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

Riding on Asymmetry: Efficient ABE for Branching Programs

In an Attribute-Based Encryption (ABE) scheme the ciphertext encrypting a message $\mu$, is associated with a public attribute vector \vecx and a secret key \sk_P is associated with a predicate $P$. The decryption returns $\mu$ if and only if P(\vecx) = 1. ABE provides efficient and simple mechanism for data sharing supporting fine-grained access control. Moreover, it is used as a critical component in constructions of succinct functional encryption, reusable garbled circuits, token-based obfuscation and more. In this work, we describe a new efficient ABE scheme for a family of branching programs with short secret keys and from a mild assumption. In particular, in our construction the size of the secret key for a branching program $P$ is |P| + \poly(\secp), where \secp is the security parameter. Our construction is secure assuming the standard Learning With Errors (LWE) problem with approximation factors $n^{\omega(1)}$. Previous constructions relied on $n^{O(\log n)}$ approximation factors of LWE (resulting in less efficient parameters instantiation) or had large secret keys of size |P| \times \poly(\secp). We rely on techniques developed by Boneh et al. (EUROCRYPT\u2714) and Brakerski et al. (ITCS\u2714) in the context of ABE for circuits and fully-homomorphic encryption

Constrained Pseudorandom Functions: Verifiable and Delegatable

Constrained pseudorandom functions (introduced independently by Boneh and Waters (CCS 2013), Boyle, Goldwasser, and Ivan (PKC 2014), and Kiayias, Papadopoulos, Triandopoulos, and Zacharias (CCS 2013)), are pseudorandom functions (PRFs) that allow the owner of the secret key $k$ to compute a constrained key $k_f$, such that anyone who possesses $k_f$ can compute the output of the PRF on any input $x$ such that $f(x) = 1$ for some predicate $f$. The security requirement of constrained PRFs state that the PRF output must still look indistinguishable from random for any $x$ such that $f(x) = 0$. Boneh and Waters show how to construct constrained PRFs for the class of bit-fixing as well as circuit predicates. They explicitly left open the question of constructing constrained PRFs that are delegatable - i.e., constrained PRFs where the owner of $k_f$ can compute a constrained key $k_{f\u27}$ for a further restrictive predicate $f\u27$. Boyle, Goldwasser, and Ivan left open the question of constructing constrained PRFs that are also verifiable. Verifiable random functions (VRFs), introduced by Micali, Rabin, and Vadhan (FOCS 1999), are PRFs that allow the owner of the secret key $k$ to prove, for any input $x$, that $y$ indeed is the output of the PRF on $x$; the security requirement of VRFs state that the PRF output must still look indistinguishable from random, for any $x$ for which a proof is not given. In this work, we solve both the above open questions by constructing constrained pseudorandom functions that are simultaneously verifiable and delegatable

Reducing Depth in Constrained PRFs: From Bit-Fixing to NC1

The candidate construction of multilinear maps by Garg, Gentry, and Halevi (Eurocrypt 2013) has lead to an explosion of new cryptographic constructions ranging from attribute-based encryption (ABE) for arbitrary polynomial size circuits, to program obfuscation, and to constrained pseudorandom functions (PRFs). Many of these constructions require k-linear maps for large k. In this work, we focus on the reduction of k in certain constructions of access control primitives that are based on k-linear maps; in particular, we consider the case of constrained PRFs and ABE. We construct the following objects: - A constrained PRF for arbitrary circuit predicates based on (n+l_{OR}-1)-linear maps (where n is the input length and l_{OR} denotes the OR-depth of the circuit). - For circuits with a specific structure, we also show how to construct such PRFs based on (n+l_{AND}-1)-linear maps (where l_{AND} denotes the AND-depth of the circuit). We then give a black-box construction of a constrained PRF for NC1 predicates, from any bit-fixing constrained PRF that fixes only one of the input bits to 1; we only require that the bit-fixing PRF have certain key homomorphic properties. This construction is of independent interest as it sheds light on the hardness of constructing constrained PRFs even for ``simple\u27\u27 predicates such as bit-fixing predicates. Instantiating this construction with the bit-fixing constrained PRF from Boneh and Waters (Asiacrypt 2013) gives us a constrained PRF for NC1 predicates that is based only on n-linear maps, with no dependence on the predicate. In contrast, the previous constructions of constrained PRFs (Boneh and Waters, Asiacrypt 2013) required (n+l+1)-linear maps for circuit predicates (where l is the total depth of the circuit) and n-linear maps even for bit-fixing predicates. We also show how to extend our techniques to obtain a similar improvement in the case of ABE and construct ABE for arbitrary circuits based on (l_{OR}+1)-linear (respectively (l_{AND}+1)-linear) maps

Iron: Functional Encryption using Intel SGX

Functional encryption (FE) is an extremely powerful cryptographic mechanism that lets an authorized entity compute on encrypted data, and learn the results in the clear. However, all current cryptographic instantiations for general FE are too impractical to be implemented. We build Iron, a practical and usable FE system using Intel\u27s recent Software Guard Extensions (SGX). We show that Iron can be applied to complex functionalities, and even for simple functions, outperforms the best known cryptographic schemes. We argue security by modeling FE in the context of hardware elements, and prove that Iron satisfies the security model

How to prove any NP statement jointly? Efficient Distributed-prover Zero-Knowledge Protocols

Traditional zero-knowledge protocols have been studied and optimized for the setting where a single prover holds the complete witness and tries to convince a verifier about a predicate on the witness, without revealing any additional information to the verifier. In this work, we study the notion of distributed-prover zero knowledge (DPZK) for arbitrary predicates where the witness is shared among multiple mutually distrusting provers and they want to convince a verifier that their shares together satisfy the predicate. We make the following contributions to the notion of distributed proof generation: (i) we propose a new MPC-style security definition to capture the adversarial settings possible for different collusion models between the provers and the verifier, (ii) we discuss new efficiency parameters for distributed proof generation such as the number of rounds of interaction and the amount of communication among the provers, and (iii) we propose a compiler that realizes distributed proof generation from the zero-knowledge protocols in the Interactive Oracle Proofs (IOP) paradigm. Our compiler can be used to obtain DPZK from arbitrary IOP protocols, but the concrete efficiency overheads are substantial in general. To this end, we contribute (iv) a new zero-knowledge IOP $\textsf{Graphene}$ which can be compiled into an efficient DPZK protocol. The $(\mathsf{D} + 1)$-DPZK protocol $\text{D-Graphene}$, with $\mathsf{D}$ provers and one verifier, admits $O(N^{1/c})$ proof size with a communication complexity of $O(\mathsf{D}^2\cdot (N^{1-2/c} + N_s))$, where $N$ is the number of gates in the arithmetic circuit representing the predicate and $N_s$ is the number of wires that depends on inputs from two or more parties. Significantly, only the distributed proof generation in $\text{D-Graphene}$ requires interaction among the provers. $\text{D-Graphene}$ compares favourably with the DPZK protocols obtained from the state-of-art zero-knowledge protocols, even those not modelled as IOPs

Private Certifier Intersection

We initiate the study of Private Certifier Intersection (PCI), which allows mutually distrusting parties to establish a trust basis for cross-validation of claims if they have one or more trust authorities (certifiers) in common. This is one of the essential requirements for verifiable presentations in Web 3.0, since it provides additional privacy without compromising on decentralization. A PCI protocol allows two or more parties holding certificates to identify a common set of certifiers while additionally validating the certificates issued by such certifiers, without leaking any information about the certifiers not in the output intersection. In this paper, we formally define the notion of multi-party PCI in the Simplified-UC framework for two different settings depending on whether certificates are required for any of the claims (called PCI-Any) or all of the claims (called PCI-All). We then design and implement two provably secure and practically efficient PCI protocols supporting validation of digital signature-based certificates: a PCI-Any protocol for ECDSA-based certificates and a PCI-All protocol for BLS-based certificates. The technical centerpiece of our proposals is the first secretsharing-based MPC framework supporting efficient computation of elliptic curve-based arithmetic operations, including elliptic curve pairings, in a black-box way. We implement this framework by building on top of the well-known MP-SPDZ library using OpenSSL and RELIC for elliptic curve operations, and use this implementation to benchmark our proposed PCI protocols in the LAN and WAN settings. In an intercontinental WAN setup with parties located in different continents, our protocols execute in less than a minute on input sets of size 40, which demonstrates the practicality of our proposed solutions

On the Security of ID Based Signcryption Schemes

A signcryption scheme is secure only if it satisfies both the confidentiality and the unforgeability properties. All the ID based signcryption schemes presented in the standard model till now do not have either the confidentiality or the unforgeability or both of these properties. Cryptanalysis of some of the schemes have been proposed already. In this work, we present the security attacks on `Secure ID based signcryption in the standard model\u27 proposed by Li-Takagi and `Further improvement of an identity-based signcryption scheme in the standard model\u27 by Li et al. and the flaws in the proof of security of `Efficient ID based signcryption in the standard model\u27 proposed by Li et al., which are the recently proposed ID based signcryption schemes in the standard model. We also present the cryptanalysis of `Construction of identity based signcryption schemes\u27 proposed by Pandey-Barua and the cryptanalysis of `Identity-Based Signcryption from Identity-Based Cryptography\u27 proposed by Lee-Seo-Lee. These schemes present the methods of constructing an ID based signcryption scheme in the random oracle model from an ID based signature scheme and an ID based encryption scheme. Since none of the existing schemes in the standard model are found to be provably secure, we analyse the security of signcryption schemes got by directly combining an ID based signature scheme and an ID based encryption scheme in the standard model

ID Based Signcryption Scheme in Standard Model

Designing an ID based signcryption scheme in the standard model is among the most interesting and important problems in cryptography. However, all the existing systems in the ID based setting, in the standard model, do not have either the unforgeability property or the indistinguishability property or both of them. In this paper, we present the first provably secure ID based signcryption scheme in the standard model with both these properties. The unforgeability property of this scheme is based on the hardness of Computational Diffie-Hellman problem and the indistinguishability property of this scheme is based on the hardness of Decisional Bilinear Diffie-Hellman problem. Our scheme is strongly unforgeable in the strong attack mode called insider security. Moreover, our scheme possess an interesting property called public verifiability of the ciphertext. Our scheme integrates cleverly, a modified version of Waters\u27 IBE and a suitably modified version of the ID based signature scheme in the standard model proposed by Paterson et al. However, our security reductions are more efficient. Specifically, while the security reductions for indistinguishability is similar to the bounds of Waters\u27 scheme, the unforgeability reductions are way better than the bounds for Paterson et al.\u27s scheme