We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 November 2024
Reseach Article

New Algorithm to Convert any Integer in TBNS

by Subhashis Maitra, Amitabha Sinha
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 51 - Number 5
Year of Publication: 2012
Authors: Subhashis Maitra, Amitabha Sinha
10.5120/8040-1355

Subhashis Maitra, Amitabha Sinha . New Algorithm to Convert any Integer in TBNS. International Journal of Computer Applications. 51, 5 ( August 2012), 40-45. DOI=10.5120/8040-1355

@article{ 10.5120/8040-1355,
author = { Subhashis Maitra, Amitabha Sinha },
title = { New Algorithm to Convert any Integer in TBNS },
journal = { International Journal of Computer Applications },
issue_date = { August 2012 },
volume = { 51 },
number = { 5 },
month = { August },
year = { 2012 },
issn = { 0975-8887 },
pages = { 40-45 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume51/number5/8040-1355/ },
doi = { 10.5120/8040-1355 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:49:37.992608+05:30
%A Subhashis Maitra
%A Amitabha Sinha
%T New Algorithm to Convert any Integer in TBNS
%J International Journal of Computer Applications
%@ 0975-8887
%V 51
%N 5
%P 40-45
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Algebraic complexity of different Algorithms in Signal Processing and Cryptography leads to a major problem and Researchers are trying to develop new Algorithms to solve these problems. To enhance the speed of the existing Algorithms, different number system have been found for point multiplication in elliptic curve cryptography and coefficient multiplication in digital signal processing manly for digital filter design. Among the different number system, DBNS, DBC, HBTJSF, w-NAF are efficient. Recently, to increase the speed again, TBNS, SDTBNS have been developed. There are different method to convert any integer or fraction into TBNS and hence SDTBNS. Here a new algorithm will be discussed which increase the conversion efficiency.

References
  1. Christophe Doche, David R. Kohel, and Francesco Sica, "Double-Base Number System for Multi- scalar Multiplications", Draft, September, 9, 2008.
  2. Doche, C. , Habsieger, L. , "A Tree-Based Approach for Computing Double-Base Chains", in: Y. Mu, W. Susilo and J. Seberry(Eds. ), ACISP 2008, LNCS 5107, PP. 433-446, 2008, Springer-Verlag Berlin Heidelberg 2008.
  3. Avanzi, R. M. , Cohen, H. , Doche, C. , Frey, G. , Nguyen, K. , Lange, T. , Vercauteren, F. : Handbook of Elliptic and Hyperelliptic Curve Cryptography, in: Discrete Mathematics and its Application, Chapman and Hall/CRC, Boca Raton(2005).
  4. J. A. Solinas, "Low-weight binary representations for pairs of integers", Center for Applied Cryptographic Research, University of Waterloo, Waterloo, ON, Canada, Research Report CORR 2001-41, 2001.
  5. Avanzi, R. M. , Dimitrov, V. S. , Doche, C. , Sica, F. : Extending Scalar Multiplication using Double Bases, in: Lai, X. , Chen, K. (Eds. ), ASIACRYPT 2006, LNCS, vol. 4284, pp. 130 – 144, Springer, Heidelberg(2006).
  6. V. Dimitrov and T. V. Cooklev, "Two algorithm for modular exponentiation based on nonstandard arithmetic", IEICE Transactions on Fundamentals of Electronics, Communications and Computer Science, vol. E78-A, no. 1, pp. 82 -87, Jan. 1995, special issue on cryptography and information security.
  7. A. D. Booth, "A Signed binary multiplication technique", Quarterly Journal of Mechanics and Applied Mathematics, vol. 4, no. 2, pp. 236 – 240, 1951, reprinted in E. E. Swartzlander, Computer Arithmetic, vol. 1, IEEE Computer Society Press Tutorial, Los Alamitos, CA, 1990.
  8. J. Adikari, V. Dimitrov, and L. Imbert. Hybrid Binary-Ternary Joint Sparse Form and its Application in Elliptic Curve Cryptography. Preprint, Available at: http://eprint. iacr. org/2008.
  9. M. Ciet, M. Joye, K. Lauter, and P. L. Montgomery. Trading Inversions for Multiplications in Elliptic Curve Cryptography. Des. Codes Cryptogr. , 39(2):189–206, 2006.
  10. C. Doche and L. Imbert, "Extended double-base number system with applications to elliptic curve cryptography", in Progress in Cryptography, INDOCRYPT'06,ser. Lecture Notes in Computer Science, vol. 4329, Springer, 006, pp. 335 – 348.
  11. M. Ciet, T. Lange, F. Sica, and J. J. Quisquater. Improved algorithms for efficient arithmetic on elliptic curves using fast endomorphism. In Advances in Cryptology – Eurocrypt 2003, volume 2656 of Lecture Notes in Comput. Sci. , pages 388– 400. Springer-Verlag, 2003.
  12. S. Maitra, A. Sinha, "Triple-Base Hybrid Joint Sparse Form and its Applications", International Journal of Computer Applications (0975 – 8887), vol. 43, No. 3, April, 2012.
  13. Pavel Sinha, Amitabha Sinha, Krishanu Mukherjee and Kenneth Alan Newton, "Triple Base Number Digital and Numerical Processing System", Patent filed under E. S. P. Microdesign Inc. , Pennsylvania, U. S. A. , U. S. Pat. App. No. 11/488, 138.
  14. S. Maitra, A. Sinha, "A Single Digit Tripple Base Number System – A New Concept for Implementing High Performance Multiplier Unit for DSP Applications", Proceedings of the sixth International Conference on Information, Communication and Signal Processing (ICICS2007), December, 10- 13,2007.
  15. V. S. Dimitrov, G. A. Jullien and W. C. Miller, "Theory and Application of Double-Base Number System", IEEE Transaction on Computers, vol. 48, No. 10, pp-1098-1106, October, 1999.
Index Terms

Computer Science
Information Sciences

Keywords

DBC DBNS Digital Filter DSP ECC HBTJSF JSF TBC TBHJSF TBNS w-NAF