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Abstrakty
This article shows how to use fast Fp2 arithmetic and twisted Hessian curves to obtain faster point scalar multiplication on elliptic curve ESW in short Weierstrass form over Fp. It is assumed that p and #ESW(Fp) are different large primes, #E(Fq) denotes number of points on curve E over field Fq and #EtSW (Fp), where Et is twist of E, is divisible by 3. For example this method is suitable for two NIST curves over Fp: NIST P-224 and NIST P-256. The presented solution may be much faster than classic approach. Presented solution should also be resistant for side channel attacks and information about Y coordinate should not be lost (using for example Brier-Joye ladder such information may be lost). If coefficient A in equation of curve ESW : y2 =x3+Ax+B in short Weierstrass curve is not of special form, presented solution is up to 30% faster than classic approach. If A=−3, proposed method may be up to 24% faster.
Rocznik
Tom
Strony
98--102
Opis fizyczny
Bibliogr. 9 poz., rys.
Twórcy
autor
- Department of Mathematics and Cryptology, Military University of Technology, Kaliskiego st 2, 00-908 Warsaw, Poland
Bibliografia
- [1] E. Brier and M. Joye, “Weierstraß elliptic curves and side-channel attacks”, in Public Key Cryptography, LNCS, vol. 2274, pp. 335–345. Springer, 2002 (doi: 10.007/3-540-45664-3 24).
- [2] S. Ghosh, D. Mukhopadhyay, and D. Roychowdhury, “High speed flexible pairing cryptoprocessor on FPGA platform”, in Pairing-Based Cryptography – Pairing 2010, S. Ghosh, D. Mukhopadhyay, and D. Roychowdhury, Eds. LNCS, vol. 6487, pp. 450–466. Springer, 2010 (doi: 10.1007/978/3/642-17455-1 28).
- [3] H. Cohen and G. Frey, Handbook of Elliptic and Hyperelliptic Curve Cryptography. New York: Chapman & Hall/CRC, 2006.
- [4] J. Renes, C. Costello, and L. Batina, “Complete addition formulas for prime order elliptic curves”, Cryptology ePrint Archive, Report 2015/1060, 2015 [Online]. Available: https://eprint.iacr.org/ 2015/1060
- [5] Explicit Formulas Database. [Online]. Available: http://hyperelliptic.org/EFD/g1p/index.html
- [6] D. Bernstein, Ch. Chuengsatiansup, D. Kohel, and T. Lange, “Twisted Hessian curves”, Cryptology ePrint Archive, Report 2015/781, 2015 [Online]. Available: https://eprint.iacr.org/2015/781
- [7] N. P. Smart, “The Hessian form of an elliptic curve”, in Cryptographic Hardware and Embedded Systems – CHES 2001, LNCS, vol. 2162, pp. 118–125. Springer, 2001 (doi: 10.1007/3-540-44709-1 11).
- [8] “Recommended Elliptic Curves For Federal Government Use”, National Institute of Standards and Technology, MA, USA, 1999 [Online]. Available: http://csrc.nist.gov/groups/ST/toolkit/documents/ dss/NISTReCur.pdf, 1999
- [9] S. Galbraith, X. Lin, and M. Scott, “Endomorphisms for faster elliptic curve cryptography on a large class of curves”, J. of Cryptol., vol. 24, no. 3, pp. 446–469, 2011.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6a9b7f25-ea25-4127-9596-613dc7f8a239