Efficient system parameters for Identity-Based Encryption using supersingular elliptic curves
نویسندگان
چکیده
منابع مشابه
Constructing Supersingular Elliptic Curves
We give an algorithm that constructs, on input of a prime power q and an integer t, a supersingular elliptic curve over Fq with trace of Frobenius t in case such a curve exists. If GRH holds true, the expected run time of our algorithm is e O((log q)). We illustrate the algorithm by showing how to construct supersingular curves of prime order. Such curves can readily be used for pairing based c...
متن کاملFinding More Non-Supersingular Elliptic Curves for Pairing-Based Cryptosystems
Finding suitable non-supersingular elliptic curves for pairing-based cryptosystems becomes an important issue for the modern public-key cryptography after the proposition of id-based encryption scheme and short signature scheme. In previous work different algorithms have been proposed for finding such elliptic curves when embedding degree k ∈ {3, 4, 6} and cofactor h ∈ {1, 2, 3, 4, 5}. In this ...
متن کاملAn Efficient Identity-Based Group Signature Scheme over Elliptic Curves
Considering such a scenario: Several network policemen consist of a group NP in a network; Every one of them can find out what kind of documents are harmful and then sign them. Any user in this network who receives the above documents would check whether a signature exists on the documents and also it is validly signed by the group NP. And then, this user can be convinced the document is really...
متن کاملMinimal Cm Liftings of Supersingular Elliptic Curves
In this paper, we give a ‘direct’ construction of the endomorphism ring of supersingular elliptic curves over a prime field Fp from ‘ideal classes’ of Q( √−p). We use the result to prove that the result of Kaneko on ‘minimal’ CM liftings of such supersingular elliptic curves is a best possible result. We also prove that the result of Elkies on ‘minimal’ CM liftings of all supersingular elliptic...
متن کاملCM liftings of supersingular elliptic curves
Assuming GRH, we present an algorithm which inputs a prime p and outputs the set of fundamental discriminants D < 0 such that the reduction map modulo a prime above p from elliptic curves with CM by OD to supersingular elliptic curves in characteristic p. In the algorithm we first determine an explicit constant Dp so that |D| > Dp implies that the map is necessarily surjective and then we compu...
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: JSIAM Letters
سال: 2014
ISSN: 1883-0609,1883-0617
DOI: 10.14495/jsiaml.6.13