A point compression method for elliptic curves
نویسنده
چکیده
Here we describe new tools to be used in fields of the form Gf(2), that help describe properties of elliptic curves defined overGF (2). Further, utilizing these tools we describe a new elliptic curve point compression method, which provides the most efficient use of bandwidth whenever the elliptic curve is defined by y + xy = x + a2x 2 + a6 and the trace of a2 is zero.
منابع مشابه
A descent method for explicit computations on curves
It is shown that the knowledge of a surjective morphism $Xto Y$ of complex curves can be effectively used to make explicit calculations. The method is demonstrated by the calculation of $j(ntau)$ (for some small $n$) in terms of $j(tau)$ for the elliptic curve with period lattice $(1,tau)$, the period matrix for the Jacobian of a family of genus-$2$ curves complementing the classi...
متن کاملPoint compression for Koblitz elliptic curves
Elliptic curves over finite fields have applications in public key cryptography. A Koblitz curve is an elliptic curve E over F2; the group E(F2n ) has convenient features for efficient implementation of elliptic curve cryptography. Wiener and Zuccherato and Gallant, Lambert and Vanstone showed that one can accelerate the Pollard rho algorithm for the discrete logarithm problem on Koblitz curves...
متن کاملGeneralized Jacobian and Discrete Logarithm Problem on Elliptic Curves
Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
متن کاملEfficient elliptic curve cryptosystems
Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...
متن کاملComplete characterization of the Mordell-Weil group of some families of elliptic curves
The Mordell-Weil theorem states that the group of rational points on an elliptic curve over the rational numbers is a finitely generated abelian group. In our previous paper, H. Daghigh, and S. Didari, On the elliptic curves of the form $ y^2=x^3-3px$, Bull. Iranian Math. Soc. 40 (2014), no. 5, 1119--1133., using Selmer groups, we have shown that for a prime $p...
متن کامل