Handbook of Elliptic and Hyperelliptic Curve Cryptography最新文献_第2页

Mathematical Countermeasures against Side-Channel Attacks 反侧信道攻击的数学对策

Handbook of Elliptic and Hyperelliptic Curve Cryptography Pub Date : 2005-07-19 DOI: 10.1201/9781420034981.ch29

T. Lange

引用次数: 3

Fast Arithmetic in Hardware 硬件中的快速算法

Handbook of Elliptic and Hyperelliptic Curve Cryptography Pub Date : 2005-07-19 DOI: 10.1201/9781420034981.pt7

K. Nguyen, A. Weigl

引用次数: 3

Algebraic Realizations of DL Systems DL系统的代数实现

Handbook of Elliptic and Hyperelliptic Curve Cryptography Pub Date : 2005-07-19 DOI: 10.1201/9781420034981.pt6

G. Frey, T. Lange

引用次数: 1

Random Numbers Generation and Testing 随机数的生成和测试

Handbook of Elliptic and Hyperelliptic Curve Cryptography Pub Date : 2005-07-19 DOI: 10.1201/9781420034981.ch30

T. Lange, D. Lubicz, A. Weigl

引用次数: 11

Arithmetic of Elliptic Curves 椭圆曲线的算法

Handbook of Elliptic and Hyperelliptic Curve Cryptography Pub Date : 2005-07-19 DOI: 10.1201/9781420034981.pt3

C. Doche, T. Lange

{"title":"Arithmetic of Elliptic Curves","authors":"C. Doche, T. Lange","doi":"10.1201/9781420034981.pt3","DOIUrl":"https://doi.org/10.1201/9781420034981.pt3","url":null,"abstract":"Elliptic curves constitute one of the main topics of this book. They have been proposed for applications in cryptography due to their fast group law and because so far no subexponential attack on their discrete logarithm problem (cf. Section 1.5) is known. We deal with security issues in later chapters and concentrate on the group arithmetic here. In an actual implementation this needs to be built on an efficient implementation of finite field arithmetic (cf. Chapter 11). In the sequel we first review the background on elliptic curves to the extent needed here. For a more general presentation of elliptic curves, see Chapter 4. Then we address the question of efficient implementation in large odd and in even characteristics. We refer mainly to [HAME+ 2003] for these sections. Note that there are several softwares packages or libraries able to work on elliptic curves, for example PARI/GP [PARI] and apecs [APECS]. The former is a linkable library that also comes with an interactive shell, whereas the latter is a Maple package. Both come with full sources. The computer algebra systems Magma [MAGMA] and SIMATH [SIMATH] can deal with elliptic curves, too. Elliptic curves have received a lot of attention throughout the past almost 20 years and many papers report experiments and timings for various field sizes and coordinates. We do not want to repeat the results but refer to [AVA 2004a, COMI+ 1998] and Section 14.7 for odd characteristic and [HALO+ 2000, LODA 1998, LODA 1999] for even characteristic. Another excellent and comprehensive reference comparing point multiplication costs and implementation results is [HAME+ 2003, Tables 3.12, 3.13 and 3.14 and Chap. 5].","PeriodicalId":131128,"journal":{"name":"Handbook of Elliptic and Hyperelliptic Curve Cryptography","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126796548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 53

Finite Field Arithmetic 有限域算法

Handbook of Elliptic and Hyperelliptic Curve Cryptography Pub Date : 2005-07-19 DOI: 10.1201/9781420034981.ch11

C. Doche

引用次数: 15

Point Counting on Elliptic and Hyperelliptic Curves 椭圆曲线和超椭圆曲线上的点计数

Handbook of Elliptic and Hyperelliptic Curve Cryptography Pub Date : 2005-07-19 DOI: 10.1201/9781420034981.pt4

R. Lercier, D. Lubicz, F. Vercauteren

引用次数: 19

Introduction to Public-Key Cryptography 公钥密码学简介

Handbook of Elliptic and Hyperelliptic Curve Cryptography Pub Date : 2005-07-19 DOI: 10.1201/9781420034981.ch1

R. Avanzi, T. Lange

{"title":"Introduction to Public-Key Cryptography","authors":"R. Avanzi, T. Lange","doi":"10.1201/9781420034981.ch1","DOIUrl":"https://doi.org/10.1201/9781420034981.ch1","url":null,"abstract":"In this chapter we introduce the basic building blocks for cryptography based on the discrete logarithm problem that will constitute the main motivation for considering the groups studied in this book. We also briefly introduce the RSA cryptosystem as for use in practice it is still an important public-key cryptosystem. Assume a situation where two people, called Alice and Bob in the sequel (the names had been used since the beginning of cryptography because they allow using the letters A and B as handy abbreviations), want to communicate via an insecure channel in a secure manner. In other words, an eavesdropper Eve (abbreviated as E) listening to the encrypted conversation should not be able to read the cleartext or change it. To achieve these aims one uses cryptographic primitives based on a problem that should be easy to set up by either Alice, or Bob, or by both, but impossible to solve for Eve. Loosely speaking, infeasibility means computational infeasibility for Eve if she does not have at least partial access to the secret information exploited by Alice and Bob to set up the problem. Examples of such primitives are RSA, cf. [PKCS], which could be solved if the integer factorization problem was easy, i.e., if one could find a nontrivial factor of a composite integer n, and the discrete logarithm problem, i.e., the problem of finding an integer k with [k]P = Q where P is a generator of a cyclic group (G,?) and Q ? G. These primitives are reviewed in Sections 1.4.3 and 1.5. They are applied in a prescribed way given by protocols. We will only briefly state the necessary problems and hardness assumptions in Section 1.6 but not go into the details. Then we go briefly into issues of primality proving and integer factorization. The next section is devoted to discrete logarithm systems. This is the category of cryptographic primitives in which elliptic and hyperelliptic curves are applied. Finally, we consider protocols, i.e., algorithms using the cryptographic primitive to establish a common key, encrypt a message for a receiver, or sign electronically.","PeriodicalId":131128,"journal":{"name":"Handbook of Elliptic and Hyperelliptic Curve Cryptography","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128298643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 31

Cohomological Background on Point Counting 点计数的上同调背景

Handbook of Elliptic and Hyperelliptic Curve Cryptography Pub Date : 2005-07-19 DOI: 10.1201/9781420034981.ch8

D. Lubicz, F. Vercauteren

引用次数: 1

Transfer of Discrete Logarithms 离散对数的传递

Handbook of Elliptic and Hyperelliptic Curve Cryptography Pub Date : 2005-07-19 DOI: 10.1201/9781420034981.ch22

G. Frey, T. Lange

引用次数: 3