Efficient generation of minimal length addition chains

SIAM Journal on Computing

Volumn 28, Issue 4, 1999, Pages 1247-1263

  Thurber, Edward G ^a  

^a BIOLA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; INTEGER PROGRAMMING; SEARCH ENGINES; TREES (MATHEMATICS);

ADDITION CHAIN; BACKTRACKING; PRUNING BOUNDS; SEARCH TREE;

COMPUTATIONAL METHODS;

EID: 0032674079     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539795295663     Document Type: Article

References (20)

1. F. BERGERON, J. BERSTEL, S. BRLEK, AND C. DUBOC, Addition chains using continued fractions, J. Algorithms, 10 (1989), pp. 403-412.
2. F. BERGERON, J. BERSTEL, AND S. BRLEK, Efficient computation of addition chains, J. de Théor. Nombres Bordeaux, 6 (1994), pp. 21-38.
3. J. BOS AND M. COSTER, Addition chain heuristics, in Proceedings CRYPTO '89, 1990, pp. 400-407.
4. A. T. BRAUER, On addition chains, Bull. Amer Math. Soc., 45 (1939), pp. 736-739.
5. Y. H. CHIN AND Y.-H. TSAI, Algorithms for finding the shortest addition chain, in Proceedings National Computer Symposium, Kaoshiung, Taiwan, Dec. 1985, pp. 1398-1414.
6. H. DELLAC, Question 49, l'Interm. des Math., 1 (1894), p. 20.
7. D. DOBKIN AND R. J. LIPTON, Addition chain methods for the evaluation of specific polynomials, SIAM J. Comput., 9 (1980), pp. 121-125.
8. P. DOWNEY, B. LEONG, AND R. SETHI, Computing sequences with addition chains, SIAM J. Comput., 10 (1981), pp. 638-646.
9. P. ERDÖS, Remarks on number theory III on addition chains, Acta Arith., 6 (1960), pp. 77-81.
10. W. HANSEN, Zum Scholz-Brauerchen Problem, J. Reine Angew. Math., 202 (1959), pp. 129-136 (in German).
11. E. DE JONQUIÈRES, Question 393, (A. Goulard), l'Interm. des Math., 2 (1985), pp. 125-126.
12. D. E. KNUTH, The Art of Computer Programming, vol. 2, 3rd ed., Addison-Wesley, Reading, MA, 1997, pp. 461-485.
13. A. SCHOLZ, Aufgabe 253, Jahresber. Deutsch. Math.-Verein., 47 (1937), pp. 41-42.
14. A. SCHÖNHAGE, A lower bound for the length of addition chains, Theoret. Comput. Sci., 1 (1975), pp. 1-12.
15. N. J. A. SLOANE AND S. PLOUFFE, The Encyclopedia of Integer Sequences, Academic Press, San Diego, 1995.
16. M. V. SUBBARAO, Addition chains - some results and problems, in Number Theory and Applications, R. A. Mollin, ed., Kluwer Academic Publishers, Dordrecht, 1989, pp. 555-574.
17. E. G. THURBER, The Scholz-Brauer problem on addition chains, Pacific J. Math., 49 (1973), pp. 229-242.
18. n - 1) = n + l(n) - 1, Discrete Math., 16 (1976), pp. 279-289.
19. E. G. THURBER, Addition chains - an erratic sequence, Discrete Math., 122 (1993), pp. 287-305.
20. W. R. UTZ, A note on the Scholz-Brauer problem on addition chains, Proc. Amer. Math. Soc., 4 (1953), pp. 462-463.