Adaptively Secure Functional Encryption for Finite Languages from DLIN Assumption

In this paper, we present Functional Encryption (FE) schemes for finite languages from standard static assumption, viz., \textit{Decisional Linear} (DLIN) assumption. These finite languages are described by Deterministic Finite Automatas (DFAs). Our first scheme is ciphertext-policy functional encryption (CP-FE), where a key \sk_w is labeled with a string $w$ over a fixed alphabet $\Sigma$ and a ciphertext \cipher_\amn is associated with a DFA \amn over the same alphabet $\Sigma$. The key \sk_w can extract the message from the ciphertext \cipher_\amn if the DFA \amn accepts the string $w$. This CP-FE scheme is constructed based on attribute-based encryption (ABE) structure of Okamoto-Takashima in Asiacrypt, 2012. To achieve the adaptive security, we put bounds on number of occurrences of any symbol in a string and in the set of transition tuples of a DFA. Due to this restriction, the size of key space (where the keys are indexed with strings) is reduced to finite. Hence, the functional scope of any DFA in our system can capture only finite language. Similarly, we obtain our second adaptively secure FE scheme in key-policy flavor from DLIN assumption. Both the schemes are shown to be secure in the standard model

New Lower Bounds on Predicate Entropy for Function Private Public-Key Predicate Encryption

We present function private public-key predicate encryption schemes from standard cryptographic assumptions, that achieve new lower bounds on the min-entropy of underlying predicate distributions. Existing function private predicate encryption constructions in the public-key setting can be divided into two broad categories. The first category of constructions are based on standard assumptions, but impose highly stringent requirements on the min-entropy of predicate distributions, thereby limiting their applicability in the context of real-world predicates. For example, the statistically function private constructions of Boneh, Raghunathan and Segev (CRYPTO\u2713 and ASIACRYPT\u2713) are inherently restricted to predicate distributions with min-entropy roughly proportional to the security parameter $\lambda$. The second category of constructions mandate more relaxed min-entropy requirements, but are either based on non-standard assumptions (such as indistinguishability obfuscation) or are secure in the generic group model. In this paper, we affirmatively bridge the gap between these categories by presenting new public-key constructions for identity-based encryption, hidden-vector encryption, and subspace-membership encryption~(a generalization of inner-product encryption) that are both data and function private under variants of the well-known DBDH, DLIN and matrix DDH assumptions, while relaxing the min-entropy requirement on the predicate distributions to $\omega(\log\lambda)$. In summary, we establish that the minimum predicate entropy necessary for any meaningful notion of function privacy in the public-key setting, is in fact, sufficient, for a fairly rich class of predicates

CP-ABE for Circuits (and more) in the Symmetric Key Setting

The celebrated work of Gorbunov, Vaikuntanathan and Wee provided the first key policy attribute based encryption scheme (ABE) for circuits from the Learning With Errors (LWE) assumption. However, the arguably more natural ciphertext policy variant has remained elusive, and is a central primitive not yet known from LWE. In this work, we construct the first symmetric key ciphertext policy attribute based encryption scheme (CP-ABE) for all polynomial sized circuits from the learning with errors (LWE) assumption. In more detail, the ciphertext for a message $m$ is labelled with an access control policy $f$, secret keys are labelled with public attributes $x$ from the domain of $f$ and decryption succeeds to yield the hidden message $m$ if and only if $f(x)=1$. The size of our public and secret key do not depend on the size of the circuits supported by the scheme -- this enables our construction to support circuits of unbounded size (but bounded depth). Our construction is secure against collusions of unbounded size. We note that current best CP-ABE schemes [BSW07,Wat11,LOSTW10,OT10,LW12,RW13,Att14,Wee14,AHY15,CGW15,AC17,KW19] rely on pairings and only support circuits in the class NC1 (albeit in the public key setting). We adapt our construction to the public key setting for the case of bounded size circuits. The size of the ciphertext and secret key as well as running time of encryption, key generation and decryption satisfy the efficiency properties desired from CP-ABE, assuming that all algorithms have RAM access to the public key. However, the running time of the setup algorithm and size of the public key depends on the circuit size bound, restricting the construction to support circuits of a-priori bounded size. We remark that the inefficiency of setup is somewhat mitigated by the fact that setup must only be run once. We generalize our construction to consider attribute and function hiding. The compiler of lockable obfuscation upgrades any attribute based encryption scheme to predicate encryption, i.e. with attribute hiding [GKW17,WZ17]. Since lockable obfuscation can be constructed from LWE, we achieve ciphertext policy predicate encryption immediately. For function privacy, we show that the most natural notion of function hiding ABE for circuits, even in the symmetric key setting, is sufficient to imply indistinguishability obfuscation. We define a suitable weakening of function hiding to sidestep the implication and provide a construction to achieve this notion for both the key policy and ciphertext policy case. Previously, the largest function class for which function private predicate encryption (supporting unbounded keys) could be achieved was inner product zero testing, by Shen, Shi and Waters [SSW09]

New Proof Techniques for DLIN-Based Adaptively Secure Attribute-Based Encryption

We propose adaptively secure attribute-based encryption (ABE) schemes for boolean formulas over large universe attributes from the decisional linear (DLIN) assumption, which allow attribute reuse in an available formula without the previously employed redundant multiple encoding technique. Thus our KP-(resp. CP-)ABE has non-redundant ciphertexts (resp. secret keys). For achieving the results, we develop a new encoding method for access policy matrix for ABE, by decoupling linear secret sharing (LSS) into its matrix and randomness, and partially randomizing the LSS shares in simulation. The new techniques are of independent interest and we expect it will find another application than ABE

Simple and Efficient FE for Quadratic Functions

This paper presents the first functional encryption schemes for quadratic functions (or degree-2 polynomials) achieving simulation-based security in the semi-adaptive model with constant-size secret key. The unique prior construction with the same security guarantee by Gay [PKC 20] has secret keys of size linear in the message size. They also enjoy shorter ciphertexts: - our first scheme is based on bilateral DLIN (decisional linear) assumption as Gay\u27s scheme and the ciphertext is 15% shorter; - our second scheme based on SXDH assumption and bilateral DLIN assumption is more efficient; it has 67% shorter ciphertext than previous SXDH-based scheme with selective indistinguishability security by Baltico et al. [CRYPTO 17]; the efficiency is comparable to their second scheme in the generic group model. Technically, we roughly combine Wee\u27s ``secret-key-to-public-key\u27\u27 compiler [TCC 17] with Gay\u27s paradigm [PKC 20]. We avoid (partial) function-hiding inner-product functional encryption used in Gay\u27s work and make our schemes conceptually simpler

Decentralized Multi-Authority ABE for NC^1 from Computational-BDH

Decentralized multi-authority attribute-based encryption (-) is a strengthening of standard ciphertext-policy attribute-based encryption so that there is no trusted central authority: any party can become an authority and there is no requirement for any global coordination other than the creation of an initial set of common reference parameters. Essentially, any party can act as an authority for some attribute by creating a public key of its own and issuing private keys to different users that reflect their attributes. This paper presents the first - proven secure under the standard search variant of bilinear Diffie-Hellman (CBDH) and in the random oracle model. Our scheme supports all access policies captured by 1 circuits. All previous constructions were proven secure in the random oracle model and additionally were based on decision assumptions such as the DLIN assumption, non-standard -type assumptions, or subspace decision assumptions over composite-order bilinear groups

FABEO: Fast Attribute-Based Encryption with Optimal Security

Attribute-based encryption (ABE) enables fine-grained access control on encrypted data and has a large number of practical applications. This paper presents FABEO: faster pairing-based ciphertext-policy and key-policy ABE schemes that support expressive policies and put no restriction on policy type or attributes, and the first to achieve optimal, adaptive security with multiple challenge ciphertexts. We implement our schemes and demonstrate that they perform better than the state-of-the-art (Bethencourt et al. S&P 2007, Agrawal et al., CCS 2017 and Ambrona et al., CCS 2017) on all parameters of practical interest

Efficient IBE with Tight Reduction to Standard Assumption in the Multi-challenge Setting

In 2015, Hofheinz et al. [PKC, 2015] extended Chen and Wee\u27s almost-tight reduction technique for identity based encryptions (IBE) [CRYPTO, 2013] to the multi-instance, multi-ciphertext (MIMC, or multi-challenge) setting, where the adversary is allowed to obtain multiple challenge ciphertexts from multiple IBE instances, and gave the first almost-tightly secure IBE in this setting using composite-order bilinear groups. Several prime-order realizations were proposed lately. However there seems to be a dilemma of high system performance (involving ciphertext/key size and encryption/decryption cost) or weak/standard security assumptions. A natural question is: can we achieve high performance without relying on stronger/non-standard assumptions? In this paper, we answer the question in the affirmative by describing a prime-order IBE scheme with the same performance as the most efficient solutions so far but whose security still relies on the standard k-linear (k-Lin) assumption. Our technical start point is Blazy et al.\u27s almost-tightly secure IBE [CRYPTO, 2014]. We revisit their concrete IBE scheme and associate it with the framework of nested dual system group. This allows us to extend Blazy et al.\u27s almost-tightly secure IBE to the MIMC setting using Gong et al.\u27s method [PKC, 2016]. We emphasize that, when instantiating our construction by the Symmetric eXternal Diffie-Hellman assumption (SXDH = 1-Lin), we obtain the most efficient concrete IBE scheme with almost-tight reduction in the MIMC setting, whose performance is even comparable to the most efficient IBE in the classical model (i.e., the single-instance, single-ciphertext setting). Besides pursuing high performance, our IBE scheme also achieves a weaker form of anonymity pointed out by Attrapadung et al. [AsiaCrypt, 2015]

Improved Inner-product Encryption with Adaptive Security and Full Attribute-hiding

In this work, we propose two IPE schemes achieving both adaptive security and full attribute-hiding in the prime-order bilinear group, which improve upon the unique existing result satisfying both features from Okamoto and Takashima [Eurocrypt \u2712] in terms of efficiency. - Our first IPE scheme is based on the standard $k$-Lin assumption and has shorter master public key and shorter secret keys than Okamoto and Takashima\u27s IPE under weaker DLIN=$2$-lin assumption. - Our second IPE scheme is adapted from the first one; the security is based on the XDLIN assumption (as Okamoto and Takashima\u27s IPE) but now it also enjoys shorter ciphertexts. Technically, instead of starting from composite-order IPE and applying existing transformation, we start from an IPE scheme in a very restricted setting but already in the prime-order group, and then gradually upgrade it to our full-fledged IPE scheme. This method allows us to integrate Chen et al.\u27s framework [Eurocrypt \u2715] with recent new techniques [TCC \u2717, Eurocrypt \u2718] in an optimized way

Mitigating the One-Use Restriction in Attribute-Based Encryption

We present a key-policy attribute-based encryption scheme that is adaptively secure under a static assumption and is not directly affected by an attribute one-use restriction. Our construction improves upon the only other such scheme (Takashima \u2717) by mitigating its downside of a ciphertext size that is dependent on the maximum size of any supported attribute set