Elliptic curve point counting over finite fields with Gaussian normal basis
نویسندگان
چکیده
منابع مشابه
Elliptic curve point counting over finite fields with Gaussian normal basis
In this paper, we present the GNB-aided MSST algorithm for the curves over finite fields that have a Gaussian normal basis of type t ≤ 2. It is based on the MSST algorithm proposed by P. Gaudry [3] at ASIACRYPT 2002. For those fields, we combine the lifting phase of the MSST algorithm and the norm computation algorithm in [6]. So the time complexity of the MSST is reduced from O(N) to O(N) and ...
متن کاملFast Elliptic Curve Point Counting Using Gaussian Normal Basis
In this paper we present an improved algorithm for counting points on elliptic curves over finite fields. It is mainly based on SatohSkjernaa-Taguchi algorithm [SST01], and uses a Gaussian Normal Basis (GNB) of small type t ≤ 4. In practice, about 42% (36% for prime N) of fields in cryptographic context (i.e., for p = 2 and 160 < N < 600) have such bases. They can be lifted from FpN to ZpN in a...
متن کاملCounting Elliptic Surfaces over Finite Fields
We count the number of isomorphism classes of elliptic curves of given height d over the field of rational functions in one variable over the finite field of q elements. We also estimate the number of isomorphism classes of elliptic surfaces over the projective line, which have a polarization of relative degree 3. This leads to an upper bound for the average 3-Selmer rank of the aforementionned...
متن کاملCounting points on elliptic curves over finite fields
-We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large; it is based on Shanks’s baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is ...
متن کاملMulti-sources Randomness Extraction over Finite Fields and Elliptic Curve
This work is based on the proposal of a deterministic randomness extractor of a random Diffie-Hellman element defined over two prime order multiplicative subgroups of a finite fields Fpn , G1 and G2. We show that the least significant bits of a random element in G1 ∗G2, are indistinguishable from a uniform bit-string of the same length. One of the main application of this extractor is to replac...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 2003
ISSN: 0386-2194
DOI: 10.3792/pjaa.79.5