Constant-round Dynamic Group Key Exchange from RLWE Assumption

In this paper, we propose a novel lattice-based group key exchange protocol with dynamic membership. Our protocol is constructed by generalizing Dutta-Barua protocol to RLWE setting, inspired by Apon et al.’s recent paper in PQCrypto 2019. We describe our (static) group key exchange protocol from Apon et al.’s paper by modifying its third round and computation step. Then, we present both authenticated and dynamic group key exchange protocol with Join and Leave algorithms. The number of rounds for authenticated group key exchange remains the same as unauthenticated one. Our protocol also supports the scalable property so that the number of rounds does not change depending on the number of group participants. By assuming the hardness of RLWE assumption and unforgeability of digital signatures, we give a full security proof for (un-)authenticated (dynamic) group key exchange protocols

Notes on Lattice-Based Cryptography

Asymmetrisk kryptering er avhengig av antakelsen om at noen beregningsproblemer er vanskelige å løse. I 1994 viste Peter Shor at de to mest brukte beregningsproblemene, nemlig det diskrete logaritmeproblemet og primtallsfaktorisering, ikke lenger er vanskelige å løse når man bruker en kvantedatamaskin. Siden den gang har forskere jobbet med å finne nye beregningsproblemer som er motstandsdyktige mot kvanteangrep for å erstatte disse to. Gitterbasert kryptografi er forskningsfeltet som bruker kryptografiske primitiver som involverer vanskelige problemer definert på gitter, for eksempel det korteste vektorproblemet og det nærmeste vektorproblemet. NTRU-kryptosystemet, publisert i 1998, var et av de første som ble introdusert på dette feltet. Problemet Learning With Error (LWE) ble introdusert i 2005 av Regev, og det regnes nå som et av de mest lovende beregningsproblemene som snart tas i bruk i stor skala. Å studere vanskelighetsgraden og å finne nye og raskere algoritmer som løser den, ble et ledende forskningstema innen kryptografi. Denne oppgaven inkluderer følgende bidrag til feltet: - En ikke-triviell reduksjon av Mersenne Low Hamming Combination Search Problem, det underliggende problemet med et NTRU-lignende kryptosystem, til Integer Linear Programming (ILP). Særlig finner vi en familie av svake nøkler. - En konkret sikkerhetsanalyse av Integer-RLWE, en vanskelig beregningsproblemvariant av LWE, introdusert av Gu Chunsheng. Vi formaliserer et meet-in-the-middle og et gitterbasert angrep for denne saken, og vi utnytter en svakhet ved parametervalget gitt av Gu, for å bygge et forbedret gitterbasert angrep. - En forbedring av Blum-Kalai-Wasserman-algoritmen for å løse LWE. Mer spesifikt, introduserer vi et nytt reduksjonstrinn og en ny gjetteprosedyre til algoritmen. Disse tillot oss å utvikle to implementeringer av algoritmen, som er i stand til å løse relativt store LWE-forekomster. Mens den første effektivt bare bruker RAM-minne og er fullt parallelliserbar, utnytter den andre en kombinasjon av RAM og disklagring for å overvinne minnebegrensningene gitt av RAM. - Vi fyller et tomrom i paringsbasert kryptografi. Dette ved å gi konkrete formler for å beregne hash-funksjon til G2, den andre gruppen i paringsdomenet, for Barreto-Lynn-Scott-familien av paringsvennlige elliptiske kurver.Public-key Cryptography relies on the assumption that some computational problems are hard to solve. In 1994, Peter Shor showed that the two most used computational problems, namely the Discrete Logarithm Problem and the Integer Factoring Problem, are not hard to solve anymore when using a quantum computer. Since then, researchers have worked on finding new computational problems that are resistant to quantum attacks to replace these two. Lattice-based Cryptography is the research field that employs cryptographic primitives involving hard problems defined on lattices, such as the Shortest Vector Problem and the Closest Vector Problem. The NTRU cryptosystem, published in 1998, was one of the first to be introduced in this field. The Learning With Error (LWE) problem was introduced in 2005 by Regev, and it is now considered one of the most promising computational problems to be employed on a large scale in the near future. Studying its hardness and finding new and faster algorithms that solve it became a leading research topic in Cryptology. This thesis includes the following contributions to the field: - A non-trivial reduction of the Mersenne Low Hamming Combination Search Problem, the underlying problem of an NTRU-like cryptosystem, to Integer Linear Programming (ILP). In particular, we find a family of weak keys. - A concrete security analysis of the Integer-RLWE, a hard computational problem variant of LWE introduced by Gu Chunsheng. We formalize a meet-in-the-middle attack and a lattice-based attack for this case, and we exploit a weakness of the parameters choice given by Gu to build an improved lattice-based attack. - An improvement of the Blum-Kalai-Wasserman algorithm to solve LWE. In particular, we introduce a new reduction step and a new guessing procedure to the algorithm. These allowed us to develop two implementations of the algorithm that are able to solve relatively large LWE instances. While the first one efficiently uses only RAM memory and is fully parallelizable, the second one exploits a combination of RAM and disk storage to overcome the memory limitations given by the RAM. - We fill a gap in Pairing-based Cryptography by providing concrete formulas to compute hash-maps to G2, the second group in the pairing domain, for the Barreto-Lynn-Scott family of pairing-friendly elliptic curves.Doktorgradsavhandlin

TRUST NO ONE; Homomorphic Encryption and its Applications

Masteroppgave i informatikkINF399MAMN-PROGMAMN-IN

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

ACORN: Input Validation for Secure Aggregation

Secure aggregation enables a server to learn the sum of client-held vectors in a privacy-preserving way, and has been successfully applied to distributed statistical analysis and machine learning. In this paper, we both introduce a more efficient secure aggregation construction and extend secure aggregation by enabling input validation, in which the server can check that clients\u27 inputs satisfy required constraints such as $L_0$, $L_2$, and $L_\infty$ bounds. This prevents malicious clients from gaining disproportionate influence on the computed aggregated statistics or machine learning model. Our new secure aggregation protocol improves the computational efficiency of the state-of-the-art protocol of Bell et al. (CCS 2020) both asymptotically and concretely: we show via experimental evaluation that it results in $2$-$8$X speedups in client computation in practical scenarios. Likewise, our extended protocol with input validation improves on prior work by more than $30$X in terms of client communiation (with comparable computation costs). Compared to the base protocols without input validation, the extended protocols incur only $0.1$X additional communication, and can process binary indicator vectors of length $1$M, or 16-bit dense vectors of length $250$K, in under $80$s of computation per client

Survey on Fully Homomorphic Encryption, Theory, and Applications

Data privacy concerns are increasing significantly in the context of Internet of Things, cloud services, edge computing, artificial intelligence applications, and other applications enabled by next generation networks. Homomorphic Encryption addresses privacy challenges by enabling multiple operations to be performed on encrypted messages without decryption. This paper comprehensively addresses homomorphic encryption from both theoretical and practical perspectives. The paper delves into the mathematical foundations required to understand fully homomorphic encryption (FHE). It consequently covers design fundamentals and security properties of FHE and describes the main FHE schemes based on various mathematical problems. On a more practical level, the paper presents a view on privacy-preserving Machine Learning using homomorphic encryption, then surveys FHE at length from an engineering angle, covering the potential application of FHE in fog computing, and cloud computing services. It also provides a comprehensive analysis of existing state-of-the-art FHE libraries and tools, implemented in software and hardware, and the performance thereof

A Practical TFHE-Based Multi-Key Homomorphic Encryption with Linear Complexity and Low Noise Growth

Fully Homomorphic Encryption enables arbitrary computations over encrypted data and it has a multitude of applications, e.g., secure cloud computing in healthcare or finance. Multi-Key Homomorphic Encryption (MKHE) further allows to process encrypted data from multiple sources: the data can be encrypted with keys owned by different parties. In this paper, we propose a new variant of MKHE instantiated with the TFHE scheme. Compared to previous attempts by Chen et al. and by Kwak et al., our scheme achieves computation runtime that is linear in the number of involved parties and it outperforms the faster scheme by a factor of 4.5-6.9x, at the cost of a slightly extended pre-computation. In addition, for our scheme, we propose and practically evaluate parameters for up to 128 parties, which enjoy the same estimated security as parameters suggested for the previous schemes (100 bits). It is also worth noting that our scheme—unlike the previous schemes—did not experience any error in any of our nine experiments, each running 1 000 trials

Physical-Layer Security, Quantum Key Distribution and Post-quantum Cryptography

The growth of data-driven technologies, 5G, and the Internet place enormous pressure on underlying information infrastructure. There exist numerous proposals on how to deal with the possible capacity crunch. However, the security of both optical and wireless networks lags behind reliable and spectrally efficient transmission. Significant achievements have been made recently in the quantum computing arena. Because most conventional cryptography systems rely on computational security, which guarantees the security against an efficient eavesdropper for a limited time, with the advancement in quantum computing this security can be compromised. To solve these problems, various schemes providing perfect/unconditional security have been proposed including physical-layer security (PLS), quantum key distribution (QKD), and post-quantum cryptography. Unfortunately, it is still not clear how to integrate those different proposals with higher level cryptography schemes. So the purpose of the Special Issue entitled “Physical-Layer Security, Quantum Key Distribution and Post-quantum Cryptography” was to integrate these various approaches and enable the next generation of cryptography systems whose security cannot be broken by quantum computers. This book represents the reprint of the papers accepted for publication in the Special Issue

Improved Robustness and Versatility of Lattice-Based Cryptography

Current public key cryptosystems that are based on the hardness of integer factorization and discrete logarithm are insecure in the presence of large-scale quantum computers. Much effort has been devoted to replacing the quantum-insecure cryptosystems with newly developed "post-quantum" cryptosystem candidates, conjectured to be secure against quantum attack. Lattice-based cryptography has been widely recognized as a prominent candidate for practical post-quantum security.This dissertation improves the robustness and versatility of lattice-based cryptography through the following three contributions: 1. Chapter 3 introduces a constant-round protocol for unauthenticated group key exchange (i.e., with security against a passive eavesdropper). Group key exchange protocols allow a set of N parties to agree on a shared, secret key by communicating over a public network. Our protocol is based on the hardness of a lattice problem, which hence yields (plausible) post-quantum security. 2. In Chapter 4, we propose a framework for cryptanalysis of lattice-based schemes when certain types of information about the secret are leaked. Our framework generalizes the primal lattice reduction attack. The generalization allows for integrating the leaked information progressively before running a final lattice reduction step. Our framework can estimate the amount of security loss caused by the leaked information, and perform lattice reduction attacks with leaked information when computationally feasible. 3. Chapter 5 introduces an approach towards a ring analogue of the Leftover Hash Lemma (LHL). The LHL is a mathematical tool often used in the analysis of various lattice-based cryptosystems, as well as their leakage-resilient counterparts. However, it does not hold in the ring setting, which is typical for efficient cryptosystems. Lyubashevsky et al. (Eurocrypt '13) proved a "regularity lemma," which is used in the ring setting instead of the LHL; however, this applies only for centered, spherical Gaussian inputs, while the LHL applies when the input is drawn from any high min-entropy distribution. Our approach generalizes the "regularity lemma" of Lyubashevsky et al. to certain conditional distributions. A number of Ring-Learning with Errors based cryptosystems can achieve certain leakage resilience properties using our results