The signs in elliptic nets
نویسندگان
چکیده
We give a generalization of a theorem of Silverman and Stephens regarding the signs in an elliptic divisibility sequence to the case of an elliptic net. We also describe applications of this theorem in the study of the distribution of the signs in elliptic nets and generating elliptic nets using the denominators of the linear combination of points on elliptic curves.
منابع مشابه
Stange ’ s Elliptic Nets and Coxeter Group F 4 Daniel
Stange, generalizingWard’s elliptic divisibility sequences, introduced elliptic nets, and showed an equivalence between elliptic nets and elliptic curves. This note relates Stange’s recursion for elliptic nets and the Coxeter group F4.
متن کاملElliptic Nets and Elliptic Curves
Elliptic divisibility sequences are integer recurrence sequences, each of which is associated to an elliptic curve over the rationals together with a rational point on that curve. In this paper we present a higher-dimensional analogue over arbitrary base fields. Suppose E is an elliptic curve over a field K, and P1, . . . , Pn are points on E defined over K. To this information we associate an ...
متن کاملCryptographic Pairings Based on Elliptic Nets
In 2007, Stange proposed a novel method for computing the Tate pairing on an elliptic curve over a finite field. This method is based on elliptic nets, which are maps from Z to a ring that satisfies a certain recurrence relation. In the present paper, we explicitly give formulae based on elliptic nets for computing the following variants of the Tate pairing: the Ate, Atei, R-Ate, and optimal pa...
متن کاملThe Tate Pairing Via Elliptic Nets
We derive a new algorithm for computing the Tate pairing on an elliptic curve over a finite field. The algorithm uses a generalisation of elliptic divisibility sequences known as elliptic nets, which are maps from Z to a ring that satisfy a certain recurrence relation. We explain how an elliptic net is associated to an elliptic curve and reflects its group structure. Then we give a formula for ...
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 کامل