Implementing fully homomorphic encryption schemes in FPGA-based systems

LLas nuevas tecnologías orientadas a la nube, el internet de las cosas o las tendencias "as a service" se basan en el almacenamiento y procesamiento de datos en servidores remotos. Para garantizar la seguridad en la comunicación de dichos datos al servidor remoto, y en el manejo de los mismos en dicho servidor, se hace uso de diferentes esquemas criptográficos. Tradicionalmente, dichos sistemas criptográficos se centran en encriptar los datos mientras no sea necesario procesarlos (es decir, durante la comunicación y almacenamiento de los mismos). Sin embargo, una vez es necesario procesar dichos datos encriptados (en el servidor remoto), es necesario desencriptarlos, momento en el cual un intruso en dicho servidor podría a acceder a datos sensibles de usuarios del mismo. Es más, este enfoque tradicional necesita que el servidor sea capaz de desencriptar dichos datos, teniendo que confiar en la integridad de dicho servidor de no comprometer los datos. Como posible solución a estos problemas, surgen los esquemas de encriptación homomórficos completos. Un esquema homomórfico completo no requiere desencriptar los datos para operar con ellos, sino que es capaz de realizar las operaciones sobre los datos encriptados, manteniendo un homomorfismo entre el mensaje cifrado y el mensaje plano. De esta manera, cualquier intruso en el sistema no podría robar más que textos cifrados, siendo imposible un robo de los datos sensibles sin un robo de las claves de cifrado. Sin embargo, los esquemas de encriptación homomórfica son, actualmente, drás-ticamente lentos comparados con otros esquemas de encriptación clásicos. Una op¬eración en el anillo del texto plano puede conllevar numerosas operaciones en el anillo del texto encriptado. Por esta razón, están surgiendo distintos planteamientos sobre como acelerar estos esquemas para un uso práctico. Una de las propuestas para acelerar los esquemas homomórficos consiste en el uso de High-Performance Computing (HPC) usando FPGAs (Field Programmable Gate Arrays). Una FPGA es un dispositivo semiconductor que contiene bloques de lógica cuya interconexión y funcionalidad puede ser reprogramada. Al compilar para FPGAs, se genera un circuito hardware específico para el algorithmo proporcionado, en lugar de hacer uso de instrucciones en una máquina universal, lo que supone una gran ventaja con respecto a CPUs. Las FPGAs tienen, por tanto, claras difrencias con respecto a CPUs: -Arquitectura en pipeline: permite la obtención de outputs sucesivos en tiempo constante -Posibilidad de tener multiples pipes para computación concurrente/paralela. Así, en este proyecto: -Se realizan diferentes implementaciones de esquemas homomórficos en sistemas basados en FPGAs. -Se analizan y estudian las ventajas y desventajas de los esquemas criptográficos en sistemas basados en FPGAs, comparando con proyectos relacionados. -Se comparan las implementaciones con trabajos relacionados New cloud-based technologies, the internet of things or "as a service" trends are based in data storage and processing in a remote server. In order to guarantee a secure communication and handling of data, cryptographic schemes are used. Tradi¬tionally, these cryptographic schemes focus on guaranteeing the security of data while storing and transferring it, not while operating with it. Therefore, once the server has to operate with that encrypted data, it first decrypts it, exposing unencrypted data to intruders in the server. Moreover, the whole traditional scheme is based on the assumption the server is reliable, giving it enough credentials to decipher data to process it. As a possible solution for this issues, fully homomorphic encryption(FHE) schemes is introduced. A fully homomorphic scheme does not require data decryption to operate, but rather operates over the cyphertext ring, keeping an homomorphism between the cyphertext ring and the plaintext ring. As a result, an outsider could only obtain encrypted data, making it impossible to retrieve the actual sensitive data without its associated cypher keys. However, using homomorphic encryption(HE) schemes impacts performance dras-tically, slowing it down. One operation in the plaintext space can lead to several operations in the cyphertext space. Because of this, different approaches address the problem of speeding up these schemes in order to become practical. One of these approaches consists in the use of High-Performance Computing (HPC) using FPGAs (Field Programmable Gate Array). An FPGA is an integrated circuit designed to be configured by a customer or a designer after manufacturing - hence "field-programmable". Compiling into FPGA means generating a circuit (hardware) specific for that algorithm, instead of having an universal machine and generating a set of machine instructions. FPGAs have, thus, clear differences compared to CPUs: - Pipeline architecture, which allows obtaining successive outputs in constant time. -Possibility of having multiple pipes for concurrent/parallel computation. Thereby, In this project: -We present different implementations of FHE schemes in FPGA-based systems. -We analyse and study advantages and drawbacks of the implemented FHE schemes, compared to related work.

Homomorphic encryption and database query privacy

Homomorphic encryption is a particular type of encryption method that enables computing over encrypted data. This has a wide range of real world ramifications such as being able to blindly compute a search result sent to a remote server without revealing its content. In the first part of this thesis, we discuss how database search queries can be made secure using a homomorphic encryption scheme based on the ideas of Gahi et al. Gahi’s method is based on the integer-based fully homomorphic encryption scheme proposed by Dijk et al. We propose a new database search scheme called the Homomorphic Query Processing Scheme, which can be used with the ring-based fully homomorphic encryption scheme proposed by Braserski. In the second part of this thesis, we discuss the cybersecurity of the smart electric grid. Specifically, we use the Homomorphic Query Processing scheme to construct a keyword search technique in the smart grid. Our work is based on the Public Key Encryption with Keyword Search (PEKS) method introduced by Boneh et al. and a Multi-Key Homomorphic Encryption scheme proposed by L´opez-Alt et al. A summary of the results of this thesis (specifically the Homomorphic Query Processing Scheme) is published at the 14th Canadian Workshop on Information Theory (CWIT).

TSKY: a dependable middleware solution for data privacy using public storage clouds

Dissertação para obtenção do Grau de Mestre em Engenharia Informática

Improved Privacy-Preserving P2P Multimedia Distribution Based on Recombined Fingerprints

Peer-reviewed

Privacy-preserving genomic testing in the clinic: a model using HIV treatment

PURPOSE The implementation of genomic-based medicine is hindered by unresolved questions regarding data privacy and delivery of interpreted results to health-care practitioners. We used DNA-based prediction of HIV-related outcomes as a model to explore critical issues in clinical genomics. METHODS We genotyped 4,149 markers in HIV-positive individuals. Variants allowed for prediction of 17 traits relevant to HIV medical care, inference of patient ancestry, and imputation of human leukocyte antigen (HLA) types. Genetic data were processed under a privacy-preserving framework using homomorphic encryption, and clinical reports describing potentially actionable results were delivered to health-care providers. RESULTS A total of 230 patients were included in the study. We demonstrated the feasibility of encrypting a large number of genetic markers, inferring patient ancestry, computing monogenic and polygenic trait risks, and reporting results under privacy-preserving conditions. The average execution time of a multimarker test on encrypted data was 865 ms on a standard computer. The proportion of tests returning potentially actionable genetic results ranged from 0 to 54%. CONCLUSIONS The model of implementation presented herein informs on strategies to deliver genomic test results for clinical care. Data encryption to ensure privacy helps to build patient trust, a key requirement on the road to genomic-based medicine.Genet Med advance online publication 14 January 2016Genetics in Medicine (2016); doi:10.1038/gim.2015.167.

A framework for implementing outsourcing schemes

En esta tesis se aborda el problema de la externalización segura de servicios de datos y computación. El escenario de interés es aquel en el que el usuario posee datos y quiere subcontratar un servidor en la nube (“Cloud”). Además, el usuario puede querer también delegar el cálculo de un subconjunto de sus datos al servidor. Se presentan dos aspectos de seguridad relacionados con este escenario, en concreto, la integridad y la privacidad y se analizan las posibles soluciones a dichas cuestiones, aprovechando herramientas criptográficas avanzadas, como el Autentificador de Mensajes Homomórfico (“Homomorphic Message Authenticators”) y el Cifrado Totalmente Homomórfico (“Fully Homomorphic Encryption”). La contribución de este trabajo es tanto teórica como práctica. Desde el punto de vista de la contribución teórica, se define un nuevo esquema de externalización (en lo siguiente, denominado con su término inglés Outsourcing), usando como punto de partida los artículos de [3] y [12], con el objetivo de realizar un modelo muy genérico y flexible que podría emplearse para representar varios esquemas de ”outsourcing” seguro. Dicho modelo puede utilizarse para representar esquemas de “outsourcing” seguro proporcionando únicamente integridad, únicamente privacidad o, curiosamente, integridad con privacidad. Utilizando este nuevo modelo también se redefine un esquema altamente eficiente, construido en [12] y que se ha denominado Outsourcinglin. Este esquema permite calcular polinomios multivariados de grado 1 sobre el anillo Z2k . Desde el punto de vista de la contribución práctica, se ha construido una infraestructura marco (“Framework”) para aplicar el esquema de “outsourcing”. Seguidamente, se ha testado dicho “Framework” con varias implementaciones, en concreto la implementación del criptosistema Joye-Libert ([18]) y la implementación del esquema propio Outsourcinglin. En el contexto de este trabajo práctico, la tesis también ha dado lugar a algunas contribuciones innovadoras: el diseño y la implementación de un nuevo algoritmo de descifrado para el esquema de cifrado Joye-Libert, en colaboración con Darío Fiore. Presenta un mejor comportamiento frente a los algoritmos propuestos por los autores de [18];la implementación de la función eficiente pseudo-aleatoria de forma amortizada cerrada (“amortized-closed-form efficient pseudorandom function”) de [12]. Esta función no se había implementado con anterioridad y no supone un problema trivial, por lo que este trabajo puede llegar a ser útil en otros contextos. Finalmente se han usado las implementaciones durante varias pruebas para medir tiempos de ejecución de los principales algoritmos.---ABSTRACT---In this thesis we tackle the problem of secure outsourcing of data and computation. The scenario we are interested in is that in which a user owns some data and wants to “outsource” it to a Cloud server. Furthermore, the user may want also to delegate the computation over a subset of its data to the server. We present the security issues related to this scenario, namely integrity and privacy and we analyse some possible solutions to these two issues, exploiting advanced cryptographic tools, such as Homomorphic Message Authenticators and Fully Homomorphic Encryption. Our contribution is both theoretical and practical. Considering our theoretical contribution, using as starting points the articles of [3] and [12], we introduce a new cryptographic primitive, called Outsourcing with the aim of realizing a very generic and flexible model that might be employed to represent several secure outsourcing schemes. Such model can be used to represent secure outsourcing schemes that provide only integrity, only privacy or, interestingly, integrity with privacy. Using our new model we also re-define an highly efficient scheme constructed in [12], that we called Outsourcinglin and that is a scheme for computing multi-variate polynomials of degree 1 over the ring Z2k. Considering our practical contribution, we build a Framework to implement the Outsourcing scheme. Then, we test such Framework to realize several implementations, specifically the implementation of the Joye-Libert cryptosystem ([18]) and the implementation of our Outsourcinglin scheme. In the context of this practical work, the thesis also led to some novel contributions: the design and the implementation, in collaboration with Dario Fiore, of a new decryption algorithm for the Joye-Libert encryption scheme, that performs better than the algorithms proposed by the authors in [18]; the implementation of the amortized-closed-form efficient pseudorandom function of [12]. There was no prior implementation of this function and it represented a non trivial work, which can become useful in other contexts. Finally we test the implementations to execute several experiments for measuring the timing performances of the main algorithms.

Métodos eficientes para criptografia baseada em reticulados.

Reticulados têm sido aplicados de diferentes maneiras em criptografia. Inicialmente utilizados para a destruição de criptossistemas, eles foram posteriormente aplicados na construção de novos esquemas, incluindo criptossistemas assimétricos, esquemas de assinatura cega e os primeiros métodos para encriptação completamente homomórfica. Contudo, seu desempenho ainda é proibitivamente lenta em muitos casos. Neste trabalho, expandimos técnicas originalmente desenvolvidas para encriptação homomórfica, tornando-as mais genéricas e aplicando-as no esquema GGH-YK-M, um esquema de encriptação de chave pública, e no esquema LMSV, a única construção homomórfica que não sucumbiu a ataques de recuperação de chaves IND-CCA1 até o momento. Em nossos testes, reduzimos o tamanho das chaves do GGH-YK-M em uma ordem de complexidade, especificamente, de O(n2 lg n) para O(n lg n), onde n é um parâmetro público do esquema. A nova técnica também atinge processamento mais rápido em todas as operações envolvidas em um criptossistema assimétrico, isto é, geração de chaves, encriptação e decriptação. A melhora mais significativa é na geração de chaves, que se torna mais de 3 ordens de magnitude mais rápida que resultados anteriores, enquanto a encriptação se torna por volta de 2 ordens de magnitude mais rápida. Para decriptação, nossa implementação é dez vezes mais rápida que a literatura. Também mostramos que é possível aumentar a segurança do esquema LMSV contra os ataques quânticos de recuperação de chaves recentemente publicados pela agência britânica GCHQ. Isso é feito através da adoção de reticulados não-ciclotômicos baseados em anéis polinomiais irredutíveis quase-circulantes. Em nossa implementação, o desempenho da encriptação é virtualmente idêntico, e a decriptação torna-se ligeiramente inferior, um pequeno preço a se pagar pelo aumento de segurança. A geração de chaves, porém, é muito mais lenta, devido à necessidade de se utilizar um método mais genérico e caro. A existência de métodos dedicados altamente eficientes para a geração de chaves nesta variante mais segura do LMSV permanece como um problema em aberto.

Phase-only optical encryption based on the zeroth-order phase-contrast technique

A phase-only encryption/decryption scheme with the readout based on the zeroth-order phase-contrast technique (ZOPCT), without the use of a phase-changing plate on the Fourier plane of an optical system based on the 4f optical correlator, is proposed. The encryption of a gray-level image is achieved by multiplying the phase distribution obtained directly from the gray-level image by a random phase distribution. The robustness of the encoding is assured by the nonlinearity intrinsic to the proposed phase-contrast method and the random phase distribution used in the encryption process. The experimental system has been implemented with liquid-crystal spatial modulators to generate phase-encrypted masks and a decrypting key. The advantage of this method is the easy scheme to recover the gray-level information from the decrypted phase-only mask applying the ZOPCT. An analysis of this decryption method was performed against brute force attacks. (C) 2009 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3223629]

A study on the encryption algorithm for RFID tag (SEED : 8 Rounds × 64 bits block)

Although it is always weak between RFID Tag and Terminal in focus of the security, there are no security skills in RFID Tag. Recently there are a lot of studying in order to protect it, but because it has some physical limitation of RFID, that is it should be low electric power and high speed, it is impossible to protect with the skills. At present, the methods of RFID security are using a security server, a security policy and security. One of them the most famous skill is the security module, then they has an authentication skill and an encryption skill. In this paper, we designed and implemented after modification original SEED into 8 Round and 64 bits for Tag.

Utilization of different encryption schemes for securing SCADA component communication

A vital role is being played by SCADA Communication for Supervisory Control and Data acquisition (SCADA) Monitoring Ststems. Devices that are designed to operate in safety-critical environments are usually designed to failsafe, but security vulnerabilities could be exploited by an attacker to disable the fail-safe mechanisms. Thus these devices must not onlybe designed for safety but also for security. This paper presents a study of the comparison of different Encryption schemes for securing SCADA Component Communication. The encryption schemes such as Symetric Key Encrypton in Wireless SCADA Environment, Assymmetric-key Encryption to Internet SCADA, and the Cross Crypto Scheme Cipher to secure communication for SCADA are analysed and the outcome is evaluated.

Implementação de sistemas de encriptação AES advanced encryption standard em hardware para segurança

Dissertação de mestrado integrado em Engenharia Electrónica Industrial e Computadores

Encryption methods using formal power series rings

Recently there has been a great deal of work on noncommutative algebraic cryptography. This involves the use of noncommutative algebraic objects as the platforms for encryption systems. Most of this work, such as the Anshel-Anshel-Goldfeld scheme, the Ko-Lee scheme and the Baumslag-Fine-Xu Modular group scheme use nonabelian groups as the basic algebraic object. Some of these encryption methods have been successful and some have been broken. It has been suggested that at this point further pure group theoretic research, with an eye towards cryptographic applications, is necessary.In the present study we attempt to extend the class of noncommutative algebraic objects to be used in cryptography. In particular we explore several different methods to use a formal power series ring R && x1; :::; xn && in noncommuting variables x1; :::; xn as a base to develop cryptosystems. Although R can be any ring we have in mind formal power series rings over the rationals Q. We use in particular a result of Magnus that a finitely generated free group F has a faithful representation in a quotient of the formal power series ring in noncommuting variables.

A public key encryption based on third order linear sequences

Based on third order linear sequences, an improvement version of the Diffie-Hellman distribution key scheme and the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Low rates of X-Y recombination, not turnovers, account for homomorphic sex chromosomes in several diploid species of Palearctic green toads (Bufo viridis subgroup).

Contrasting with birds and mammals, most ectothermic vertebrates present homomorphic sex chromosomes, which might be due either to a high turnover rate or to occasional X-Y recombination. We tested these two hypotheses in a group of Palearctic green toads that diverged some 3.3 million years ago. Using sibship analyses of sex-linked markers, we show that all four species investigated share the same pair of sex chromosomes and a pattern of male heterogamety with drastically reduced X-Y recombination in males. Phylogenetic analyses of sex-linked sequences show that X and Y alleles cluster by species, not by gametolog. We conclude that X-Y homomorphy and fine-scale sequence similarity in these species do not stem from recent sex-chromosome turnovers, but from occasional X-Y recombination.

Esquemes de xifrat homomòrfics per a votació electrònica

This bachelor's degree thesis deals with homomorphic public-key cryptography, or in other words cryptosystems with special addition properties. Such cryptosystems are widely used in real life situations, for instance to make electronic voting secure. In Chapter 1 a few basic algebra results and other key concepts are introduced. Chapters 2 and 3 contain the algorithms and properties of the two cryptosystems which are considered to be the best for e-voting: Paillier and Joye-Libert. The thesis is concluded in Chapter 4, by comparing running times of the two above-mentioned cryptosystems, in simulations of real-life e-voting systems, with up to tens of thousands of voters, and different levels of security. Through these simulations, we discern the situations where each of the two cryptosystems is preferable.