Elliptic periods for finite fields
نویسندگان
چکیده
We construct two new families of basis for finite field extensions. Bases in the first family, the so-called elliptic bases, are not quite normal bases, but they allow very fast Frobenius exponentiation while preserving sparse multiplication formulas. Bases in the second family, the so-called normal elliptic bases are normal bases and allow fast (quasi-linear) arithmetic. We prove that all extensions admit models of this kind.
منابع مشابه
Efficient implementation of low time complexity and pipelined bit-parallel polynomial basis multiplier over binary finite fields
This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF (2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. In the second structure only even powers of the polynomial variable are used. The par...
متن کاملElliptic curves over finite fields with fixed subgroups
We prove that for any given group Zm⊕Zn, where m divides n, and any rational elliptic curve, for a positive density of the rational primes p ∈ P, Zm ⊕ Zn is isomorphic to a subgroup of E(Fp). Our methods are effective and we demonstrate how to construct elliptic curves such that for a large density of the primes p, the given group is isomorphic to a subgroup of E(Fp). We show that for some grou...
متن کاملElliptic Thermal Correlation Functions and Modular Forms in a Globally Conformal Invariant Qft
Global conformal invariance (GCI) of quantum field theory (QFT) in two and higher space–time dimensions implies the Huygens’ principle, and hence, rationality of correlation functions of observable fields [29]. The conformal Hamiltonian H has discrete spectrum assumed here to be finitely degenerate. We then prove that thermal expectation values of field products on compactified Minkowski space ...
متن کاملAcceleration of the Elliptic Cryptography with Vector Finite Fields
Special form of finite fields (FFs), called vector FFs (VFFs), is defined in the vector spaces over the ground finite field GF (p) using particular types of the multiplication operation over vectors. Implementation of the cryptographic algorisms based on elliptic curves (ECs) over VFFs provides significantly higher performance than the implementation of the EC-based algorithms, in which the ECs...
متن کاملElliptic curves with weak coverings over cubic extensions of finite fields with odd characteristics
In this paper, we present a classification of classes of elliptic curves defined over cubic extension of finite fields with odd characteristics, which have coverings over the finite fields therefore can be attacked by the GHS attack. We then show the density of these weak curves with hyperelliptic and non-hyperelliptic coverings respectively. In particular, we shown for elliptic curves defined ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Finite Fields and Their Applications
دوره 15 شماره
صفحات -
تاریخ انتشار 2009