Efficient and Secure ECDSA Algorithm and its Applications: A Survey

Public-key cryptography algorithms, especially elliptic curve cryptography (ECC)and elliptic curve digital signature algorithm (ECDSA) have been attracting attention frommany researchers in different institutions because these algorithms provide security andhigh performance when being used in many areas such as electronic-healthcare, electronicbanking,electronic-commerce, electronic-vehicular, and electronic-governance. These algorithmsheighten security against various attacks and the same time improve performanceto obtain efficiencies (time, memory, reduced computation complexity, and energy saving)in an environment of constrained source and large systems. This paper presents detailedand a comprehensive survey of an update of the ECDSA algorithm in terms of performance,security, and applications

Elliptic Curve Cryptography Services for Mobile Operating Systems

Mobile devices as smartphones, tablets and laptops, are nowadays considered indispensable objects by most people in developed countries. A s personal and work assistant s , some of th e s e devices store , process and transmit sensitive and private data. Naturally , the number of mobile applications with integrated cryptographic mechanisms or offering security services has been significantly increasing in the last few years. Unfortunately, not all of those applications are secure by design, while other may not implement the cryptographic primitives correctly. Even the ones that implement them correctly may suffer from longevity problems, since cryptographic primitives that are considered secure nowadays may become obsolete in the next few years. Rivest, Shamir and Adleman (RSA) is an example of an widely used cryptosystem that may become depleted shorty . While the security issues in the mobile computing environment may be of median severity for casual users, they may be critical for several professional classes, namely lawyers, journalists and law enforcement agents. As such, it is important to approach these problems in a structured manner. This master’s program is focused on the engineering and implementation of a mobile application offering a series of security services. The application was engineered to be secure by design for the Windows Phone 8.1 Operating System (OS) which, at the time of writing this dissertation, was the platform with the most discreet offer in terms of applications of this type. The application provides services such as secure exchange of a cryptographic secret, encryption and digital signature of messages and files, management of contacts and encryption keys and secure password generation and storage. Part of the cryptographic primitives used in this work are from the Elliptic Curve Cryptography (ECC) theory, for which the discrete logarithm problem is believed to be harder and key handling is easier. The library defining a series of curves and containing the procedures and operations supporting the ECC primitives was implemented from scratch, since there was none available, comprising one of the contributions of this work. The work evolved from the analysis of the state-of-the-art to the requirements analysis and software engineering phase, thoroughly described herein, ending up with the development of a prototype. The engineering of the application included the definition of a trust model for the exchange of public keys and the modeling of the supporting database. The most visible outcomes of this master’s program are the fully working prototype of a mobile application offering the aforementioned security services, the implementation of an ECC library for the .NET framework, and this dissertation. The source code for the ECC library was made available online on GitHub with the name ECCryptoLib [Ana15]. Its development and improvement was mostly dominated by unit testing. The library and the mobile application were developed in C?. The level of security offered by the application is guaranteed via the orchestration and combination of state-of-the-art symmetric key cryptography algorithms, as the Advanced Encryption Standard (AES) and Secure Hash Algorithm 256 (SHA256) with the ECC primitives. The generation of passwords is done by using several sensors and inputs as entropy sources, which are fed to a cryptographically secure hash function. The passwords are stored in an encrypted database, whose encryption key changes every time it is opened, obtained using a Password-Based Key Derivation Function 2 (PBKDF2) from a master password. The trust model for the public keys designed in the scope of this work is inspired in Pretty Good Privacy (PGP), but granularity of the trust levels is larger.Dispositivos móveis como computadores portáteis, smartphones ou tablets, são, nos dias de hoje, considerados objectos indispensáveis pela grande maioria das pessoas residentes em países desenvolvidos. Por serem utilizados como assistentes pessoais ou de trabalho, alguns destes dispositivos guardam, processam e transmitem dados sensíveis ou privados. Naturalmente, o número de aplicações móveis com mecanismos criptográficos integrados ou que oferecem serviços de segurança, tem vindo a aumentar de forma significativa nos últimos anos. Infelizmente, nem todas as aplicações são seguras por construção, e outras podem não implementar as primitivas criptográficas corretamente. Mesmo aquelas que as implementam corretamente podem sofrer de problemas de longevidade, já que primitivas criptográficas que são hoje em dia consideradas seguras podem tornar-se obsoletas nos próximos anos. O Rivest, Shamir and Adleman (RSA) constitui um exemplo de um sistema criptográfico muito popular que se pode tornar obsoleto a curto prazo. Enquanto que os problemas de segurança em ambientes de computação móvel podem ser de média severidade para utilizadores casuais, estes são normalmente críticos para várias classes profissionais, nomeadamente advogados, jornalistas e oficiais da justiça. É, por isso, importante, abordar estes problemas de uma forma estruturada. Este programa de mestrado foca-se na engenharia e implementação de uma aplicação móvel que oferece uma série de serviços de segurança. A aplicação foi desenhada para ser segura por construção para o sistema operativo Windows Phone 8.1 que, altura em que esta dissertação foi escrita, era a plataforma com a oferta mais discreta em termos de aplicações deste tipo. A aplicação fornece funcionalidades como trocar um segredo criptográfico entre duas entidades de forma segura, cifra, decifra e assinatura digital de mensagens e ficheiros, gestão de contactos e chaves de cifra, e geração e armazenamento seguro de palavras-passe. Parte das primitivas criptográficas utilizadas neste trabalho fazem parte da teoria da criptografia em curvas elípticas, para a qual se acredita que o problema do logaritmo discreto é de mais difícil resolução e para o qual a manipulação de chaves é mais simples. A biblioteca que define uma série de curvas, e contendo os procedimentos e operações que suportam as primitivas criptográficas, foi totalmente implementada no âmbito deste trabalho, dado ainda não existir nenhuma disponível no seu início, compreendendo assim uma das suas contribuições. O trabalho evoluiu da análise do estado da arte para o levantamento dos requisitos e para a fase de engenharia de software, aqui descrita detalhadamente, culminando no desenvolvimento de um protótipo. A engenharia da aplicação incluiu a definição de um sistema de confiança para troca de chaves públicas e também modelação da base de dados de suporte. Os resultados mais visíveis deste programa de mestrado são o protótipo da aplicação móvel, completamente funcional e disponibilizando as funcionalidades de segurança acima mencionadas, a implementação de uma biblioteca Elliptic Curve Cryptography (ECC) para framework .NET, e esta dissertação. O código fonte com a implementação da biblioteca foi publicada online. O seu desenvolvimento e melhoramento foi sobretudo dominado por testes unitários. A biblioteca e a aplicação móvel foram desenvolvidas em C?. O nível de segurança oferecido pela aplicação é garantido através da orquestração e combinação de algoritmos da criptografia de chave simétrica atuais, como o Advanced Encryption Standard (AES) e o Secure Hash Algorithm 256 (SHA256), com as primitivas ECC. A geração de palavras-passe é feita recorrendo utilizando vários sensores e dispoitivos de entrada como fontes de entropia, que posteriormente são alimentadas a uma função de hash criptográfica. As palavras-passe são guardadas numa base de dados cifrada, cuja chave de cifra muda sempre que a base de dados é aberta, sendo obtida através da aplicação de um Password-Based Key Derivation Function 2 (PBKDF2) a uma palavrapasse mestre. O modelo de confiança para chaves públicas desenhado no âmbito deste trabalho é inspirado no Pretty Good Privacy (PGP), mas a granularidade dos níveis de confiança é superior

Elliptic curve and pseudo-inverse matrix based cryptosystem for wireless sensor networks

Applying asymmetric key security to wireless sensor network (WSN) has been challenging task for the researcher of this field. One common trade-off is that asymmetric key architecture does provide good enough security than symmetric key but on the other hand, sensor network has some resource limitations to implement asymmetric key approach. Elliptic curve cryptography (ECC) has significant advantages than other asymmetric key system like RSA, D-H etc. The most important feature of ECC is that it has much less bit requirement and at the same time, ensures better security compared to others. Hence, ECC can be a better option for implementing asymmetric key approach for sensor network. We propose a new cryptosystem which is based on Pseudo-inverse matrix and Elliptic Curve Cryptography. We establish a relationship between these two different concepts and evaluate our proposed system on the basis of the results of similar works as well as our own simulation done in TinyOS environment

MicroWalk: A Framework for Finding Side Channels in Binaries

Microarchitectural side channels expose unprotected software to information leakage attacks where a software adversary is able to track runtime behavior of a benign process and steal secrets such as cryptographic keys. As suggested by incremental software patches for the RSA algorithm against variants of side-channel attacks within different versions of cryptographic libraries, protecting security-critical algorithms against side channels is an intricate task. Software protections avoid leakages by operating in constant time with a uniform resource usage pattern independent of the processed secret. In this respect, automated testing and verification of software binaries for leakage-free behavior is of importance, particularly when the source code is not available. In this work, we propose a novel technique based on Dynamic Binary Instrumentation and Mutual Information Analysis to efficiently locate and quantify memory based and control-flow based microarchitectural leakages. We develop a software framework named \tool~for side-channel analysis of binaries which can be extended to support new classes of leakage. For the first time, by utilizing \tool, we perform rigorous leakage analysis of two widely-used closed-source cryptographic libraries: \emph{Intel IPP} and \emph{Microsoft CNG}. We analyze $15$ different cryptographic implementations consisting of $112$ million instructions in about $105$ minutes of CPU time. By locating previously unknown leakages in hardened implementations, our results suggest that \tool~can efficiently find microarchitectural leakages in software binaries

Efficient Side-Channel Aware Elliptic Curve Cryptosystems over Prime Fields

Elliptic Curve Cryptosystems (ECCs) are utilized as an alternative to traditional public-key cryptosystems, and are more suitable for resource limited environments due to smaller parameter size. In this dissertation we carry out a thorough investigation of side-channel attack aware ECC implementations over finite fields of prime characteristic including the recently introduced Edwards formulation of elliptic curves, which have built-in resiliency against simple side-channel attacks. We implement Joye\u27s highly regular add-always scalar multiplication algorithm both with the Weierstrass and Edwards formulation of elliptic curves. We also propose a technique to apply non-adjacent form (NAF) scalar multiplication algorithm with side-channel security using the Edwards formulation. Our results show that the Edwards formulation allows increased area-time performance with projective coordinates. However, the Weierstrass formulation with affine coordinates results in the simplest architecture, and therefore has the best area-time performance as long as an efficient modular divider is available

Efficient Arithmetic for the Implementation of Elliptic Curve Cryptography

The technology of elliptic curve cryptography is now an important branch in public-key based crypto-system. Cryptographic mechanisms based on elliptic curves depend on the arithmetic of points on the curve. The most important arithmetic is multiplying a point on the curve by an integer. This operation is known as elliptic curve scalar (or point) multiplication operation. A cryptographic device is supposed to perform this operation efficiently and securely. The elliptic curve scalar multiplication operation is performed by combining the elliptic curve point routines that are defined in terms of the underlying finite field arithmetic operations. This thesis focuses on hardware architecture designs of elliptic curve operations. In the first part, we aim at finding new architectures to implement the finite field arithmetic multiplication operation more efficiently. In this regard, we propose novel schemes for the serial-out bit-level (SOBL) arithmetic multiplication operation in the polynomial basis over F_2^m. We show that the smallest SOBL scheme presented here can provide about 26-30\% reduction in area-complexity cost and about 22-24\% reduction in power consumptions for F_2^{163} compared to the current state-of-the-art bit-level multiplier schemes. Then, we employ the proposed SOBL schemes to present new hybrid-double multiplication architectures that perform two multiplications with latency comparable to the latency of a single multiplication. Then, in the second part of this thesis, we investigate the different algorithms for the implementation of elliptic curve scalar multiplication operation. We focus our interest in three aspects, namely, the finite field arithmetic cost, the critical path delay, and the protection strength from side-channel attacks (SCAs) based on simple power analysis. In this regard, we propose a novel scheme for the scalar multiplication operation that is based on processing three bits of the scalar in the exact same sequence of five point arithmetic operations. We analyse the security of our scheme and show that its security holds against both SCAs and safe-error fault attacks. In addition, we show how the properties of the proposed elliptic curve scalar multiplication scheme yields an efficient hardware design for the implementation of a single scalar multiplication on a prime extended twisted Edwards curve incorporating 8 parallel multiplication operations. Our comparison results show that the proposed hardware architecture for the twisted Edwards curve model implemented using the proposed scalar multiplication scheme is the fastest secure SCA protected scalar multiplication scheme over prime field reported in the literature

Efficient and secure ECDSA algorithm and its applications: a survey

Public-key cryptography algorithms, especially elliptic curve cryptography (ECC) and elliptic curve digital signature algorithm (ECDSA) have been attracting attention from many researchers in different institutions because these algorithms provide security and high performance when being used in many areas such as electronic-healthcare, electronic-banking, electronic-commerce, electronic-vehicular, and electronic-governance. These algorithms heighten security against various attacks and the same time improve performance to obtain efficiencies (time, memory, reduced computation complexity, and energy saving) in an environment of constrained source and large systems. This paper presents detailed and a comprehensive survey of an update of the ECDSA algorithm in terms of performance, security, and applications

Fault attacks on RSA and elliptic curve cryptosystems

This thesis answered how a fault attack targeting software used to program EEPROM can threaten hardware devices, for instance IoT devices. The successful fault attacks proposed in this thesis will certainly warn designers of hardware devices of the security risks their devices may face on the programming leve

Key Randomization Countermeasures to Power Analysis Attacks on Elliptic Curve Cryptosystems

It is essential to secure the implementation of cryptosystems in embedded devices agains side-channel attacks. Namely, in order to resist differential (DPA) attacks, randomization techniques should be employed to decorrelate the data processed by the device from secret key parts resulting in the value of this data. Among the countermeasures that appeared in the literature were those that resulted in a random representation of the key known as the binary signed digit representation (BSD). We have discovered some interesting properties related to the number of possible BSD representations for an integer and we have proposed a different randomization algorithm. We have also carried our study to the $\tau$-adic representation of integers which is employed in elliptic curve cryptosystems (ECCs) using Koblitz curves. We have then dealt with another randomization countermeasure which is based on randomly splitting the key. We have investigated the secure employment of this countermeasure in the context of ECCs