Geodesic
Optimizing memory cost of multi-scalar multiplication
Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 2, pp. 53-60 
S. V. Grebnev. Optimizing memory cost of multi-scalar multiplication. Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 2, pp. 53-60. http://geodesic.mathdoc.fr/item/MVK_2016_7_2_a4/
@article{MVK_2016_7_2_a4,
     author = {S. V. Grebnev},
     title = {Optimizing memory cost of multi-scalar multiplication},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {53--60},
     year = {2016},
     volume = {7},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MVK_2016_7_2_a4/}
}
TY  - JOUR
AU  - S. V. Grebnev
TI  - Optimizing memory cost of multi-scalar multiplication
JO  - Matematičeskie voprosy kriptografii
PY  - 2016
SP  - 53
EP  - 60
VL  - 7
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MVK_2016_7_2_a4/
LA  - en
ID  - MVK_2016_7_2_a4
ER  - 
%0 Journal Article
%A S. V. Grebnev
%T Optimizing memory cost of multi-scalar multiplication
%J Matematičeskie voprosy kriptografii
%D 2016
%P 53-60
%V 7
%N 2
%U http://geodesic.mathdoc.fr/item/MVK_2016_7_2_a4/
%G en
%F MVK_2016_7_2_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

We present a modification of the non-adjacent form representation for multi-scalar multiplication which allows efficient performance-memory tradeoffs. Simultaneously we fix a feature of the original algorithm which prevented it from using all possible bases.

[1] Doche C., Kohel D. R., Sica F., “Double-base number systems for multi-scalar multiplications”, Advances in Cryptology-EUROCRYPT 2009, Lect. Notes Comput. Sci., 5479, 2009, 502–517 | DOI | MR | Zbl

[2] Dygin D. M., Grebnev S. V., “Efficient implementation of the GOST R 34.10 digital signature scheme using modern approaches to elliptic curve scalar multiplication”, Matematicheskie voprosy kriptografii (Math. Aspects Cryptogr.), 4:2 (2013), 47–57

[3] Bernstein D. J., Lange T., Explicit-Formulas Database, , 2012 http://hyperelliptic.org/EFD

[4] Hişil H., Elliptic Curves, Group Law and Efficient Computation, Ph. D. thesis, Inform. Secur. Inst., Queensland Univ. Technology, Brisbane, 2010, xx+225 pp. http://eprints.qut.edu.au/33233/

[5] Kalinin M., An Implementation of the GOST R 34.10 Digital Signature Scheme Using Novel Algorithms of Elliptic Curve Scalar Multiplication, Master thesis, Lomonosov State Univ., M., 2010, 50 pp. (In Russian)

[6] Longa P., Accelerating the Scalar Multiplication on Elliptic Curve Cryptosystems over Prime Fields, Master Sci. thesis, Univ. Ottawa, Ottawa, 2007, xv+173 pp. http://eprint.iacr.org/2008/100

[7] Longa P., Gebotys C., Setting Speed Records with the (Fractional) Multibase Non-Adjacent Form Method for Efficient Elliptic Curve Scalar Multiplication, CACR Tech. Rep., , Centre Appl. Cryptogr. Res., Univ. Waterloo, Waterloo, 2008, 40 pp. https://eprint.iacr.org/2008/118.pdf

[8] Longa P., Miri A., New multibase non-adjacent form scalar multiplication and its application to elliptic curve cryptosystems, , 2008, 39 pp. http://eprint.iacr.org/2008/052

[9] Solinas J. A., Low-Weight Binary Representations for Pairs of Integers, , Univ. Waterloo, Waterloo, 2001 http://cacr.uwaterloo.ca/