On-line evaluation of powers using Euclid's algorithm
Brlek, Srećko ; Castéran, Pierre ; Habsieger, Laurent ; Mallette, Richard
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 29 (1995), p. 431-450 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1995-01-01
@article{ITA_1995__29_5_431_0,
     author = {Brlek, Sre\'cko and Cast\'eran, Pierre and Habsieger, Laurent and Mallette, Richard},
     title = {On-line evaluation of powers using Euclid's algorithm},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     volume = {29},
     year = {1995},
     pages = {431-450},
     mrnumber = {1360669},
     zbl = {0838.68044},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ITA_1995__29_5_431_0}
}

Brlek, Srećko; Castéran, Pierre; Habsieger, Laurent; Mallette, Richard. On-line evaluation of powers using Euclid's algorithm. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 29 (1995) pp. 431-450. http://gdmltest.u-ga.fr/item/ITA_1995__29_5_431_0/

1. A. Brauer, On Addition Chains, Bull. Amer. Math. Soc., 1939, 45, pp. 736-739. | JFM 65.0154.02 | MR 245

2. F. Bergeron, J. Berstel and S. Brlek, A Unifying Approach to the Generation of Addition Chains, Proc. XV Latin American Conf. on Informatics, Santiago, Chile, July 10-14, 1989, pp. 29-38.

3. F. Bergeron, J. Berstel and S. Brlek, Efficient Computation of Addition Chains, J. Théorie des Nombres de Bordeaux, 1994, 6, pp. 21-38. | Numdam | MR 1305286 | Zbl 0812.11072

4. F. Bergeron, J. Berstel, S. Brlek and C. Duboc, Addition Chains Using Continued Fractions, J. Algorithms, 1989, 10, pp. 403-412. | MR 1006993 | Zbl 0682.68025

5. F. Bergeron and J. Olivos, Vectorial Addition Chains Using Euclid's Algorithm, Submitted.

6. J. Bos and M. Coster, Addition Chain Heuristics, Proceedings of CRYPTO 89, 1989. - Some algorithms on addition chains and their complexity Tech. Rep. Center for Mathematics and Computer Sc. Amsterdam, 1990.

7. S. Brlek, P. Castéran and R. Strandh, Chaînes d'additions et structures de contrôle, Journées JFLA 91, 28-29 janvier 1991, Gresse-en-Vercors, France, Bigre, 1991, 72, pp. 54-63.

8. S. Brlek, P. Castéran and R. Strandh, On Addition Schemes, Proceedings of TAPSOFT91, April 8-12, 1991, Brighton, England, Lect. Notes in Comp. Sci., 1991, 494, pp. 379-393.

9. P. Downey, B. Leong and R. Sethi, Computing Sequences with Addition Chains, SIAM J. Computing, 1981, 10, pp. 638-646. | MR 623072 | Zbl 0462.68021

10. D. E. Knuth, The Art of Computer Programming, vol. 2, Addison-Wesley, 1981. | MR 633878 | Zbl 0477.65002

11. F. Morain and J. Olivos, Speeding up the computations on an elliptic curve using addition-substraction chains, RAIRO Theo. Informatics and Appl., 1990, 6, 24, pp. 531-543. | Numdam | Zbl 0724.11068

12. A. Schönhage, A Lower Bound for the Length of Addition Chains, Theoretical Comp. Sci., 1975, pp. 1-12. | Zbl 0307.68032

13. E. G. Thurber, On Addition Chains l(mn) ≤ l(n) - b and Lower Bounds for c (r), Duke Math., J., 1973, 40, pp. 907-913. | Zbl 0275.10027

14. A. C.-C. Yao, On the Evaluation of Powers, SIAM J. Comp., 1976, 9, pp. 100-103. | Zbl 0326.68025