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Elliptic curve cryptography: Generation and validation of domain parameters in binary Galois Fields.

机译：椭圆曲线密码术：二进制Galois字段中域参数的生成和验证。

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摘要

Elliptic curve cryptography (ECC) is an increasingly popular method for securing many forms of data and communication via public key encryption. The algorithm utilizes key parameters, referred to as the domain parameters. These parameters must adhere to specific characteristics in order to be valid for use in the algorithm.;The American National Standards Institute (ANSI), in ANSI X9.62, provides the process for generating and validating these parameters. The National Institute of Standards and Technology (NIST) has identified fifteen sets of parameters; five for prime fields, five for binary fields, and five for Koblitz curves.;The parameter generation and validation processes have several key issues. The first is the fast reduction within the proper modulus. The modulus chosen is an irreducible polynomial having degree greater than 160. Choosing irreducible polynomials of a particular order is less critical since they have isomorphic properties, mathematically. However, since there are differences in performance, there are standards that determine the specific polynomials chosen. The NIST standards are also based on word lengths of 32 bits. Processor architecture, primality, and validation of irreducibility are other important characteristics.;The area of ECC that is researched is the generation and validation processes, as they are specified for binary Galois Fields F (2m). The rationale for the parameters, as computed for 32 bit and 64 bit computer architectures, and the algorithms used for implementation, as specified by ANSI, NIST and others, are examined. The methods for fast reduction are also examined as a baseline for understanding these parameters. Another aspect of the research is to determine a set of parameters beyond the 571-bit length that meet the necessary criteria as determined by the standards.
机译：椭圆曲线密码术（ECC）是一种越来越流行的方法，用于通过公钥加密保护多种形式的数据和通信。该算法利用关键参数，称为域参数。这些参数必须遵守特定的特征才能有效地在算法中使用。ANSI X9.62中的美国国家标准协会（ANSI）提供了生成和验证这些参数的过程。美国国家标准技术研究院（NIST）已确定15套参数；五个用于素数字段，五个用于二进制字段，五个用于Koblitz曲线。;参数生成和验证过程有几个关键问题。首先是在适当的模量内快速减小。所选模数是阶数大于160的不可约多项式。选择特定阶数的不可约多项式的重要性较低，因为它们在数学上具有同构性质。但是，由于性能存在差异，因此存在确定所选择的特定多项式的标准。 NIST标准还基于32位的字长。处理器的体系结构，原始性和不可约性的验证是其他重要特征。研究的ECC领域是生成和验证过程，因为它们是针对二进制Galois字段F（2m）指定的。检查了针对32位和64位计算机体系结构计算出的参数的基本原理，以及由ANSI，NIST等指定的用于实现的算法。快速还原的方法也作为了解这些参数的基准进行了检查。研究的另一方面是确定超过571位长度的一组参数，这些参数满足标准确定的必要标准。

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  • 作者

    Wozny, Peter.;

  • 作者单位

    Rochester Institute of Technology.;

  • 授予单位 Rochester Institute of Technology.;
  • 学科 Computer Science.
  • 学位 M.S.
  • 年度 2008
  • 页码 67 p.
  • 总页数 67
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 自动化技术、计算机技术;
  • 关键词

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