Preventing Adaptive Key Recovery Attacks on the Gentry-Sahai-Waters Leveled Homomorphic Encryption Scheme

A major open problem is to protect leveled homomorphic encryption from adaptive attacks that allow an adversary to learn the private key. The only positive results in this area are by Loftus, May, Smart and Vercauteren. They use a notion of valid ciphertexts and obtain an IND-CCA1 scheme under a strong knowledge assumption, but they also show their scheme is not secure under a natural adaptive attack based on a ciphertext validity oracle . However, due to recent cryptanalysis their scheme is no longer considered secure. The main contribution of this paper is to explore a new approach to achieving this goal, which does not rely on a notion of valid ciphertexts . The idea is to generate a one-time private key every time the decryption algorithm is run, so that even if an attacker can learn some bits of the one-time private key from each decryption query, this does not allow them to compute a valid private key. This is the full version of the paper. The short version, which appeared in Provsec 2016, presented a variant of the Gentry-Sahai-Waters (GSW) levelled homomorphic encryption scheme. Damien Stehle pointed out an attack on our variant of this scheme that had not been anticipated in the Provsec paper; we explain the attack in this full version. This version of the paper also contains a new dual version of the GSW scheme. We give an explanation of why the known attacks no longer break the system. It remains an open problem to develop a scheme for which one can prove IND-CCA1 security

A Practical Adaptive Key Recovery Attack on the LGM (GSW-like) Cryptosystem

Under embargo until: 2022-07-15We present an adaptive key recovery attack on the leveled homomorphic encryption scheme suggested by Li, Galbraith and Ma (Provsec 2016), which itself is a modification of the GSW cryptosystem designed to resist key recovery attacks by using a different linear combination of secret keys for each decryption. We were able to efficiently recover the secret key for a realistic choice of parameters using a statistical attack. In particular, this means that the Li, Galbraith and Ma strategy does not prevent adaptive key recovery attacks.acceptedVersio

Survey on securing data storage in the cloud

Cloud Computing has become a well-known primitive nowadays; many researchers and companies are embracing this fascinating technology with feverish haste. In the meantime, security and privacy challenges are brought forward while the number of cloud storage user increases expeditiously. In this work, we conduct an in-depth survey on recent research activities of cloud storage security in association with cloud computing. After an overview of the cloud storage system and its security problem, we focus on the key security requirement triad, i.e., data integrity, data confidentiality, and availability. For each of the three security objectives, we discuss the new unique challenges faced by the cloud storage services, summarize key issues discussed in the current literature, examine, and compare the existing and emerging approaches proposed to meet those new challenges, and point out possible extensions and futuristic research opportunities. The goal of our paper is to provide a state-of-the-art knowledge to new researchers who would like to join this exciting new field

Studies on the Security of Selected Advanced Asymmetric Cryptographic Primitives

The main goal of asymmetric cryptography is to provide confidential communication, which allows two parties to communicate securely even in the presence of adversaries. Ever since its invention in the seventies, asymmetric cryptography has been improved and developed further, and a formal security framework has been established around it. This framework includes different security goals, attack models, and security notions. As progress was made in the field, more advanced asymmetric cryptographic primitives were proposed, with other properties in addition to confidentiality. These new primitives also have their own definitions and notions of security. This thesis consists of two parts, where the first relates to the security of fully homomorphic encryption and related primitives. The second part presents a novel cryptographic primitive, and defines what security goals the primitive should achieve. The first part of the thesis consists of Article I, II, and III, which all pertain to the security of homomorphic encryption schemes in one respect or another. Article I demonstrates that a particular fully homomorphic encryption scheme is insecure in the sense that an adversary with access only to the public material can recover the secret key. It is also shown that this insecurity mainly stems from the operations necessary to make the scheme fully homomorphic. Article II presents an adaptive key recovery attack on a leveled homomorphic encryption scheme. The scheme in question claimed to withstand precisely such attacks, and was the only scheme of its kind to do so at the time. This part of the thesis culminates with Article III, which is an overview article on the IND-CCA1 security of all acknowledged homomorphic encryption schemes. The second part of the thesis consists of Article IV, which presents Vetted Encryption (VE), a novel asymmetric cryptographic primitive. The primitive is designed to allow a recipient to vet who may send them messages, by setting up a public filter with a public verification key, and providing each vetted sender with their own encryption key. There are three different variants of VE, based on whether the sender is identifiable to the filter and/or the recipient. Security definitions, general constructions and comparisons to already existing cryptographic primitives are provided for all three variants.Doktorgradsavhandlin

On the IND-CCA1 Security of FHE Schemes

Fully homomorphic encryption (FHE) is a powerful tool in cryptography that allows one to perform arbitrary computations on encrypted material without having to decrypt it first. There are numerous FHE schemes, all of which are expanded from somewhat homomorphic encryption (SHE) schemes, and some of which are considered viable in practice. However, while these FHE schemes are semantically (IND-CPA) secure, the question of their IND-CCA1 security is much less studied, and we therefore provide an overview of the IND-CCA1 security of all acknowledged FHE schemes in this paper. To give this overview, we grouped the SHE schemes into broad categories based on their similarities and underlying hardness problems. For each category, we show that the SHE schemes are susceptible to either known adaptive key recovery attacks, a natural extension of known attacks, or our proposed attacks. Finally, we discuss the known techniques to achieve IND-CCA1-secure FHE and SHE schemes. We concluded that none of the proposed schemes were IND-CCA1-secure and that the known general constructions all had their shortcomings.publishedVersio

Privacy-enhancing distributed protocol for data aggregation based on blockchain and homomorphic encryption

The recent increase in reported incidents of security breaches compromising users' privacy call into question the current centralized model in which third-parties collect and control massive amounts of personal data. Blockchain has demonstrated that trusted and auditable computing is possible using a decentralized network of peers accompanied by a public ledger. Furthermore, Homomorphic Encryption (HE) guarantees confidentiality not only on the computation but also on the transmission, and storage processes. The synergy between Blockchain and HE is rapidly increasing in the computing environment. This research proposes a privacy-enhancing distributed and secure protocol for data aggregation backboned by Blockchain and HE technologies. Blockchain acts as a distributed ledger which facilitates efficient data aggregation through a Smart Contract. On the top, HE will be used for data encryption allowing private aggregation operations. The theoretical description, potential applications, a suggested implementation and a performance analysis are presented to validate the proposed solution.This work has been partially supported by the Basque Country Government under the ELKARTEK program, project TRUSTIND (KK- 2020/00054). It has also been partially supported by the H2020 TERMINET project (GA 957406)

Keyed-Fully Homomorphic Encryption without Indistinguishability Obfuscation

(Fully) homomorphic encryption ((F)HE) allows users to publicly evaluate circuits on encrypted data. Although public homomorphic evaluation property has various applications, (F)HE cannot achieve security against chosen ciphertext attacks (CCA2) due to its nature. To achieve both the CCA2 security and homomorphic evaluation property, Emura et al. (PKC 2013) introduced keyed-homomorphic public key encryption (KH-PKE) and formalized its security denoted by KH-CCA security. KH-PKE has a homomorphic evaluation key that enables users to perform homomorphic operations. Intuitively, KH-PKE achieves the CCA2 security unless adversaries have a homomorphic evaluation key. Although Lai et al. (PKC 2016) proposed the first keyed-fully homomorphic encryption (keyed-FHE) scheme, its security relies on the indistinguishability obfuscation (iO), and this scheme satisfies a weak variant of KH-CCA security. Here, we propose a generic construction of a KH-CCA secure keyed-FHE scheme from an FHE scheme secure against non-adaptive chosen ciphertext attack (CCA1) and a strong dual-system simulation-sound non-interactive zero-knowledge (strong DSS-NIZK) argument system by using the Naor-Yung paradigm. We show that there are a strong DSS-NIZK and an IND-CCA1 secure FHE scheme that are suitable for our generic construction. This shows that there exists a keyed-FHE scheme from simpler primitives than iO

vr2^2FHE- Securing FHE from Reaction-based Key Recovery Attacks

Fully Homomorphic Encryption (FHE) promises to secure our data on the untrusted cloud, by allowing arbitrary computations on encrypted data. However, the malleability and flexibility provided by FHE schemes also open up arena for integrity issues where a cloud server can intentionally or accidentally perturb client’s data. Contemporary FHE schemes do not provide integrity guarantees and, thus, assume a honest-but-curious server who, although curious to glean sensitive information, performs all operations judiciously. However, in practice, a server can also be malicious as well as compromised, where it can perform crafted perturbations in the cloud-stored data and computational results to entice the client into providing feedback. While some effort has been made to protect FHE schemes against such adversaries, they do not completely stop such attacks, given the wide scope of deployment of contemporary FHE schemes in modern-day applications. In this work, we demonstrate reaction-based full-key recovery attack on two of the well-known FHE schemes, TFHE and FHEW. We first define practical scenarios where a client pursuing FHE services from a malicious server can inadvertently act as a Ciphertext Verification Oracle (CVO) by reacting to craftily perturbed computations. In particular, we propose two novel and distinct reaction attacks on both TFHE and FHEW. In the first attack, the adversary (malicious server) extracts the underlying error values to form an exact system of Learning with Errors (LWE) equations. As the security of LWE collapses with the leakage of the errors, the adversary is capable of extracting the secret key. In the second attack, we show that the attacker can directly recover the secret key in a bit-by-bit fashion by taking advantage of the key distribution of these FHE schemes. The results serve as a stark reminder that FHE schemes need to be secured at the application level apart from being secure at the primitive level so that the security of participants against realistic attacks can be ensured. As the currently available verifiable FHE schemes in literature cannot stop such attacks, we propose vr$^2$FHE (Verify - then - Repair or React) that is built on top of present implementations of TFHE and FHEW, using the concept of the Merkle tree. vr$^2$FHE first verifies the computational results at the client end and then, depending on the perturbation pattern, either repairs the message or chooses to request for recomputation. We show that such requests are benign as they do not leak exploitable information to the server, thereby thwarting both the attacks on TFHE and FHEW

User-Controlled Computations in Untrusted Computing Environments

Computing infrastructures are challenging and expensive to maintain. This led to the growth of cloud computing with users renting computing resources from centralized cloud providers. There is also a recent promise in providing decentralized computing resources from many participating users across the world. The compute on your own server model hence is no longer prominent. But, traditional computer architectures, which were designed to give a complete power to the owner of the computing infrastructure, continue to be used in deploying these new paradigms. This forces users to completely trust the infrastructure provider on all their data. The cryptography and security community research two different ways to tackle this problem. The first line of research involves developing powerful cryptographic constructs with formal security guarantees. The primitive of functional encryption (FE) formalizes the solutions where the clients do not interact with the sever during the computation. FE enables a user to provide computation-specific secret keys which the server can use to perform the user specified computations (and only those) on her encrypted data. The second line of research involves designing new hardware architectures which remove the infrastructure owner from the trust base. The solutions here tend to have better performance but their security guarantees are not well understood. This thesis provides contributions along both lines of research. In particular, 1) We develop a (single-key) functional encryption construction where the size of secret keys do not grow with the size of descriptions of the computations, while also providing a tighter security reduction to the underlying computational assumption. This construction supports the computation class of branching programs. Previous works for this computation class achieved either short keys or tighter security reductions but not both. 2) We formally model the primitive of trusted hardware inspired by Intel's Software Guard eXtensions (SGX). We then construct an FE scheme in a strong security model using this trusted hardware primitive. We implement this construction in our system Iron and evaluate its performance. Previously, the constructions in this model relied on heavy cryptographic tools and were not practical. 3) We design an encrypted database system StealthDB that provides complete SQL support. StealthDB is built on top of Intel SGX and designed with the usability and security limitations of SGX in mind. The StealthDB implementation on top of Postgres achieves practical performance (30% overhead over plaintext evaluation) with strong leakage profile against adversaries who get snapshot access to the memory of the system. It achieves a more gradual degradation in security against persistent adversaries than the prior designs that aimed at practical performance and complete SQL support. We finally survey the research on providing security against quantum adversaries to the building blocks of SGX

Practical yet Provably Secure: Complex Database Query Execution over Encrypted Data

Encrypted databases provide security for outsourced data. In this work novel encryption schemes supporting different database query types are presented enabling complex database queries over encrypted data. For specific constructions enabling exact keyword queries, range queries, database joins and substring queries over encrypted data we prove security in a formal framework, present a theoretical runtime analysis and provide an assessment of practical performance characteristics