Leakage-Resilient Attribute-Based Encryption with Attribute-Hiding

In this work, we present two generic frameworks for leakage-resilient attribute-based encryption (ABE), which is an improved version of ABE that can be proven secure even when part of the secret key is leaked. Our frameworks rely on the standard assumption ($k$-Lin) over prime-order groups. The first framework is designed for leakage-resilient ABE with attribute-hiding in the bounded leakage model. Prior to this work, no one had yet derived a generic leakage-resilient ABE framework with attribute-hiding. The second framework provides a generic method to construct leakage-resilient ABE in the continual leakage model. It is compatible with Zhang et al.\u27s work [DCC 2018] but more generic. Concretely, Zhang et al.\u27s framework cannot act on some specific ABE schemes while ours manages to do that. Technically, our frameworks are built on the predicate encoding of Chen et al.\u27s [EUROCRYPT 2015] combined with a method of adding redundancy. At last, several instantiations are derived from our frameworks, which cover the cases of zero inner-product predicate and non-zero inner-product predicate

Indistinguishability Obfuscation Without Multilinear Maps: New Paradigms via Low Degree Weak Pseudorandomness and Security Amplification

The existence of secure indistinguishability obfuscators (iO) has far-reaching implications, significantly expanding the scope of problems amenable to cryptographic study. All known approaches to constructing iO rely on $d$-linear maps. While secure bilinear maps are well established in cryptographic literature, the security of candidates for $d>2$ is poorly understood. We propose a new approach to constructing iO for general circuits. Unlike all previously known realizations of iO, we avoid the use of $d$-linear maps of degree $d \ge 3$. At the heart of our approach is the assumption that a new weak pseudorandom object exists. We consider two related variants of these objects, which we call perturbation resilient generator ($\Delta$RG) and pseudo flawed-smudging generator (PFG), respectively. At a high level, both objects are polynomially expanding functions whose outputs partially hide (or smudge) small noise vectors when added to them. We further require that they are computable by a family of degree-3 polynomials over $\mathbb{Z}$. We show how they can be used to construct functional encryption schemes with weak security guarantees. Finally, we use novel amplification techniques to obtain full security. As a result, we obtain iO for general circuits assuming: - Subexponentially secure LWE - Bilinear Maps - $\textrm{poly}(\lambda)$-secure 3-block-local PRGs - $\Delta$RGs or PFG

Leakage-resilient Identity-based Encryption in Bounded Retrieval Model with Nearly Optimal Leakage-Ratio

We propose new constructions of leakage-resilient public-key encryption (PKE) and identity-based encryption (IBE) schemes in the bounded retrieval model (BRM). In the BRM, adversaries are allowed to obtain at most $\ell$-bit leakage from a secret key and we can increase $\ell$ only by increasing the size of secret keys without losing efficiency in any other performance measure. We call $\ell/|\textsf{sk}|$ leakage-ratio where $|\textsf{sk}|$ denotes a bit-length of a secret key. Several PKE/IBE schemes in the BRM are known. However, none of these constructions achieve a constant leakage-ratio under a standard assumption in the standard model. Our PKE/IBE schemes are the first schemes in the BRM that achieve leakage-ratio $1-\epsilon$ for any constant $\epsilon>0$ under standard assumptions in the standard model. As previous works, we use identity-based hash proof systems (IB-HPS) to construct IBE schemes in the BRM. It is known that a parameter for IB-HPS called the universality-ratio is translated into the leakage-ratio of the resulting IBE scheme in the BRM. We construct an IB-HPS with universality-ratio $1-\epsilon$ for any constant $\epsilon>0$ based on any inner-product predicate encryption (IPE) scheme with compact secret keys. Such IPE schemes exist under the $d$-linear, subgroup decision, learning with errors, or computational bilinear Diffie-Hellman assumptions. As a result, we obtain IBE schemes in the BRM with leakage-ratio $1-\epsilon$ under any of these assumptions. Our PKE schemes are immediately obtained from our IBE schemes

Indistinguishability Obfuscation from Well-Founded Assumptions

In this work, we show how to construct indistinguishability obfuscation from subexponential hardness of four well-founded assumptions. We prove: Let $\tau \in (0,\infty), \delta \in (0,1), \epsilon \in (0,1)$ be arbitrary constants. Assume sub-exponential security of the following assumptions, where $\lambda$ is a security parameter, and the parameters $\ell,k,n$ below are large enough polynomials in $\lambda$: - The SXDH assumption on asymmetric bilinear groups of a prime order $p = O(2^\lambda)$, - The LWE assumption over $\mathbb{Z}_{p}$ with subexponential modulus-to-noise ratio $2^{k^\epsilon}$, where $k$ is the dimension of the LWE secret, - The LPN assumption over $\mathbb{Z}_p$ with polynomially many LPN samples and error rate $1/\ell^\delta$, where $\ell$ is the dimension of the LPN secret, - The existence of a Boolean PRG in $\mathsf{NC}^0$ with stretch $n^{1+\tau}$, Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exists

Leakage-Resilient Inner-Product Functional Encryption in the Bounded-Retrieval Model

We propose a leakage-resilient inner-product functional encryption scheme (IPFE) in the bounded-retrieval model (BRM). This is the first leakage-resilient functional encryption scheme in the BRM. In our leakage model, an adversary is allowed to obtain at most $l$-bit knowledge from each secret key. And our scheme can flexibly tolerate arbitrarily leakage bound $l$, by only increasing the size of secret keys, while keeping all other parts small and independent of $l$. Technically, we develop a new notion: Inner-product hash proof system (IP-HPS). IP-HPS is a variant of traditional hash proof systems. Its output of decapsulation is an inner-product value, instead of the encapsulated key. We propose an IP-HPS scheme under DDH-assumption. Then we show how to make an IP-HPS scheme to tolerate $l\u27$-bit leakage, and we can achieve arbitrary large $l\u27$ by only increasing the size of secret keys. Finally, we show how to build a leakage-resilient IPFE in the BRM with leakage bound $l=\frac{l\u27}{n}$ from our IP-HPS scheme

Advances in Functional Encryption

Functional encryption is a novel paradigm for public-key encryption that enables both fine-grained access control and selective computation on encrypted data, as is necessary to protect big, complex data in the cloud. In this thesis, I provide a brief introduction to functional encryption, and an overview of my contributions to the area

How to leverage hardness of constant degree expanding polynomials over R to build iO

In this work, we introduce and construct $D$-restricted Functional Encryption (FE) for any constant $D \ge 3$, based only on the SXDH assumption over bilinear groups. This generalizes the notion of $3$-restricted FE recently introduced and constructed by Ananth et al. (ePrint 2018) in the generic bilinear group model. A $D=(d+2)$-restricted FE scheme is a secret key FE scheme that allows an encryptor to efficiently encrypt a message of the form $M=(\vec{x},\vec{y},\vec{z})$. Here, $\vec{x}\in F_{p}^{d\times n}$ and $\vec{y},\vec{z}\in F_{p}^n$. Function keys can be issued for a function $f=\Sigma_{\vec{I}=(i_1,..,i_d,j,k)}\ c_{\vec{I}}\cdot \vec{x}[1,i_1] \cdots \vec{x}[d,i_d] \cdot \vec{y}[j]\cdot \vec{z}[k]$ where the coefficients $c_{\vec{I}}\in F_{p}$. Knowing the function key and the ciphertext, one can learn $f(\vec{x},\vec{y},\vec{z})$, if this value is bounded in absolute value by some polynomial in the security parameter and $n$. The security requirement is that the ciphertext hides $\vec{y}$ and $\vec{z}$, although it is not required to hide $\vec{x}$. Thus $\vec{x}$ can be seen as a public attribute. $D$-restricted FE allows for useful evaluation of constant-degree polynomials, while only requiring the SXDH assumption over bilinear groups. As such, it is a powerful tool for leveraging hardness that exists in constant-degree expanding families of polynomials over $\mathbb{R}$. In particular, we build upon the work of Ananth et al. to show how to build indistinguishability obfuscation (iO) assuming only SXDH over bilinear groups, LWE, and assumptions relating to weak pseudorandom properties of constant-degree expanding polynomials over $\mathbb{R}$

Adaptive-secure identity-based inner-product functional encryption and its leakage-resilience

There are lots of applications of inner-product functional encryption (IPFE). In this paper, we consider two important extensions of it. One is to enhance IPFE with access control such that only users with a pre-defined identity are allowed to compute the inner product, referred as identity-based inner-product functional encryption (IBIPFE). We formalize the definition of IBIPFE, and propose the first adaptive-secure IBIPFE scheme from Decisional Bilinear Diffie-Hellman (DBDH) assumption. In an IBIPFE scheme, the ciphertext is related to a vector $\vec{x}$ and a new parameter, identity ID. Each secret key is also related to a vector $\vec{y}$ and an identity ID\u27. The decryption algorithm will output the inner-product value $$ only if ID $=$ ID\u27. The other extension is to make IBIPFE leakage resilient. We consider the bounded-retrieval model (BRM) in which an adversary can learn at most $l$ bits information from each secret key. Here, $l$ is the leakage bound determined by some external parameters, and it can be set arbitrarily large. After giving the security definition of leakage-resilient IBIPFE, we extend our IBIPFE scheme into a leakage-resilient IBIPFE scheme in the BRM by hash proof system (HPS)

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