Cryptanalysis of an NTRU-based Proxy Encryption Scheme from ASIACCS\u2715

In ASIACCS 2015, Nuñez, Agudo, and Lopez proposed a proxy re-encryption scheme, NTRUReEncrypt, based on NTRU, which allows a proxy to translate ciphertext under the delegator\u27s public key into a re-encrypted ciphertext that can be decrypted correctly by delegatee\u27s private key. In addition to its potential resistance to quantum algorithm, the scheme was also considered to be efficient. However, in this paper we point out that the re-encryption process will increase the decryption error, and the increased decryption error will lead to a reaction attack that enables the proxy to recover the private key of the delegator and the delegatee. Moreover, we also propose a second attack which enables the delegatee to recover the private key of the delegator when he collects enough re-encrypted ciphertexts from a same message. We reevaluate the security of NTRUReEncrypt, and also give suggestions and discussions on potential mitigation methods

Cryptanalysis of ITRU

ITRU cryptosystem is a public key cryptosystem and one of the known variants of NTRU cryptosystem. Instead of working in a truncated polynomial ring, ITRU cryptosystem is based on the ring of integers. The authors claimed that ITRU has better features comparing to the classical NTRU, such as having a simple parameter selection algorithm, invertibility, and successful message decryption, and better security. In this paper, we present an attack technique against the ITRU cryptosystem, and it is mainly based on a simple frequency analysis on the letters of ciphertexts

Provably secure NTRU instances over prime cyclotomic rings

Due to its remarkable performance and potential resistance to quantum attacks, NTRUEncrypt has drawn much attention recently; it also has been standardized by IEEE. However, classical NTRUEncrypt lacks a strong security guarantee and its security still relies on heuristic arguments. At Eurocrypt 2011, Stehlé and Steinfeld first proposed a variant of NTRUEncrypt with a security reduction from standard problems on ideal lattices. This variant is restricted to the family of rings ℤ[X]/(Xn + 1) with n a power of 2 and its private keys are sampled by rejection from certain discrete Gaussian so that the public key is shown to be almost uniform. Despite the fact that partial operations, especially for RLWE, over ℤ[X]/(Xn + 1) are simple and efficient, these rings are quite scarce and different from the classical NTRU setting. In this work, we consider a variant of NTRUEncrypt over prime cyclotomic rings, i.e. ℤ[X]/(Xn-1 +…+ X + 1) with n an odd prime, and obtain IND-CPA secure results in the standard model assuming the hardness of worst-case problems on ideal lattices. In our setting, the choice of the rings is much more flexible and the scheme is closer to the original NTRU, as ℤ[X]/(Xn-1+…+X+1) is a large subring of the NTRU ring ℤ[X]/(Xn-1). Some tools for prime cyclotomic rings are also developed

Homomorphic Encryption and Cryptanalysis of Lattice Cryptography

The vast amount of personal data being collected and analyzed through internet connected devices is vulnerable to theft and misuse. Modern cryptography presents several powerful techniques that can help to solve the puzzle of how to harness data for use while at the same time protecting it---one such technique is homomorphic encryption that allows computations to be done on data while it is still encrypted. The question of security for homomorphic encryption relates to the broader field of lattice cryptography. Lattice cryptography is one of the main areas of cryptography that promises to be secure even against quantum computing. In this dissertation, we will touch on several aspects of homomorphic encryption and its security based on lattice cryptography. Our main contributions are: 1. proving some heuristics that are used in major results in the literature for controlling the error size in bootstrapping for fully homomorphic encryption, 2. presenting a new fully homomorphic encryption scheme that supports k-bit arbitrary operations and achieves an asymptotic ciphertext expansion of one, 3. thoroughly studying certain attacks against the Ring Learning with Errors problem, 4. precisely characterizing the performance of an algorithm for solving the Approximate Common Divisor problem

Security of Ubiquitous Computing Systems

The chapters in this open access book arise out of the EU Cost Action project Cryptacus, the objective of which was to improve and adapt existent cryptanalysis methodologies and tools to the ubiquitous computing framework. The cryptanalysis implemented lies along four axes: cryptographic models, cryptanalysis of building blocks, hardware and software security engineering, and security assessment of real-world systems. The authors are top-class researchers in security and cryptography, and the contributions are of value to researchers and practitioners in these domains. This book is open access under a CC BY license

Security of Ubiquitous Computing Systems

The chapters in this open access book arise out of the EU Cost Action project Cryptacus, the objective of which was to improve and adapt existent cryptanalysis methodologies and tools to the ubiquitous computing framework. The cryptanalysis implemented lies along four axes: cryptographic models, cryptanalysis of building blocks, hardware and software security engineering, and security assessment of real-world systems. The authors are top-class researchers in security and cryptography, and the contributions are of value to researchers and practitioners in these domains. This book is open access under a CC BY license

Privacy in rfid and mobile objects

Los sistemas RFID permiten la identificación rápida y automática de etiquetas RFID a través de un canal de comunicación inalámbrico. Dichas etiquetas son dispositivos con cierto poder de cómputo y capacidad de almacenamiento de información. Es por ello que los objetos que contienen una etiqueta RFID adherida permiten la lectura de una cantidad rica y variada de datos que los describen y caracterizan, por ejemplo, un código único de identificación, el nombre, el modelo o la fecha de expiración. Además, esta información puede ser leída sin la necesidad de un contacto visual entre el lector y la etiqueta, lo cual agiliza considerablemente los procesos de inventariado, identificación, o control automático. Para que el uso de la tecnología RFID se generalice con éxito, es conveniente cumplir con varios objetivos: eficiencia, seguridad y protección de la privacidad. Sin embargo, el diseño de protocolos de identificación seguros, privados, y escalables es un reto difícil de abordar dada las restricciones computacionales de las etiquetas RFID y su naturaleza inalámbrica. Es por ello que, en la presente tesis, partimos de protocolos de identificación seguros y privados, y mostramos cómo se puede lograr escalabilidad mediante una arquitectura distribuida y colaborativa. De este modo, la seguridad y la privacidad se alcanzan mediante el propio protocolo de identificación, mientras que la escalabilidad se logra por medio de novedosos métodos colaborativos que consideran la posición espacial y temporal de las etiquetas RFID. Independientemente de los avances en protocolos inalámbricos de identificación, existen ataques que pueden superar exitosamente cualquiera de estos protocolos sin necesidad de conocer o descubrir claves secretas válidas ni de encontrar vulnerabilidades en sus implementaciones criptográficas. La idea de estos ataques, conocidos como ataques de “relay”, consiste en crear inadvertidamente un puente de comunicación entre una etiqueta legítima y un lector legítimo. De este modo, el adversario usa los derechos de la etiqueta legítima para pasar el protocolo de autenticación usado por el lector. Nótese que, dada la naturaleza inalámbrica de los protocolos RFID, este tipo de ataques representa una amenaza importante a la seguridad en sistemas RFID. En esta tesis proponemos un nuevo protocolo que además de autenticación realiza un chequeo de la distancia a la cual se encuentran el lector y la etiqueta. Este tipo de protocolos se conocen como protocolos de acotación de distancia, los cuales no impiden este tipo de ataques, pero sí pueden frustrarlos con alta probabilidad. Por último, afrontamos los problemas de privacidad asociados con la publicación de información recogida a través de sistemas RFID. En particular, nos concentramos en datos de movilidad que también pueden ser proporcionados por otros sistemas ampliamente usados tales como el sistema de posicionamiento global (GPS) y el sistema global de comunicaciones móviles. Nuestra solución se basa en la conocida noción de k-anonimato, alcanzada mediante permutaciones y microagregación. Para este fin, definimos una novedosa función de distancia entre trayectorias con la cual desarrollamos dos métodos diferentes de anonimización de trayectorias.Els sistemes RFID permeten la identificació ràpida i automàtica d’etiquetes RFID a través d’un canal de comunicació sense fils. Aquestes etiquetes són dispositius amb cert poder de còmput i amb capacitat d’emmagatzematge de informació. Es per això que els objectes que porten una etiqueta RFID adherida permeten la lectura d’una quantitat rica i variada de dades que els descriuen i caracteritzen, com per exemple un codi únic d’identificació, el nom, el model o la data d’expiració. A més, aquesta informació pot ser llegida sense la necessitat d’un contacte visual entre el lector i l’etiqueta, la qual cosa agilitza considerablement els processos d’inventariat, identificació o control automàtic. Per a que l’ús de la tecnologia RFID es generalitzi amb èxit, es convenient complir amb diversos objectius: eficiència, seguretat i protecció de la privacitat. No obstant això, el disseny de protocols d’identificació segurs, privats i escalables, es un repte difícil d’abordar dades les restriccions computacionals de les etiquetes RFID i la seva naturalesa sense fils. Es per això que, en la present tesi, partim de protocols d’identificació segurs i privats, i mostrem com es pot aconseguir escalabilitat mitjançant una arquitectura distribuïda i col•laborativa. D’aquesta manera, la seguretat i la privacitat s’aconsegueixen mitjançant el propi protocol d’identificació, mentre que l’escalabilitat s’aconsegueix per mitjà de nous protocols col•laboratius que consideren la posició espacial i temporal de les etiquetes RFID. Independentment dels avenços en protocols d’identificació sense fils, existeixen atacs que poden passar exitosament qualsevol d’aquests protocols sense necessitat de conèixer o descobrir claus secretes vàlides, ni de trobar vulnerabilitats a les seves implantacions criptogràfiques. La idea d’aquestos atacs, coneguts com atacs de “relay”, consisteix en crear inadvertidament un pont de comunicació entre una etiqueta legítima i un lector legítim. D’aquesta manera, l’adversari utilitza els drets de l’etiqueta legítima per passar el protocol d’autentificació utilitzat pel lector. Es important tindre en compte que, dada la naturalesa sense fils dels protocols RFID, aquests tipus d’atacs representen una amenaça important a la seguretat en sistemes RFID. En aquesta dissertació proposem un nou protocol que, a més d’autentificació, realitza una revisió de la distància a la qual es troben el lector i l’etiqueta. Aquests tipus de protocols es coneixen com a “distance-boulding protocols”, els quals no prevenen aquests tipus d’atacs, però si que poden frustrar-los amb alta probabilitat. Per últim, afrontem els problemes de privacitat associats amb la publicació de informació recol•lectada a través de sistemes RFID. En concret, ens concentrem en dades de mobilitat, que també poden ser proveïdes per altres sistemes àmpliament utilitzats tals com el sistema de posicionament global (GPS) i el sistema global de comunicacions mòbils. La nostra solució es basa en la coneguda noció de privacitat “k-anonymity” i parcialment en micro-agregació. Per a aquesta finalitat, definim una nova funció de distància entre trajectòries amb la qual desenvolupen dos mètodes diferents d’anonimització de trajectòries.Radio Frequency Identification (RFID) is a technology aimed at efficiently identifying and tracking goods and assets. Such identification may be performed without requiring line-of-sight alignment or physical contact between the RFID tag and the RFID reader, whilst tracking is naturally achieved due to the short interrogation field of RFID readers. That is why the reduction in price of the RFID tags has been accompanied with an increasing attention paid to this technology. However, since tags are resource-constrained devices sending identification data wirelessly, designing secure and private RFID identification protocols is a challenging task. This scenario is even more complex when scalability must be met by those protocols. Assuming the existence of a lightweight, secure, private and scalable RFID identification protocol, there exist other concerns surrounding the RFID technology. Some of them arise from the technology itself, such as distance checking, but others are related to the potential of RFID systems to gather huge amount of tracking data. Publishing and mining such moving objects data is essential to improve efficiency of supervisory control, assets management and localisation, transportation, etc. However, obvious privacy threats arise if an individual can be linked with some of those published trajectories. The present dissertation contributes to the design of algorithms and protocols aimed at dealing with the issues explained above. First, we propose a set of protocols and heuristics based on a distributed architecture that improve the efficiency of the identification process without compromising privacy or security. Moreover, we present a novel distance-bounding protocol based on graphs that is extremely low-resource consuming. Finally, we present two trajectory anonymisation methods aimed at preserving the individuals' privacy when their trajectories are released

Revisiting Security Estimation for LWE with Hints from a Geometric Perspective

The Distorted Bounded Distance Decoding Problem (DBDD) was introduced by Dachman-Soled et al. [Crypto ’20] as an intermediate problem between LWE and unique-SVP (uSVP). They presented an approach that reduces an LWE instance to a DBDD instance, integrates side information (or “hints”) into the DBDD instance, and finally reduces it to a uSVP instance, which can be solved via lattice reduction. They showed that this principled approach can lead to algorithms for side-channel attacks that perform better than ad-hoc algorithms that do not rely on lattice reduction. The current work focuses on new methods for integrating hints into a DBDD instance. We view hints from a geometric perspective, as opposed to the distributional perspective from the prior work. Our approach provides the rigorous promise that, as hints are integrated into the DBDD instance, the correct solution remains a lattice point contained in the specified ellipsoid. We instantiate our approach with two new types of hints: (1) Inequality hints, corresponding to the region of intersection of an ellipsoid and a halfspace; (2) Combined hints, corresponding to the region of intersection of two ellipsoids. Since the regions in (1) and (2) are not necessarily ellipsoids, we replace them with ellipsoidal approximations that circumscribe the region of intersection. Perfect hints are reconsidered as the region of intersection of an ellipsoid and a hyperplane, which is itself an ellipsoid. The compatibility of “approximate,” “modular,” and “short vector” hints from the prior work is examined. We apply our techniques to the decryption failure and side-channel attack settings. We show that “inequality hints” can be used to model decryption failures, and that our new approach yields a geometric analogue of the “failure boosting” technique of D’anvers et al. [ePrint, ’18]. We also show that “combined hints” can be used to fuse information from a decryption failure and a side-channel attack, and provide rigorous guarantees despite the data being non-Gaussian. We provide experimental data for both applications. The code that we have developed to implement the integration of hints and hardness estimates extends the Toolkit from prior work and has been released publicly