Speeding up the computations on an elliptic curve using addition-subtraction chains
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 24 (1990) no. 6, pp. 531-543.
@article{ITA_1990__24_6_531_0,
     author = {Morain, Fran\c{c}ois 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},
     pages = {531--543},
     publisher = {EDP-Sciences},
     volume = {24},
     number = {6},
     year = {1990},
     zbl = {0724.11068},
     mrnumber = {1082914},
     language = {en},
     url = {http://www.numdam.org/item/ITA_1990__24_6_531_0/}
}
TY  - JOUR
AU  - Morain, François
AU  - Olivos, Jorge
TI  - Speeding up the computations on an elliptic curve using addition-subtraction chains
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 1990
DA  - 1990///
SP  - 531
EP  - 543
VL  - 24
IS  - 6
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/ITA_1990__24_6_531_0/
UR  - https://zbmath.org/?q=an%3A0724.11068
UR  - https://www.ams.org/mathscinet-getitem?mr=1082914
LA  - en
ID  - ITA_1990__24_6_531_0
ER  - 
%0 Journal Article
%A Morain, François
%A Olivos, Jorge
%T Speeding up the computations on an elliptic curve using addition-subtraction chains
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 1990
%P 531-543
%V 24
%N 6
%I EDP-Sciences
%G en
%F 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, Volume 24 (1990) no. 6, pp. 531-543. http://www.numdam.org/item/ITA_1990__24_6_531_0/

1.A. O. L. Atkin, Manuscript.

2.F. Bergeron, J. Berstel, S. Brlek and C. Duboc, Addition Chains using Continued Fractions, Journal of Algorithms, 10, 3, 1989, pp. 403-412. | MR | Zbl

3.W. Bosma, Primality Testing using Elliptic Curves, Report 85-12, Math. Instituut, Universeit van Amsterdam.

4.A. Brauer, On Addition Chains, Bull. Amer Math. Soc, 45, 1939, pp. 736-739. | JFM | MR

5.R. P. Brent, Some Integer Factorization Algorithms using Elliptic Curves, Research Report CMA-R32-85, The Australian National University, Canberra, 1985.

6.J. Brillhart, D. H. Lehmer, B. Tuckerman and S. S. Jr. Wagstaff, Factorizations of bn±1, B = 2, 3, 5, 6, 1, 10, 11, 12 up to High Powers, Contemporary Math., A. M. S., 1983, | Zbl

7. J. W. S. Cassels, Diophantine Equations with Special References to Elliptic Curves, J. London Math. Soc., 1966, pp. 193-291. | MR | Zbl

8. B. W. Char, K. O. Geddes, G. H. Gonnet and S. M. Watt, MAPLE, Reference Marmal, Fourth Edition, Symbolic Computation Group, Department of Computer Science, University of Waterloo, 1985.

9. D. V. Chudnovsky and G. V. Chudnovsky, 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. H. Cohen and A. K. Lenstra, Implementation of a New Primality Test, Math. Comp., 1987, 177, pp. 103-121. | MR | Zbl

11. P. Erdös, Remarks on Number Theory III : On Addition Chains, Acta Arithmetica, 1960, pp. 77-81. | MR | Zbl

12. P. Flajolet, B. Salvy and P. Zimmermann, 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 | Zbl

13. P. Flajolet, B. Salvy and P. Zimmermann, Lambda-Upsilon-Omega : The, 1989 Cookbook, Research Report 1073, Institut National de Recherche en Informatique et en Automatique, August 1989, 116 pages.

14. S. Goldwasser and J. Kilian, Almost all Primes can be quickly Certified. Proc. 18th A.C.M. Symp. on the Theory of Compt., Berkeley, 1986, pp. 316-329.

15. G. H. Gonnet, Handbook of Algorithms and Data Structures, Addison-Wesley, 1984. | Zbl

16. D. H. Greene, Labelled Formal Languages and Their Uses, Technical Report STAN-CS-83-982, Stanford University, 1983.

17. B. S. Jr. Kaliski, A Pseudo-Random Bit Generator Based on Elliptic Logarithms, Proc. Crypto 86, pp. 13-1, 13-21. | Zbl

18. D. E. Knuth, Seminumerical Algorithms, The Art of Computer Programming, T. II, Addisoon-Wesley. | Zbl

19. N. Koblitz, Elliptic curve cryptosystems. Math. Comp., 1987, 48, 177, pp. 203-209. | MR | Zbl

20. H. W. Jr. Lenstra, Factoring with Elliptic Curves, Report 86-18, Math. Inst., Univ. Amsterdam, 1986. | Zbl

21. H. W. Jr. Lenstra, Elliptic Curves and Number Theoretic Algorithms, Report 86-19, Math. Inst., Univ. Amsterdam, 1986. | MR

22. H. W. Jr. Lenstra, Factoring integers with elliptic curves. Annals of Math., 1987, 126, pp. 649-673. | MR | Zbl

23. D. P. Mccarthy, The Optimal Algorithm to Evaluate xn using Elementary Multiplication Methods, Math. Comp., 1977, 31, 137, pp. 251-256. | MR | Zbl

24. D. P. Mccarthy, Effect to Improved Multiplication Efficiency on Exponentiation Algorithms Derived from Addition Chains, Math. Comp., 1986, 46, 174, pp. 603-608. | MR | Zbl

25. P. L. Montgomery, Modular Multiplication without Trial Division, Math. Comp., 1985, 44, 170, pp. 519-521. | MR | Zbl

26. F. Morain, Implementation of the Atkin-Goldwasser-Kilian test. I.N.R.I.A. Research, Report 911, 1988.

27. F. Morain and J. Olivos, 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. J. Olivos, On Vectorial Additions Chains. J. of Algorithms, 1981, 2, pp. 13-21. | MR | Zbl

29. J.-M. Pollard, Theorems on factorization and primality testing. Proc. Cambridge Phil. Soc., 1974, 76, pp. 521-528. | MR | Zbl

30. R. L. Rivest, A. Shamir and L. Adleman, A Method for Obtaining Digital Signatures and Public-Key Cryptosystems, Comm. of the A.C.M., 1978, 21, 2, pp. 120-126. | MR | Zbl

31. A. Schönhage, A Lower Bound for the Length of Addition Chains, Theor. Comput. Science, 1975, 1, 1, pp. 1-12. | MR | Zbl

32. J. T. Tate, The Arithmetic of Elliptic Curves, Inventiones Math., 1974, 23, pp.179-206. | MR | Zbl