Implementing Complete Formulas on Weierstrass Curves in Hardware
نویسندگان
چکیده
This work revisits the recent complete addition formulas for prime order elliptic curves of Renes, Costello and Batina in light of parallelization. We introduce the first hardware implementation of the new formulas on an FPGA based on three arithmetic units performing Montgomery multiplication. Our results are competitive with current literature and show the potential of the new complete formulas in hardware design. Furthermore, we present algorithms to compute the formulas using anywhere between two and six processors, using the minimum number of parallel field multiplications.
منابع مشابه
Analogues of Vélu's formulas for isogenies on alternate models of elliptic curves
Isogenies are the morphisms between elliptic curves, and are accordingly a topic of interest in the subject. As such, they have been wellstudied, and have been used in several cryptographic applications. Vélu’s formulas show how to explicitly evaluate an isogeny, given a specification of the kernel as a list of points. However, Vélu’s formulas only work for elliptic curves specified by a Weiers...
متن کاملComplete Addition Formulas for Prime Order Elliptic Curves
An elliptic curve addition law is said to be complete if it correctly computes the sum of any two points in the elliptic curve group. One of the main reasons for the increased popularity of Edwards curves in the ECC community is that they can allow a complete group law that is also relatively efficient (e.g., when compared to all known addition laws on Edwards curves). Such complete addition fo...
متن کاملFaster Pairing Computation
This paper proposes new explicit formulas for the doubling and addition step in Miller’s algorithm to compute pairings. For Edwards curves the formulas come from a new way of seeing the arithmetic. We state the first geometric interpretation of the group law on Edwards curves by presenting the functions which arise in the addition and doubling. Computing the coefficients of the functions and th...
متن کاملFaster Computation of Tate Pairings
This paper proposes new explicit formulas for the doubling and addition step in Miller’s algorithm to compute the Tate pairing. For Edwards curves the formulas come from a new way of seeing the arithmetic. We state the first geometric interpretation of the group law on Edwards curves by presenting the functions which arise in the addition and doubling. Computing the coefficients of the function...
متن کاملHolomorphic Curves and Toda Systems *
Geometry of holomorphic curves from point of view of open Toda systems is discussed. Parametrization of curves related this way to non-exceptional simple Lie algebras is given. This gives rise to explicit formulas for minimal surfaces in real, complex and quaternionic projective spaces or complex quadrics. The paper generalizes the well known connection between minimal surfaces in E3, their Wei...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2016 شماره
صفحات -
تاریخ انتشار 2016