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

Representing the field elements with respect to the polynomial (or standard) basis, we consider bit parallel architectures for multiplication over the finite field GF(2m). In this effect, first we derive a new formulation for polynomial basis multiplication in terms of the reduction matrix Q. The main advantage of this new formulation is that it can be used with any field defining irreducible polynomial. Using this formulation, we then develop a generalized architecture for the multiplier and analyze the time and gate complexities of the proposed multiplier as a function of degree m and the reduction matrix Q. To the best of our knowledge, this is the first time that these complexities are given in terms of Q. Unlike most other articles on bit parallel finite field multipliers, here we also consider the number of signals to be routed in hardware implementation and we show that, compared to the well-known Mastrovito's multiplier, the proposed architecture has fewer routed signals. The proposed generalized architecture is further optimized for three special types of polynomials, namely, equally spaced polynomials, trinomials, and pentanomials. We have obtained explicit formulas and complexities of the multipliers for these three special irreducible polynomials. This makes it very easy for a designer to implement the proposed multipliers using hardware description languages like VHDL and Verilog with minimum knowledge of finite field arithmetic.

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Low complexity bit parallel architectures for polynomial basis multiplication over GF(2m)

With the development of cloud computing, outsourcing data to cloud server attracts lots of attentions. To guarantee the security and achieve flexibly fine-grained file access control, attribute based encryption (ABE) was proposed and used in cloud storage system. However, user revocation is the primary issue in ABE schemes. In this article, we provide a ciphertext-policy attribute based encryption (CP-ABE) scheme with efficient user revocation for cloud storage system. The issue of user revocation can be solved efficiently by introducing the concept of user group. When any user leaves, the group manager will update users’ private keys except for those who have been revoked. Additionally, CP-ABE scheme has heavy computation cost, as it grows linearly with the complexity for the access structure. To reduce the computation cost, we outsource high computation load to cloud service providers without leaking file content and secret keys. Notably, our scheme can withstand collusion attack performed by revoked users cooperating with existing users. We prove the security of our scheme under the divisible computation Diffie-Hellman assumption. The result of our experiment shows computation cost for local devices is relatively low and can be constant. Our scheme is suitable for resource constrained devices.

Flexible and Fine-Grained Attribute-Based Data Storage in Cloud Computing

Smart grid is a technological innovation that improves efficiency, reliability, economics, and sustainability of electricity services. It plays a crucial role in modern energy infrastructure. The main challenges of smart grids, however, are how to manage different types of front-end intelligent devices such as power assets and smart meters efficiently; and how to process a huge amount of data received from these devices. Cloud computing, a technology that provides computational resources on demands, is a good candidate to address these challenges since it has several good properties such as energy saving, cost saving, agility, scalability, and flexibility. In this paper, we propose a secure cloud computing based framework for big data information management in smart grids, which we call “Smart-Frame.” The main idea of our framework is to build a hierarchical structure of cloud computing centers to provide different types of computing services for information management and big data analysis. In addition to this structural framework, we present a security solution based on identity-based encryption, signature and proxy re-encryption to address critical security issues of the proposed framework.

A Secure Cloud Computing Based Framework for Big Data Information Management of Smart Grid

Security and privacy challenges in mobile cloud computing

Outsourcing data to the cloud are beneficial for reasons of economy, scalability, and accessibility, but significant technical challenges remain. Sensitive data stored in the cloud must be protected from being read in the clear by a cloud provider that is honest-but-curious. Additionally, cloud-based data are increasingly being accessed by resource-constrained mobile devices for which the processing and communication cost must be minimized. Novel modifications to attribute-based encryption are proposed to allow authorized users access to cloud data based on the satisfaction of required attributes such that the higher computational load from cryptographic operations is assigned to the cloud provider and the total communication cost is lowered for the mobile user. Furthermore, data re-encryption may be optionally performed by the cloud provider to reduce the expense of user revocation in a mobile user environment while preserving the privacy of user data stored in the cloud. The proposed protocol has been realized on commercially popular mobile and cloud platforms to demonstrate real-world benchmarks that show the efficacy of the scheme. A simulation calibrated with the benchmark results shows the scalability potential of the scheme in the context of a realistic workload in a mobile cloud computing system.

Hybrid Attribute- and Re-Encryption-Based Key Management for Secure and Scalable Mobile Applications in Clouds

In many of cryptographic schemes, the most time consuming basic arithmetic operation is the finite field multiplication and its hardware implementation may require millions of logic gates. It is a complex and costly task to develop such large finite field multipliers which will always yield error free outputs. In this effect, this paper considers fault tolerant multiplication in finite fields. It deals with detection of errors of bit-parallel and bit-serial polynomial basis multipliers over finite fields of characteristic two. Our approach is to partition the multiplier structure into a number of smaller computational units and use the parity prediction technique to detect errors.

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Error Detection in Polynomial Basis Multipliers over Binary Extension Fields

Cloud computing confers strong economic advantages, but many clients are reluctant to implicitly trust a third-party cloud provider. To address these security concerns, data may be transmitted and stored in encrypted form. Major challenges exist concerning the aspects of the generation, distribution, and usage of encryption keys in cloud systems, such as the safe location of keys, and serving the recent trend of users that tend to connect to contemporary cloud applications using resource-constrained mobile devices in extremely large numbers simultaneously; these characteristics lead to difficulties in achieving efficient and highly scalable key management. In this work, a model for key distribution based on the principle of dynamic data re-encryption is applied to a cloud computing system in a unique way to address the demands of a mobile device environment, including limitations on client wireless data usage, storage capacity, processing power, and battery life. The proposed cloud-based re-encryption model is secure, efficient, and highly scalable in a cloud computing context, as keys are managed by the client for trust reasons, processor-intensive data re-encryption is handled by the cloud provider, and key redistribution is minimized to conserve communication costs on mobile devices. A versioning history mechanism effectively manages keys for a continuously changing user population. Finally, an implementation on commercial mobile and cloud platforms is used to validate the performance of the model. Keywords-Distributed systems, mobile computing, security.

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Re-Encryption-Based Key Management Towards Secure and Scalable Mobile Applications in Clouds.

In this article, an extremely simple and highly regular architecture for finite field multiplier using redundant basis is presented, where redundant basis is a new basis taking advantage of the elegant multiplicative structure of the set of primitive nth roots of unity over F2 that forms a basis of F2m over F2. The architecture has an important feature of implementation complexity trade-off which enables the multiplier to be implemented in a partial parallel fashion. The squaring operation using the redundant basis is simply a permutation of the coefficients. We also show that with redundant basis the inversion problem is equivalent to solving a set of linear equations with a circulant matrix. The basis appear to be suitable for hardware implementation of elliptic curve cryptosystems.

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Highly Regular Architectures for Finite Field Computation Using Redundant Basis

For cryptographic applications, normal bases have received considerable attention, especially for hardware implementation. In this article, we consider fast software algorithms for normal basis multiplication over the extended binary field GF(2m). We present a vector-level algorithm which essentially eliminates the bit-wise inner products needed in the conventional approach to the normal basis multiplication. We then present another algorithm which significantly reduces the dynamic instruction counts. Both algorithms utilize the full width of the datapath of the general purpose processor on which the software is to be executed. We also consider composite fields and present an algorithm which can provide further speed-up and an added flexibility toward hardwaresoftware co-design of processors for very large finite fields.

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M. Anwarul Hasan

Papers

Hybrid Attribute- and Re-Encryption-Based Key Management for Secure and Scalable Mobile Applications in Clouds

Error Detection in Polynomial Basis Multipliers over Binary Extension Fields

Re-Encryption-Based Key Management Towards Secure and Scalable Mobile Applications in Clouds.

Highly Regular Architectures for Finite Field Computation Using Redundant Basis

Fast Normal Basis Multiplication Using General Purpose Processors