After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application. Features & Benefits: * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology * Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic* Distills complex mathematics and algorithms for easy understanding* Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software toolsThis comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.

https://cdn.preterhuman.net/texts/cryptography/Hankerson,%20Menezes,%20Vanstone.%20Guide%20to%20elliptic%20curve%20cryptography%20(Springer,%202004)(ISBN%20038795273X)(332s)_CsCr_.pdf

Guide to Elliptic Curve Cryptography

Digital watermarking is a key ingredient to copyright protection. It provides a solution to illegal copying of digital material and has many other useful applications such as broadcast monitoring and the recording of electronic transactions. Now, for the first time, there is a book that focuses exclusively on this exciting technology. Digital Watermarking covers the crucial research findings in the field: it explains the principles underlying digital watermarking technologies, describes the requirements that have given rise to them, and discusses the diverse ends to which these technologies are being applied. As a result, additional groundwork is laid for future developments in this field, helping the reader understand and anticipate new approaches and applications.

Digital Watermarking

Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/non-Hamiltonian.In this paper a computational complexity theory of the “knowledge” contained in a proof is developed. Zero-knowledge proofs are defined as those proofs that convey no additional knowledge other than the correctness of the proposition in question. Examples of zero-knowledge proof systems are given for the languages of quadratic residuosity and 'quadratic nonresiduosity. These are the first examples of zero-knowledge proofs for languages not known to be efficiently recognizable.

/pdf/the-knowledge-complexity-of-interactive-proof-systems-31apre0ecf.pdf

The knowledge complexity of interactive proof-systems

We provide the first formal treatment of entity authentication and authenticated key distribution appropriate to the distributed environment. Addressed in detail are the problems of mutual authentication and authenticated key exchange for the symmetric, two-party setting. For each we present a definition, protocol, and proof that the protocol meets its goal, assuming only the existence of a pseudorandom function.

/pdf/entity-authentication-and-key-distribution-4q9ydugprh.pdf

Entity authentication and key distribution

In this paper we present a new type of signature for a group of persons, called a group signature, which has the following properties: (i) only members of the group can sign messages; (ii) the receiver can verify that it is a valid group signature, but cannot discover which group member made it; (iii) if necessary, the signature can be "opened", so that the person who signed the message is revealed.

The group signatures are a "generalization" of the credential/ membership authentication schemes, in which one person proves that he belongs to a certain group.

We present four schemes that satisfy the properties above. Not all these schemes arc based on the same cryptographic assumption. In some of the schemes a trusted centre is only needed during the setup; and in other schemes, each pason can create the group he belongs to.

Group signatures

This paper proposes a fast algorithm for computing multiplicative inverses in GF(2 m ) using normal bases. Normal bases have the following useful property: In the case that an element x in GF(2 m ) is represented by normal bases, 2 k power operation of an element x in GF(2 m ) can be carried out by k times cyclic shift of its vector representation. C. C. Wang et al. proposed an algorithm for computing multiplicative inverses using normal bases, which requires ( m − 2) multiplications in GF(2 m ) and ( m − 1) cyclic shifts. The fast algorithm proposed in this paper also uses normal bases, and computes multiplicative inverses iterating multiplications in GF(2 m ). It requires at most 2[log 2 ( m − 1)] multiplications in GF(2 m ) and ( m − 1) cyclic shifts, which are much less than those required in the Wang's method. The same idea of the proposed fast algorithm is applicable to the general power operation in GF(2 m ) and the computation of multiplicative inverses in GF( q m ) ( q = 2 n ).

A fast algorithm for computing multiplicative inverses in GF(2 m ) using normal bases

This paper presents a configuration of parallel multipliers for GF (2 m ) based on canonical bases. The possible parallel multipliers by the proposed configuration are limited to a class of fields GF (2 m ). However they can be constructed by O(m 2 ) AND-gates and O(m 2 ) EOR-gates with the structural modularity (this is a desirable feature for the hardware implementation), and their operation time is about (log m ) T , where m is the dimension of GF (2 m ) and T is the delay time of an EOR-gate. In order to construct such parallel multipliers, we define two types of polynomials of special form over GF (2), one is called all one polynomial (denoted by AOP) and the other is called equally spaced polynomial (denoted by ESP). Furthermore, we show a necessary and sufficient condition for ESPs to be irreducible over GF (2) and the uniqueness of the irreducible ESPs over GF (2). Finally, we propose the configuration of parallel multipliers for a class of fields GF (2 m ) based on irreducible AOPs and ESPs over GF (2).

Structure of parallel multipliers for a class of fields GF(2 m )

In this paper we provide a new cryptographic primitive that generalizes several existing zero-knowledge proofs and show that if a languageL induces the primitive, then there exists a perfect zero-knowledge proof forL. In addition, we present several kinds of languages inducing the primitive, some of which are not known to have a perfect zero-knowledge proof.

/pdf/a-language-dependent-cryptographic-primitive-1ydltgfdgk.pdf

A language-dependent cryptographic primitive

A (k, δ, e)-locally decodable code $C:{\bf F}_{q}^{n} \ ightarrow {\bf F}_{q}^{N}$ is an error-correcting code that encodes $\vec{x}=(x_{1},x_{2},\ldots,x_{n}) \in {\bf F}_{q}^{n}$ to $C(\vec{x}) \in {\bf F}_{q}^{N}$ and has the following property: For any $\vec{y} \in {\bf F}_{q}^{N}$ such that $d(\vec{y},C(\vec{x})) \leq \delta N$ and each 1 l i l n, the symbol xi of $ of $\vec{x}$ can be recovered with probability at least 1 - e by a randomized decoding algorithm looking at only k coordinates of $\vec{y}$. The efficiency of a (k, δ, e)-locally decodable code $C:{\bf F}_{q}^{n} \ ightarrow {\bf F}_{q}^{N}$ is measured by the code length N and the number k of queries. For a k-query locally decodable code $C:{\bf F}_{q}^{n} \ ightarrow {\bf F}_{q}^{N}$, the code length N was conjectured to be exponential of n, i.e., N = exp(nΩ(1)), however, this was disproved. Yekhanin [In Proc. of STOC, 2007] showed that there exists a 3-query locally decodable code $C:{\bf F}_{2}^{n} \ ightarrow {\bf F}_{2}^{N}$ such that N=exp(n1/log log n) assuming that infinitely many Mersenne primes exist. For a 3-query locally decodable code $C:{\bf F}_{q}^{n} \ ightarrow {\bf F}_{q}^{N}$, Efremenko [ECCC Report No.69, 2008] further reduced the code length to $N=\exp(n^{O((\log \log n/ \log n)^{1/2})})$, and in general showed that for any integer r > 1, there exists a 2r-query locally decodable code $C:{\bf F}_{q}^{n} \ ightarrow {\bf F}_{q}^{N}$ such that $N=\exp(n^{O((\log \log n/ \log n)^{1-1/r})})$. In this paper, we will present improved constructions for query-efficient locally decodable codes by introducing a technique of “composition of locally decodable codes,” and show that for any integer r > 5, there exists a 9 · 2r-4-query locally decodable code $C:{\bf F}_{q}^{n} \ ightarrow {\bf F}_{q}^{N}$ such that $N=\exp(n^{O((\log \log n/ \log n)^{1-1/r})})$.

https://www.jstage.jst.go.jp/article/transinf/E93.D/2/E93.D_2_263/_pdf

Improved Constructions for Query-Efficient Locally Decodable Codes of Subexponential Length

The letter presents an ID-based cryptosystem using the discrete logarithm problem. The proposed cryptosystem is based on El-Gamal's public-key cryptosystem; however, it does not need a large public-key file. The system is one of the earliest realisations of ID-based cryptosystem whose concept was proposed by Shamir.

Toshiya Itoh

Papers

A fast algorithm for computing multiplicative inverses in GF(2 m ) using normal bases

Structure of parallel multipliers for a class of fields GF(2 m )

A language-dependent cryptographic primitive

Improved Constructions for Query-Efficient Locally Decodable Codes of Subexponential Length

ID-based cryptosystem using discrete logarithm problem