A Survey on Homomorphic Encryption Schemes: Theory and Implementation

Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encryption (HE), a special kind of encryption scheme, can address these concerns as it allows any third party to operate on the encrypted data without decrypting it in advance. Although this extremely useful feature of the HE scheme has been known for over 30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE) scheme, which allows any computable function to perform on the encrypted data, was introduced by Craig Gentry in 2009. Even though this was a major achievement, different implementations so far demonstrated that FHE still needs to be improved significantly to be practical on every platform. First, we present the basics of HE and the details of the well-known Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which are important pillars of achieving FHE. Then, the main FHE families, which have become the base for the other follow-up FHE schemes are presented. Furthermore, the implementations and recent improvements in Gentry-type FHE schemes are also surveyed. Finally, further research directions are discussed. This survey is intended to give a clear knowledge and foundation to researchers and practitioners interested in knowing, applying, as well as extending the state of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the survey that is being submitted to ACM CSUR and has been uploaded to arXiv for feedback from stakeholder

EFFICIENT AND SCALABLE NETWORK SECURITY PROTOCOLS BASED ON LFSR SEQUENCES

The gap between abstract, mathematics-oriented research in cryptography and the engineering approach of designing practical, network security protocols is widening. Network researchers experiment with well-known cryptographic protocols suitable for different network models. On the other hand, researchers inclined toward theory often design cryptographic schemes without considering the practical network constraints. The goal of this dissertation is to address problems in these two challenging areas: building bridges between practical network security protocols and theoretical cryptography. This dissertation presents techniques for building performance sensitive security protocols, using primitives from linear feedback register sequences (LFSR) sequences, for a variety of challenging networking applications. The significant contributions of this thesis are: 1. A common problem faced by large-scale multicast applications, like real-time news feeds, is collecting authenticated feedback from the intended recipients. We design an efficient, scalable, and fault-tolerant technique for combining multiple signed acknowledgments into a single compact one and observe that most signatures (based on the discrete logarithm problem) used in previous protocols do not result in a scalable solution to the problem. 2. We propose a technique to authenticate on-demand source routing protocols in resource-constrained wireless mobile ad-hoc networks. We develop a single-round multisignature that requires no prior cooperation among nodes to construct the multisignature and supports authentication of cached routes. 3. We propose an efficient and scalable aggregate signature, tailored for applications like building efficient certificate chains, authenticating distributed and adaptive content management systems and securing path-vector routing protocols. 4. We observe that blind signatures could form critical building blocks of privacypreserving accountability systems, where an authority needs to vouch for the legitimacy of a message but the ownership of the message should be kept secret from the authority. We propose an efficient blind signature that can serve as a protocol building block for performance sensitive, accountability systems. All special forms digital signatures—aggregate, multi-, and blind signatures—proposed in this dissertation are the first to be constructed using LFSR sequences. Our detailed cost analysis shows that for a desired level of security, the proposed signatures outperformed existing protocols in computation cost, number of communication rounds and storage overhead

LEDAkem: a post-quantum key encapsulation mechanism based on QC-LDPC codes

This work presents a new code-based key encapsulation mechanism (KEM) called LEDAkem. It is built on the Niederreiter cryptosystem and relies on quasi-cyclic low-density parity-check codes as secret codes, providing high decoding speeds and compact keypairs. LEDAkem uses ephemeral keys to foil known statistical attacks, and takes advantage of a new decoding algorithm that provides faster decoding than the classical bit-flipping decoder commonly adopted in this kind of systems. The main attacks against LEDAkem are investigated, taking into account quantum speedups. Some instances of LEDAkem are designed to achieve different security levels against classical and quantum computers. Some performance figures obtained through an efficient C99 implementation of LEDAkem are provided.Comment: 21 pages, 3 table

New Security Definitions, Constructions and Applications of Proxy Re-Encryption

La externalización de la gestión de la información es una práctica cada vez más común, siendo la computación en la nube (en inglés, cloud computing) el paradigma más representativo. Sin embargo, este enfoque genera también preocupación con respecto a la seguridad y privacidad debido a la inherente pérdida del control sobre los datos. Las soluciones tradicionales, principalmente basadas en la aplicación de políticas y estrategias de control de acceso, solo reducen el problema a una cuestión de confianza, que puede romperse fácilmente por los proveedores de servicio, tanto de forma accidental como intencionada. Por lo tanto, proteger la información externalizada, y al mismo tiempo, reducir la confianza que es necesario establecer con los proveedores de servicio, se convierte en un objetivo inmediato. Las soluciones basadas en criptografía son un mecanismo crucial de cara a este fin. Esta tesis está dedicada al estudio de un criptosistema llamado recifrado delegado (en inglés, proxy re-encryption), que constituye una solución práctica a este problema, tanto desde el punto de vista funcional como de eficiencia. El recifrado delegado es un tipo de cifrado de clave pública que permite delegar en una entidad la capacidad de transformar textos cifrados de una clave pública a otra, sin que pueda obtener ninguna información sobre el mensaje subyacente. Desde un punto de vista funcional, el recifrado delegado puede verse como un medio de delegación segura de acceso a información cifrada, por lo que representa un candidato natural para construir mecanismos de control de acceso criptográficos. Aparte de esto, este tipo de cifrado es, en sí mismo, de gran interés teórico, ya que sus definiciones de seguridad deben balancear al mismo tiempo la seguridad de los textos cifrados con la posibilidad de transformarlos mediante el recifrado, lo que supone una estimulante dicotomía. Las contribuciones de esta tesis siguen un enfoque transversal, ya que van desde las propias definiciones de seguridad del recifrado delegado, hasta los detalles específicos de potenciales aplicaciones, pasando por construcciones concretas

Remote electronic voting: studying and improving Helios

Dissertação de mestrado em Engenharia InformáticaA former North American President once said that the ballot is stronger than the bullet. In fact, the most civilized and organized way for a people express their opinion is by voting. However, there are people with bad intentions that affect voting and elections, being normal situations of coercion, collusion, fraud or forgery that disturb and cause alterations in the outcome of a vote. Thus, it becomes necessary to find ways to protect the voters, through vote secrecy and transparency, so that in end of a voting, democracy and justice prevail. Since the secret ballot papers until the electronic voting machines, passing through punched cards, technology in voting systems is evolving to ensure a greater security in elections, as well as greater efficiency, lower costs and other characteristics wanted in this type of systems. Nowadays, remote electronic voting is seen as the ultimate goal to achieve. The difficulty of developing such system is to ensure that it meets all the security requirements without infringing each other and without compromising the usability of the system itself. Thus, cryptography becomes an essential tool for obtaining security and integrity on electronic voting systems. This master thesis focuses on the world of electronic voting, in particular, the remote electronic voting. The objective is to find a system of this kind, with real world applications, to be studied and analyzed in a security point of view. Hence, we made a research on voting and, more deeply, a research on electronic voting schemes, in order to learn how to conceive it, which include the different stages that compose an election, types of voting and the entities involved, and what requirements to fulfill, both the security and functional. Because cryptography is used in most schemes, a detailed study was also performed on the primitives most common in protocols of electronic voting. However, there are not many schemes that pass from theory to practice. Fortunately, we found Helios, a well known scheme that implements various cryptographic techniques for everyone, under certain assumptions, be able to audit polls conducted with this system. A study was performed in order to explain how it was constructed and to identify its strengths and weaknesses. We also present some ongoing work by different people to improve Helios. Finally, we propose improvements on our own, to fight against coercion, to decrease the levels of assumptions and overcome corruption issues. Furthermore, we propose measures to protect the virtual voting booth and a mobile application to cast votes.Um antigo Presidente norte americano disse um dia que o voto é 'mais forte que a bala. De facto, a forma mais civilizada e organizada de um povo exprimir as suas opiniões é através de votações. Infelizmente, também este mundo é afectado por pessoas com más intenções, sendo normais as situações de coação, conluio, fraude ou falsificação que perturbam e causam alterações no resultado de urna votação. Assim, torna-se necessário arranjar formas de proteger os votantes, através de segredo de voto e transparência, de forma que, no final, a democracia e justiça de uma votação prevaleçam. Desde dos boletins de papel secreto até às máquinas de voto electrónico, passando pelas punched cards, a tecnologia em sistemas de votação vem evoluindo de modo a garantir uma maior segurança em eleições, assim como maior eficiência, menor custos e outras características que se querem neste tipo de sistemas. Nos dias de hoje, o voto electrónico remoto é visto como o grande objectivo a cumprir. A grande dificuldade de se desenvolver tal sistema é garantir que o sistema cumpra todos os requisitos de segurança sem que se violem entre si e sem que isso prejudique a usabilidade do sistema em si. Assim, a criptografia torna-se uma ferramenta essencial para se obter segurança e integridade em sistemas de voto electrónico. Esta tese de mestrado foca-se no mundo do voto electrónico, mais especificamente o voto electrónico remoto. O grande objectivo seria arranjar um sistema desse tipo, que tivesse aplicação real, para ser estudado e analisado do ponto de vista de segurança. Fez-se então uma pesquisa necessária sobre votações e, mais aprofundada, uma sobre esquemas de voto electrónico, de modo a aprender como se concebem, tanto as fases que a constituem como as entidades que normalmente fazem parte, e quais os requisitos a cumprir, tanto os funcionais como os de segurança. Como a criptografia entra em grande parte dos esquemas, também um estudo aprofundado foi realizado sobre as primitivas mais comuns em protocolos de voto electrónico. No entanto, não existem muitos esquemas que passem da teoria à prática. Felizmente, encontrou-se o Helios, um sistema que põe em prática diversas técnicas criptográficas para que qualquer pessoa, dentro de certas assumpções, possa auditar votações conduzidas por este sistema, ficando a privacidade nas mãos do Helios. Um estudo foi realizado de modo a explicar como foi construído e identificar os seus pontos fortes e fracos. Também são apresentados alguns trabalhos em curso sobre este sistema. Finalmente, propõem-se outros tipos de melhoramentos que visam: combater coação, diminuir o nível das assumpções e ultrapassar problemas de corrupção. Propõem-se ainda medidas para proteger a cabine virtual de votação e uma aplicação móvel

Homomorphic Encryption for Machine Learning in Medicine and Bioinformatics

Machine learning techniques are an excellent tool for the medical community to analyzing large amounts of medical and genomic data. On the other hand, ethical concerns and privacy regulations prevent the free sharing of this data. Encryption methods such as fully homomorphic encryption (FHE) provide a method evaluate over encrypted data. Using FHE, machine learning models such as deep learning, decision trees, and naive Bayes have been implemented for private prediction using medical data. FHE has also been shown to enable secure genomic algorithms, such as paternity testing, and secure application of genome-wide association studies. This survey provides an overview of fully homomorphic encryption and its applications in medicine and bioinformatics. The high-level concepts behind FHE and its history are introduced. Details on current open-source implementations are provided, as is the state of FHE for privacy-preserving techniques in machine learning and bioinformatics and future growth opportunities for FHE

On the Role of Hash-Based Signatures in Quantum-Safe Internet of Things:Current Solutions and Future Directions

The Internet of Things (IoT) is gaining ground as a pervasive presence around us by enabling miniaturized things with computation and communication capabilities to collect, process, analyze, and interpret information. Consequently, trustworthy data act as fuel for applications that rely on the data generated by these things, for critical decision-making processes, data debugging, risk assessment, forensic analysis, and performance tuning. Currently, secure and reliable data communication in IoT is based on public-key cryptosystems such as Elliptic Curve Cryptosystem (ECC). Nevertheless, reliance on the security of de-facto cryptographic primitives is at risk of being broken by the impending quantum computers. Therefore, the transition from classical primitives to quantum-safe primitives is indispensable to ensure the overall security of data en route. In this paper, we investigate applications of one of the post-quantum signatures called Hash-Based Signature (HBS) schemes for the security of IoT devices in the quantum era. We give a succinct overview of the evolution of HBS schemes with emphasis on their construction parameters and associated strengths and weaknesses. Then, we outline the striking features of HBS schemes and their significance for the IoT security in the quantum era. We investigate the optimal selection of HBS in the IoT networks with respect to their performance-constrained requirements, resource-constrained nature, and design optimization objectives. In addition to ongoing standardization efforts, we also highlight current and future research and deployment challenges along with possible solutions. Finally, we outline the essential measures and recommendations that must be adopted by the IoT ecosystem while preparing for the quantum world.Comment: 18 pages, 7 tables, 7 figure

Secure Outsourced Computation on Encrypted Data

Homomorphic encryption (HE) is a promising cryptographic technique that supports computations on encrypted data without requiring decryption first. This ability allows sensitive data, such as genomic, financial, or location data, to be outsourced for evaluation in a resourceful third-party such as the cloud without compromising data privacy. Basic homomorphic primitives support addition and multiplication on ciphertexts. These primitives can be utilized to represent essential computations, such as logic gates, which subsequently can support more complex functions. We propose the construction of efficient cryptographic protocols as building blocks (e.g., equality, comparison, and counting) that are commonly used in data analytics and machine learning. We explore the use of these building blocks in two privacy-preserving applications. One application leverages our secure prefix matching algorithm, which builds on top of the equality operation, to process geospatial queries on encrypted locations. The other applies our secure comparison protocol to perform conditional branching in private evaluation of decision trees. There are many outsourced computations that require joint evaluation on private data owned by multiple parties. For example, Genome-Wide Association Study (GWAS) is becoming feasible because of the recent advances of genome sequencing technology. Due to the sensitivity of genomic data, this data is encrypted using different keys possessed by different data owners. Computing on ciphertexts encrypted with multiple keys is a non-trivial task. Current solutions often require a joint key setup before any computation such as in threshold HE or incur large ciphertext size (at best, grows linearly in the number of involved keys) such as in multi-key HE. We propose a hybrid approach that combines the advantages of threshold and multi-key HE to support computations on ciphertexts encrypted with different keys while vastly reducing ciphertext size. Moreover, we propose the SparkFHE framework to support large-scale secure data analytics in the Cloud. SparkFHE integrates Apache Spark with Fully HE to support secure distributed data analytics and machine learning and make two novel contributions: (1) enabling Spark to perform efficient computation on large datasets while preserving user privacy, and (2) accelerating intensive homomorphic computation through parallelization of tasks across clusters of computing nodes. To our best knowledge, SparkFHE is the first addressing these two needs simultaneously

The Theory and Applications of Homomorphic Cryptography

Homomorphic cryptography provides a third party with the ability to perform simple computations on encrypted data without revealing any information about the data itself. Typically, a third party can calculate one of the encrypted sum or the encrypted product of two encrypted messages. This is possible due to the fact that the encryption function is a group homomorphism, and thus preserves group operations. This makes homomorphic cryptosystems useful in a wide variety of privacy preserving protocols. A comprehensive survey of known homomorphic cryptosystems is provided, including formal definitions, security assumptions, and outlines of security proofs for each cryptosystem presented. Threshold variants of several homomorphic cryptosystems are also considered, with the first construction of a threshold Boneh-Goh-Nissim cryptosystem given, along with a complete proof of security under the threshold semantic security game of Fouque, Poupard, and Stern. This approach is based on Shoup's approach to threshold RSA signatures, which has been previously applied to the Paillier and Damg\aa rd-Jurik cryptosystems. The question of whether or not this approach is suitable for other homomorphic cryptosystems is investigated, with results suggesting that a different approach is required when decryption requires a reduction modulo a secret value. The wide variety of protocols utilizing homomorphic cryptography makes it difficult to provide a comprehensive survey, and while an overview of applications is given, it is limited in scope and intended to provide an introduction to the various ways in which homomorphic cryptography is used beyond simple addition or multiplication of encrypted messages. In the case of strong conditional oblivious tranfser, a new protocol implementing the greater than predicate is presented, utilizing some special properties of the Boneh-Goh-Nissim cryptosystem to achieve security against a malicious receiver