. Moreover, for traditional brute force attack, y’s points must be computed all loops computation. In this paper, the new method based on brute force attack, is called Resolving Elliptic Curve Discrete Logarithm Problem by Decreasing Inversion Processes and Finding only x’s points (RIX-ECDLP), is proposed. The key is to remove some inversion processes and y’s points out of the computation. In fact, every two point additions can be done with only one inversion process. The experimental results show that RIX-ECDLP can reduce time about 10–20% based on size of k and prime number.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public key cryptosystems. J. Commun. ACM 21(2), 120–126 (1978)
Koblitz, N.: Elliptic Curve Cryptosystems. Math. Comput. 48, 203–209 (1987)
Elbirt, A.J.: Under Standing and Applying Cryptography and Data Security. Auerbach Publications, USA (2009)
Miller, V.S.: Uses of elliptic curves in cryptography. In: Williams, H.C. (ed.) Lecture Notes in Computer Science, vol. 218, pp. 417–428. Springer, Heidelberg (1986)
Amara, M., Siad, A.: Elliptic curve cryptography and its application. In: 7th International Workshop on Systems, Signal Processing and their Applications, Tipaza, Algeria, pp. 247–250 (2011)
Subhranil, S., Rana, M., Sandip, D.: Elliptic curve cryptography: a dynamic paradigm. In: International Conference on Infocom Technologies and Unmanned Systems, Dubai, UAE, pp. 427–431 (2017)
Singh, L.D., Debbrama, T.: A new approach to Elliptic curve cryptography. In: International Conference on Advanced Communication Control and Computing Technologies, Ramanathapuram, India, pp. 78–82 (2014)
Eisentrager, K., Lauter, K., Montgomery, P.L.: Fast Elliptic curve arithmetic and improved Weil pairing evaluation. In: Joye, M. (ed.) Lecture Notes in Computer Science, vol. 2612, pp. 343–354. Springer, Heidelberg (2003)
Ciet, M., Joye, M., Lauter, K., Montgomery, P.L.: Trading inversions for multiplications in Elliptic curve cryptography. J. Des. Codes and Cryptogr. 39(2), 189–206 (2005)
Li, Y., Feng, L.: Overview of scalar multiplication in Elliptic curve cryptography. In: International Conference on Computer Science and Network Technology, Harbin, China, pp. 2670–2673 (2011)
Attacks on the curve-based discrete logarithm problem. http://ecc2011.loria.fr/slides/summerschool-vitse.pdf
Neamah, A.A.: New Collisions to Improve Pollard’s Rho Method of Solving the Discrete Logarithm Problem on Elliptic Curves. https://arxiv.org/ftp/arxiv/papers/1607/1607.05901.pdf
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Somsuk, K., Sanemueang, C. (2019). The New Modified Methodology to Solve ECDLP Based on Brute Force Attack. In: Unger, H., Sodsee, S., Meesad, P. (eds) Recent Advances in Information and Communication Technology 2018. IC2IT 2018. Advances in Intelligent Systems and Computing, vol 769. Springer, Cham. https://doi.org/10.1007/978-3-319-93692-5_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-93692-5_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-93691-8
Online ISBN: 978-3-319-93692-5
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)