Have a personal or library account? Click to login
On the Construction of Short Addition-Subtraction Chains and their Applications Cover

On the Construction of Short Addition-Subtraction Chains and their Applications

By: Moussa Ngom and  Amadou Tall  
Open Access
|Mar 2023

References

  1. [1] BERGERON, F.—BERSTEL, J.—BRLEK, S.—DUBOC, C.: Addition chains using continued fractions, J. Algorithms 10 (1989), no. 3, 403–412.
  2. [2] BLEICHENBACHER, D.—FLAMMENKAMP, A.: An effcient algorithm for computing shortest addition chains, SIAM J. Discrete Math. 10 (1997), no. 1, 15–17.
  3. [3] DOWNEY, P.—LEONG, B.—SETHI, R.: Computing sequences with addition chains, SIAM J. Comput. 10 (1981), no. 3, 638–646.
  4. [4] VOLGER, H.: Some results on addition-subtraction chains, Inform. Process. Lett. 20 (1985), no. 3, 155–160.
  5. [5] KNUTH, D. E.: The Art of Computer Programming, Vol. 2. Seminumerical Algorithms. Second edition. Addison-Wesley Series in Computer Science and Information Processing. Addison-Wesley Publishing Co., Reading, Mass., 1981.
  6. [6] MIGNOTTE, M.—TALL, A.: A note on addition chains, Int. J. Algebra, 5 (2011), no. 6, 269–274.
  7. [7] TAKAGI, T.—REIS, D.—YEN, S.—WU, B.: Radix-r non-adjacent form and its application to pairing-based cryptosystem, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E89-A (2006), no. 1, 115–123. DOI: 10.1093/ietfec/e89-a.1.11510.1093/ietfec/e89-a.1.115
  8. [8] TALL, A.: A generalization of Lucas addition chains, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 55(103) (2012), no. 1, 79–93.
  9. [9] YACOBI, Y.: Exponentiating faster with addition chains, In: Advances in cryptology—EUROCRYPT ’90 (Aarhus, 1990), Lecture Notes in Comput. Sci., Vol. 473, Springer-Verlag, Berlin, 1991. pp. 222–229,10.1007/3-540-46877-3_20
  10. [10] MORRAIN, F.—OLIVOS, J.: Speeding up the computation on an elliptic curve using addition-subtraction chains,RAIROInformatique Théor. Appl. 24 (1990), no. 6, 531–543.
  11. [11] GORDON, D. M.: A survey of fast exponentiation methods J. Algorithms 27 (1998), no. 1, 129–146.
  12. [12] TALL, A.: A generalization of Lucas addition chains, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 55 (103) (2012), 79–93.
DOI: https://doi.org/10.2478/tmmp-2023-0010 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 131 - 144
Submitted on: Dec 3, 2022
Published on: Mar 7, 2023
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2023 Moussa Ngom, Amadou Tall, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.