@article{ITA_1990__24_6_531_0,
author = {Morain, Fran\c cois and Olivos, Jorge},
title = {Speeding up the computations on an elliptic curve using addition-subtraction chains},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {24},
year = {1990},
pages = {531-543},
mrnumber = {1082914},
zbl = {0724.11068},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_1990__24_6_531_0}
}
Morain, François; Olivos, Jorge. Speeding up the computations on an elliptic curve using addition-subtraction chains. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 24 (1990) pp. 531-543. http://gdmltest.u-ga.fr/item/ITA_1990__24_6_531_0/
1., Manuscript.
2., , and , Addition Chains using Continued Fractions, Journal of Algorithms, 10, 3, 1989, pp. 403-412. | MR 1006993 | Zbl 0682.68025
3., Primality Testing using Elliptic Curves, Report 85-12, Math. Instituut, Universeit van Amsterdam.
4., On Addition Chains, Bull. Amer Math. Soc, 45, 1939, pp. 736-739. | JFM 65.0154.02 | MR 245
5., Some Integer Factorization Algorithms using Elliptic Curves, Research Report CMA-R32-85, The Australian National University, Canberra, 1985.
6., , and , Factorizations of bn±1, B = 2, 3, 5, 6, 1, 10, 11, 12 up to High Powers, Contemporary Math., A. M. S., 1983, | Zbl 0527.10001
7. , Diophantine Equations with Special References to Elliptic Curves, J. London Math. Soc., 1966, pp. 193-291. | MR 199150 | Zbl 0138.27002
8. , , and , MAPLE, Reference Marmal, Fourth Edition, Symbolic Computation Group, Department of Computer Science, University of Waterloo, 1985.
9. and , Sequences of Numbers Generated by Addition in Formal Groups and New primality and Factorization Tests, Research report RC 11262, I.B.M., Yorktown Heights, 1985.
10. and , Implementation of a New Primality Test, Math. Comp., 1987, 177, pp. 103-121. | MR 866102 | Zbl 0608.10001
11. , Remarks on Number Theory III : On Addition Chains, Acta Arithmetica, 1960, pp. 77-81. | MR 121346 | Zbl 0219.10064
12. , and , Lambda-Upsilon-Omega : An assistant algorithms analyzer. In Applied Algebra, Algebraic Algotithms and Error-Correcting Codes (1989), T. MORA, Ed., Lecture Notes in Comp. Sci., 357, pp. 201-212. (Proceedings AAECC'6, Rome, July 1988). | MR 1008504 | Zbl 0681.68064
13. , and , Lambda-Upsilon-Omega : The, 1989 Cookbook, Research Report 1073, Institut National de Recherche en Informatique et en Automatique, August 1989, 116 pages.
14. and , Almost all Primes can be quickly Certified. Proc. 18th A.C.M. Symp. on the Theory of Compt., Berkeley, 1986, pp. 316-329.
15. , Handbook of Algorithms and Data Structures, Addison-Wesley, 1984. | Zbl 0665.68001
16. , Labelled Formal Languages and Their Uses, Technical Report STAN-CS-83-982, Stanford University, 1983.
17. , A Pseudo-Random Bit Generator Based on Elliptic Logarithms, Proc. Crypto 86, pp. 13-1, 13-21. | Zbl 0635.94011
18. , Seminumerical Algorithms, The Art of Computer Programming, T. II, Addisoon-Wesley. | Zbl 0895.65001
19. , Elliptic curve cryptosystems. Math. Comp., 1987, 48, 177, pp. 203-209. | MR 866109 | Zbl 0622.94015
20. , Factoring with Elliptic Curves, Report 86-18, Math. Inst., Univ. Amsterdam, 1986. | Zbl 0596.10007
21. , Elliptic Curves and Number Theoretic Algorithms, Report 86-19, Math. Inst., Univ. Amsterdam, 1986. | MR 934218
22. , Factoring integers with elliptic curves. Annals of Math., 1987, 126, pp. 649-673. | MR 916721 | Zbl 0629.10006
23. , The Optimal Algorithm to Evaluate xn using Elementary Multiplication Methods, Math. Comp., 1977, 31, 137, pp. 251-256. | MR 428791 | Zbl 0348.65041
24. , Effect to Improved Multiplication Efficiency on Exponentiation Algorithms Derived from Addition Chains, Math. Comp., 1986, 46, 174, pp. 603-608. | MR 829630 | Zbl 0608.68027
25. , Modular Multiplication without Trial Division, Math. Comp., 1985, 44, 170, pp. 519-521. | MR 777282 | Zbl 0559.10006
26. , Implementation of the Atkin-Goldwasser-Kilian test. I.N.R.I.A. Research, Report 911, 1988.
27. and , Un algorithmo de Evaluación de Potencia utilizando Cadenas de Suma y Resta, Proc. XIV Conference Latinoamericana de Informatica (C.L.E.I., Expodata), Buesnos Aires, September 1988.
28. , On Vectorial Additions Chains. J. of Algorithms, 1981, 2, pp. 13-21. | MR 640507 | Zbl 0466.68034
29. , Theorems on factorization and primality testing. Proc. Cambridge Phil. Soc., 1974, 76, pp. 521-528. | MR 354514 | Zbl 0294.10005
30. , and , A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, Comm. of the A.C.M., 1978, 21, 2, pp. 120-126. | MR 700103 | Zbl 0368.94005
31. , A Lower Bound for the Length of Addition Chains, Theor. Comput. Science, 1975, 1, 1, pp. 1-12. | MR 478756 | Zbl 0307.68032
32. , The Arithmetic of Elliptic Curves, Inventiones Math., 1974, 23, pp.179-206. | MR 419359 | Zbl 0296.14018