Abstract
At present, the joint sparse form and the joint binary-ternary method are the most efficient representation systems for calculating multi-scalar multiplications [k]Pā+ā[l]Q, where k,l are scalars and P,Q are points on the same elliptic curve. We introduce the concept of a joint triple-base chain. Our algorithm, named the joint binary-ternary-quintuple method, is able to find a shorter joint triple-base chain for the sparseness of triple-base number systems. With respect to the joint sparse form, this algorithm saves 32% of the additions, saving 13% even compared with the joint binary-ternary method. The joint binary-ternary-quintuple method is the fastest method among the existing algorithms, which speeds up the signature verification of the elliptic curve digital signature algorithm. It is very suitable for software implementation.
Supported in part by National Basic Research Program of China(973) under Grant No.2013CB338002, in part by National Research Foundation of China under Grant No. 60970153 and 61070171, and in part by the Strategic Priority Research Program of Chinese Academy of Sciences under Grant XDA06010702.
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References
Straus, E.G.: Addition chains of vectors (problem 5125). American Mathematical MonthlyĀ 70, 806ā808 (1964)
Solinas, J.A.: Low-weight binary representations for pairs of integers. Combinatorics and Optimization Research Report CORR 2001-41, University of Waterloo (2001)
Adikari, J., Dimitrov, V.S., Imbert, L.: Hybrid binary ternary number system for elliptic curve cryptosystems. IEEE Transactions on ComputersĀ 60, 254ā265 (2011)
Dimitrov, V., Imbert, L., Mishra, P.K.: Efficient and Secure Elliptic Curve Point Multiplication using Double-Base Chains. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol.Ā 3788, pp. 59ā78. Springer, Heidelberg (2005)
Doche, C., Kohel, D.R., Sica, F.: Double Base Number System for multi scalar multiplications. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol.Ā 5479, pp. 502ā517. Springer, Heidelberg (2009)
Mishra, P.K., Dimitrov, V.S.: Efficient Quintuple Formulas for Elliptic Curves and Efficient Scalar Multiplication Using Multibase Number Representation. In: Garay, J.A., Lenstra, A.K., Mambo, M., Peralta, R. (eds.) ISC 2007. LNCS, vol.Ā 4779, pp. 390ā406. Springer, Heidelberg (2007)
Longa, P.: Accelerating the Scalar Multiplication on Elliptic Curve Cryptosystems over Prime Fields, Master Thesis, University of Ottawa (2007)
Purohit, G.N., Rawat, A.S.: Fast Scalar Multiplication in ECC Using The Multi base Number System, http://eprint.iacr.org/2011/044.pdf
Hankerson, D., Menezes, A., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer (2004)
Longa, P., Gebotys, C.: Fast multibase methods and other several optimizations for elliptic curve scalar multiplication. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol.Ā 5443, pp. 443ā462. Springer, Heidelberg (2009)
Cohen, H., Miyaji, A., Ono, T.: Efficient elliptic curve exponentiation using mixed coordinates. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol.Ā 1514, pp. 51ā65. Springer, Heidelberg (1998)
Hisil, H., Wong, K.K.-H., Carter, G., Dawson, E.: Faster group operations on elliptic curves. In: Australasian Information Security Conference (AISC 2009), Wellington, New Zealand. Conferences in Research and Practice in Information Technology (CRPIT), vol.Ā 98, pp. 7ā19 (January 2009)
Hisil, H., Wong, K., Carter, G., Dawson, E.: An Intersection Form for Jacobi-Quartic Curves. Personal Communication (2008)
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Yu, W., Wang, K., Li, B., Tian, S. (2013). Joint Triple-Base Number System for Multi-Scalar Multiplication. In: Deng, R.H., Feng, T. (eds) Information Security Practice and Experience. ISPEC 2013. Lecture Notes in Computer Science, vol 7863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38033-4_12
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DOI: https://doi.org/10.1007/978-3-642-38033-4_12
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