Efficient Quintuple Formulas for Elliptic Curves and Efficient Scalar Multiplication Using Multibase Number Representation

Pradeep Kumar Mishra; Vassil Dimitrov

Paper 2007/040

Efficient Quintuple Formulas for Elliptic Curves and Efficient Scalar Multiplication Using Multibase Number Representation

Pradeep Kumar Mishra and Vassil Dimitrov

Abstract

In the current work we propose two efficient formulas for computing the $5$-fold ($5P$) of an elliptic curve point $P$. One formula is for curves over finite fields of even characteristic and the other is for curves over prime fields. Double base number systems (DBNS) have been gainfully exploited to compute scalar multiplication efficiently in ECC. Using the proposed point quintupling formulas one can use 2,5 and 3,5 (besides 3,5) as bases of the double base number system. In the current work we propose a scalar multiplication algorithm, which expands the scalar using three bases 2, 3 and 5 and computes the scalar multiplication very efficiently. The proposed scheme is faster than all sequential scalar multiplication algorithms reported in literature.

Metadata

Available format(s): PDF PS
Publication info: Published elsewhere. Unknown where it was published
Keywords: Elliptic Curve Cryptosystems Scalar Multiplication Quintupling Efficient Curve Arithmetic
Contact author(s): pradeep @ math ucalgary ca
History: 2007-04-10: last of 2 revisions; 2007-02-14: received; See all versions
Short URL: https://ia.cr/2007/040
License: CC BY

BibTeX

@misc{cryptoeprint:2007/040,
      author = {Pradeep Kumar Mishra and Vassil Dimitrov},
      title = {Efficient Quintuple Formulas for Elliptic Curves and Efficient Scalar Multiplication Using Multibase Number Representation},
      howpublished = {Cryptology ePrint Archive, Paper 2007/040},
      year = {2007},
      note = {\url{https://eprint.iacr.org/2007/040}},
      url = {https://eprint.iacr.org/2007/040}
}