On Randomness Extraction in Elliptic Curves

机译：椭圆曲线的随机性提取

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A deterministic extractor for an elliptic curve, that converts a uniformly random point on the curve to a random κ-bit-string with a distribution close to uniform, is an important tool in cryptography. Such extractors can be used for example in key derivation functions, in key exchange protocols and to design cryptographically secure pseudorandom number generator. In this paper, we present a simple and efficient deterministic extractor for an elliptic curve E defined over F_q~n, where q is prime and n is a positive integer. Our extractor, denoted by D_κ, for a given random point P on E, outputs the κ-first F_q-coordinates of the abscissa of the point P. This extractor confirms the two conjectures stated by R. R. Farashahi and R. Pellikaan in [6] and by R. R. Farashahi, A. Sidorenko and R. Pellikaan in [7], related to the extraction of bits from coordinates of a point of an elliptic curve.

机译：椭圆曲线的确定性提取器将曲线上的均匀随机点转换为分布接近均匀的随机κ位字符串，是密码学中的重要工具。这样的提取器可以例如在密钥导出功能，密钥交换协议中使用，并且可以设计密码学安全的伪随机数生成器。在本文中，我们为定义在F_q〜n上的椭圆曲线E提供了一种简单有效的确定性提取器，其中q为素数，n为正整数。对于D上给定的随机点P，我们的提取器以D_κ表示，输出点P的横坐标的κ-第一F_q坐标。该提取器确认了RR Farashahi和R. Pellikaan在[6]中提出的两个猜想。 RR Farashahi，A。Sidorenko和R. Pellikaan在[7]中涉及从椭圆曲线的点的坐标中提取位。

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来源
《Progress in cryptology - AFRICACRYPT 2011》|2011年|p.290-297|共8页
会议地点 Dakar(SN);Dakar(SN)
作者
Abdoul Aziz Ciss; Djiby Sow;
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作者单位

Ecole doctorale de Mathematiques et d'Informatique, Universite Cheikh Anta Diop de Dakar, Senegal BP: 5005, Dakar Fann;

Ecole doctorale de Mathematiques et d'Informatique, Universite Cheikh Anta Diop de Dakar, Senegal BP: 5005, Dakar Fann;

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会议组织
原文格式 PDF
正文语种 eng
中图分类密码、密码机;
关键词
elliptic curves; randomness extraction; character sums;

机译：椭圆曲线随机性提取；字符总和;

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专利

1. RSA and Public-Key Cryptography Introduction to Cryptography Cryptography: Theory and Practice Algebraic Aspects of Cryptography Elliptic Curves: Number Theory and Cryptography Elliptic Curves in Cryptography Modern Cryptography, Probabilistic Proofs, and Pseudorandomness Foundations of Cryptography: Basic Tools The Design of Rijndael: AES --- the Advanced Encryption Standard Handbook of Applied Cryptography [J] . Susan Landau Bulletin of the American Mathematical Society . 2004,第3期

机译：RSA和公钥密码学密码学简介密码学：密码学的理论和实践椭圆曲线的密码学：密码学中的数论和密码学椭圆曲线现代密码学，概率证明和伪随机性基础密码学：基本工具Rijndael的设计： -应用密码学高级加密标准手册
2. Random Binary and Non-Binary Sequences Derived from Random Sequence of Points on Cyclic Elliptic Curve Over Finite Field GF(2~m) and Their Properties [J] . S. V. Sathyanarayana, M. Aswatha Kumar, K. N. Hari Bhat Information security journal . 2010,第2期

机译：有限域GF（2〜m）上椭圆曲线上点随机序列的随机二元和非二元序列及其性质
3. A New Variant Nevine Maurice Ebied’s Key Randomization Counter Measures to Power Analysis Attacks on Elliptic Curve Cryptosystems [J] . E.Kesavulu Reddy, V.V.Lakshmi Prasad International journal of computer science and network security . 2009,第2期

机译：一种新的变种Neur Maurice Ebied的密钥随机化对策，用于对椭圆曲线密码系统的功效分析攻击
4. On Randomness Extraction in Elliptic Curves [C] . Abdoul Aziz Ciss, Djiby Sow International Conference on Cryptology in Africa . 2011

机译：关于椭圆曲线中的随机性提取
5. Key randomization countermeasures to power analysis attacks on elliptic curve cryptosystems. [D] . Ebeid, Nevine Maurice. 2007

机译：椭圆曲线密码系统上的功率分析攻击的关键随机对策。
6. Colloquium Paper: Parametrizations of elliptic curves by Shimura curves and by classical modular curves [O] . Kenneth A. Ribet, Shuzo Takahashi 1997

机译：座谈会论文：Shimura曲线和by的椭圆曲线参数化经典模曲线
7. Two-sources Randomness Extractors for Elliptic Curves [O] . Ciss, Abdoul Aziz 2014

机译：椭圆曲线的双源随机抽取器

On Randomness Extraction in Elliptic Curves

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