密码学报2018，Vol.5Issue(3)：301-314,14.DOI:10.13868/j.cnki.jcr.000241
从有限域到椭圆曲线上的编码映射构造与应用综述
On Construction and Application of Deterministic Encoding Functions into Elliptic Curves
摘要
Abstract
In this paper, we summarize deterministic encodings from finite field Fq into elliptic curves. Based on these encodings, various Hash functions from bit-strings into elliptic curves are con-structed, which are indifferentiable from random oracles. Such Hash functions can be applied in plenty of cryptographic protocols. For instance, some identity-based cryptosystems can utilize these Hash functions to generate public-keys efficiently. On the other side, by constructing injective maps from large subset of a finite field to elliptic curves, one can present points on curves as strings with distri-bution indistinguishable from the uniform distribution of bit strings, hence censorship circumvention can be achieved when transmitting public keys. When q≡3 (mod 4), SWU algorithm and its varients are applied to construct deterministic encodings into elliptic curves, while Icart's algorithm and its varients are applied in the case of q ≡ 2 (mod 3). The time complexity of these algorithms are all O(log3q). For some hyperelliptic curves, deterministic encodings can also be constructed.关键词
椭圆曲线/确定性编码/散列函数/随机谕言/Elligator算法Key words
elliptic curves/deterministic encoding/Hash function/random oracle/Elligator algo-rithm分类
信息技术与安全科学引用本文复制引用
何晓阳,于伟,王鲲鹏..从有限域到椭圆曲线上的编码映射构造与应用综述[J].密码学报,2018,5(3):301-314,14.基金项目
国家自然科学基金(61502487,61672030) （61502487,61672030）
National Natural Science Foundation of China (61502487, 61672030) （61502487, 61672030）
