Interrelation of families of points of high order on the Edwards curve over a prime field

Problems of Information Transmission - 2016
A. V. Bessalov1, O. V. Tsygankova1
1Institute of Physics and Technology, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Kyiv, Ukraine

Tóm tắt

We propose a modification of the addition law on the Edwards curve over a prime field. We prove three theorems on properties of coordinates of high-order points and on a degenerate pair of twisted curves. We propose an algorithm for reconstructing all unknown points kP of the Edwards curve when only 1/8 of the points are known.

Từ khóa


Tài liệu tham khảo

Edwards, H.M., A Normal Form for Elliptic Curves, Bull. Amer. Math. Soc. (N.S.), 2007, vol. 44, no. 3, pp. 393–422.

Bernstein, D.J. and Lange, T., Faster Addition and Doubling on Elliptic Curves, Advances in Cryptology-ASIACRYPT’2007 (Proc. 13th Int. Conf. on the Theory and Application of Cryptology and Information Security, Kuching, Malaysia, Dec. 2–6, 2007), Kurosawa, K., Ed., Lect. Notes Comp. Sci., vol. 4833, Berlin: Springer, 2007, pp. 29–50.

Bessalov, A.V., The Number of Isomorphisms and Torsion Pairs of Edwards Curves over a Prime Field, Radiotekhnika, 2011, vol. 167, pp. 203–208.

Bessalov, A.V., Dividing a Point by Two for the Edwards Curve over a Prime Field, Prikl. Radioelektron., 2013, vol. 12, no. 2, pp. 278–279.

Bessalov, A.V., Kriptosistemy na ellipticheskikh krivykh (Cryptosystems on Elliptic Curves), Kyiv: Politekhnika, 2004.

Bessalov, A.V., Constructing an Edwards Curve Based on an Isomorphic Canonical-Form Elliptic Curve, Prikl. Radioelektron., 2014, vol. 13, no. 3, pp. 286–289.

Thông tin
Thông tin xuất bản

Problems of Information Transmission

Thông tin tác giả