Abstract
Elliptic curves find numerous applications. This paper describes a simple strategy to speed up their arithmetic in right-to-left methods. In certain settings, this leads to a non-negligible performance increase compared to the left-to-right counterparts.
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References
Bernstein, D.J., Lange, T.: Explicit-formulas database, http://www.hyperelliptic.org/EFD/jacobian.html
Bernstein, D.J., Lange, T.: Fast scalar multiplication on elliptic curves. In: Mullen, G., Panario, D., Shparlinski, I. (eds.) 8th International Conference on Finite Fields and Applications, Contemporary Mathematics. American Mathematical Society (to appear)
Chevallier-Mames, B., Ciet, M., Joye, M.: Low-cost solutions for preventing simple side-channel analysis: Side-channel atomicity. IEEE Transactions on Computers 53(6), 760–768 (2004)
Chudnovsky, D.V., Chudnovsky, G.V.: Sequences of numbers generated by addition in formal groups and new primality and factorization tests. Advances in Applied Mathematics 7(4), 385–434 (1986)
Cohen, H.: A Course in Computational Algebraic Number Theory. Graduate Texts in Mathematics, vol. 138. Springer, Heidelberg (1993)
Cohen, H., Miyaji, A., Ono, T.: Efficient elliptic curve exponentiation using mixed coordinates. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 51–65. Springer, Heidelberg (1998)
Fouque, P.-A., Valette, F.: The doubling attack - Why upwards is better than downwards. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds.) CHES 2003. LNCS, vol. 2779, pp. 269–280. Springer, Heidelberg (2003)
Gordon, D.M.: A survey of fast exponentiation methods. Journal of Algorithms 27(1), 129–146 (1998)
IEEE 1363-2000. Standard specifications for public key cryptography. IEEE Standards (August 2000)
Knuth, D.E.: The Art of Computer Programming, 2nd edn. Addison-Welsey (1981)
Kocher, P., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)
López, J., Dahab, R.: Fast multiplication on elliptic curves over GF(2m) without precomputation. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 316–327. Springer, Heidelberg (1999)
Montgomery, P.L.: Speeding the Pollard and elliptic curve methods of factorization. Mathematics of Computation 48(177), 243–264 (1987)
Morain, F., Olivos, J.: Speeding up the computations on an elliptic curve using addition-subtraction chains. RAIRO Theoretical Informatics and Applications 24(6), 531–543 (1990)
Reitwiesner, G.W.: Binary arithmetic. Advances in Computers 1, 231–308 (1960)
Silverman, J.H.: The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, vol. 106. Springer, Heidelberg (1986)
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Joye, M. (2008). Fast Point Multiplication on Elliptic Curves without Precomputation. In: von zur Gathen, J., Imaña, J.L., Koç, Ç.K. (eds) Arithmetic of Finite Fields. WAIFI 2008. Lecture Notes in Computer Science, vol 5130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69499-1_4
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DOI: https://doi.org/10.1007/978-3-540-69499-1_4
Publisher Name: Springer, Berlin, Heidelberg
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