EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 24 / No 6 (1990) RAIRO-Theor. Inf. Appl., 24 6 (1990) 531-543 References
Free Access
Issue
RAIRO-Theor. Inf. Appl.
Volume 24, Number 6, 1990
Page(s) 531 - 543
DOI https://doi.org/10.1051/ita/1990240605311
Published online 01 February 2017
  1. 1.A. O. L. ATKIN, Manuscript. [Google Scholar]
  2. 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: 1006993] [Zbl: 0682.68025] [Google Scholar]
  3. 3.W. BOSMA, Primality Testing using Elliptic Curves, Report 85-12, Math. Instituut, Universeit van Amsterdam. [Zbl: 1103.11039] [Google Scholar]
  4. 4.A. BRAUER, On Addition Chains, Bull. Amer Math. Soc, 45, 1939, pp. 736-739. [Zbl: 65.0154.02] [MR: 245] [JFM: 65.0154.02] [Google Scholar]
  5. 5.R. P. BRENT, Some Integer Factorization Algorithms using Elliptic Curves, Research Report CMA-R32-85, The Australian National University, Canberra, 1985. [Google Scholar]
  6. 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: 0527.10001] [Google Scholar]
  7. 7. J. W. S. CASSELS, Diophantine Equations with Special References to Elliptic Curves, J. London Math. Soc., 1966, pp. 193-291. [MR: 199150] [Zbl: 0138.27002] [Google Scholar]
  8. 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. [Google Scholar]
  9. 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. [Zbl: 0614.10004] [Google Scholar]
  10. 10. H. COHEN and A. K. LENSTRA, Implementation of a New Primality Test, Math. Comp., 1987, 177, pp. 103-121. [MR: 866102] [Zbl: 0608.10001] [Google Scholar]
  11. 11. P. ERDÖS, Remarks on Number Theory III : On Addition Chains, Acta Arithmetica, 1960, pp. 77-81. [EuDML: 206704] [MR: 121346] [Zbl: 0219.10064] [Google Scholar]
  12. 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: 1008504] [Zbl: 0681.68064] [Google Scholar]
  13. 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. [Google Scholar]
  14. 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. [Google Scholar]
  15. 15. G. H. GONNET, Handbook of Algorithms and Data Structures, Addison-Wesley, 1984. [Zbl: 0665.68001] [Google Scholar]
  16. 16. D. H. GREENE, Labelled Formal Languages and Their Uses, Technical Report STAN-CS-83-982, Stanford University, 1983. [Google Scholar]
  17. 17. B. S. Jr. KALISKI, A Pseudo-Random Bit Generator Based on Elliptic Logarithms, Proc. Crypto 86, pp. 13-1, 13-21. [Zbl: 0635.94011] [Google Scholar]
  18. 18. D. E. KNUTH, Seminumerical Algorithms, The Art of Computer Programming, T. II, Addisoon-Wesley. [Zbl: 0895.65001] [Google Scholar]
  19. 19. N. KOBLITZ, Elliptic curve cryptosystems. Math. Comp., 1987, 48, 177, pp. 203-209. [MR: 866109] [Zbl: 0622.94015] [Google Scholar]
  20. 20. H. W. Jr. LENSTRA, Factoring with Elliptic Curves, Report 86-18, Math. Inst., Univ. Amsterdam, 1986. [Zbl: 0596.10007] [Google Scholar]
  21. 21. H. W. Jr. LENSTRA, Elliptic Curves and Number Theoretic Algorithms, Report 86-19, Math. Inst., Univ. Amsterdam, 1986. [MR: 934218] [Google Scholar]
  22. 22. H. W. Jr. LENSTRA, Factoring integers with elliptic curves. Annals of Math., 1987, 126, pp. 649-673. [MR: 916721] [Zbl: 0629.10006] [Google Scholar]
  23. 23. D. P. MCCARTHY, The Optimal Algorithm to Evaluate xn using Elementary Multiplication Methods, Math. Comp., 1977, 31, 137, pp. 251-256. [MR: 428791] [Zbl: 0348.65041] [Google Scholar]
  24. 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: 829630] [Zbl: 0608.68027] [Google Scholar]
  25. 25. P. L. MONTGOMERY, Modular Multiplication without Trial Division, Math. Comp., 1985, 44, 170, pp. 519-521. [MR: 777282] [Zbl: 0559.10006] [Google Scholar]
  26. 26. F. MORAIN, Implementation of the Atkin-Goldwasser-Kilian test. I.N.R.I.A. Research, Report 911, 1988. [Google Scholar]
  27. 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. [Google Scholar]
  28. 28. J. OLIVOS, On Vectorial Additions Chains. J. of Algorithms, 1981, 2, pp. 13-21. [MR: 640507] [Zbl: 0466.68034] [Google Scholar]
  29. 29. J.-M. POLLARD, Theorems on factorization and primality testing. Proc. Cambridge Phil. Soc., 1974, 76, pp. 521-528. [MR: 354514] [Zbl: 0294.10005] [Google Scholar]
  30. 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: 700103] [Zbl: 0368.94005] [Google Scholar]
  31. 31. A. SCHÖNHAGE, A Lower Bound for the Length of Addition Chains, Theor. Comput. Science, 1975, 1, 1, pp. 1-12. [MR: 478756] [Zbl: 0307.68032] [Google Scholar]
  32. 32. J. T. TATE, The Arithmetic of Elliptic Curves, Inventiones Math., 1974, 23, pp.179-206. [EuDML: 142261] [MR: 419359] [Zbl: 0296.14018] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.