International Association for Cryptologic Research

International Association
for Cryptologic Research


Rachit Garg


Dynamic Collusion Functional Encryption and Multi-Authority Attribute-Based Encryption
Rachit Garg Rishab Goyal George Lu
Functional Encryption (FE) is a powerful notion of encryp- tion which enables computations and partial message recovery of en- crypted data. In FE, each decryption key is associated with a function f such that decryption recovers the function evaluation f(m) from an encryption of m. Informally, security states that a user with access to function keys skf1 , skf2 , . . . (and so on) can only learn f1(m), f2(m), . . . (and so on) but nothing more about the message. The system is said to be q-bounded collusion resistant if the security holds as long as an adversary gets access to at most q = q(�) decryption keys. However, until very recently, all these works studied bounded col- lusion resistance in a static model, where the collusion bound q was a global system parameter. While the static model has led to many great applications, it has major drawbacks. Recently, Agrawal et al. (Crypto 2021) and Garg et al. (Eurocrypt 2022) introduced the dynamic model for bounded collusion resistance, where the collusion bound q was a fluid parameter, not globally set, but chosen by each encryptor. The dynamic model enabled harnessing many virtues of the static model, while avoid- ing its various drawbacks. In this work, we provide a generic compiler to upgrade any FE scheme from the static model to the dynamic model. We also extend our techniques to multi-authority attribute-based en- cryption (MA-ABE). We show that bounded collusion MA-ABE sup- porting predicates that can be represented as an e�cient computational secret sharing (CSS) scheme can be built from minimal assumptions. Ef- ficient CSS schemes are known for access structures whose characteristic function can be computed by a polynomial-size monotone circuit under the existence of one-way functions [Yao89, unpublished]. Thus, our MA- ABE construction is the first MA-ABE scheme from standard assump- tions for predicates beyond polynomial-size monotone boolean formula. Our construction also satisfies full adaptive security in the Random Or- acle Model.
Time-Lock Puzzles with Efficient Batch Solving
Time-Lock Puzzles (TLPs) are a powerful tool for concealing messages until a predetermined point in time. When solving multiple puzzles, it becomes crucial to have the ability to \emph{batch-solve} puzzles, i.e., simultaneously open multiple puzzles while working to solve a \emph{single one}. Unfortunately, all previously known TLP constructions equipped for batch solving have been contingent upon super-polynomially secure indistinguishability obfuscation, rendering them impractical in real-world applications. In light of this challenge, we present novel TLP constructions that offer batch-solving capabilities without using heavy cryptographic hammers. Our proposed schemes are characterized by their simplicity in concept and efficiency in practice, and they can be constructed based on well-established cryptographic assumptions based on pairings or learning with errors (LWE). Along the way, we introduce new constructions of puncturable key-homomorphic PRFs both in the lattice and in the pairing setting, which may be of independent interest. Our analysis benefits from an interesting connection to Hall's marriage theorem and incorporates an optimized combinatorial approach, enhancing the practicality and feasibility of our TLP schemes. Furthermore, we introduce the concept of ``rogue-puzzle attacks", wherein maliciously crafted puzzle instances may disrupt the batch-solving process of honest puzzles. In response, we demonstrate the construction of concrete and efficient TLPs designed to thwart such attacks.
On Non-uniform Security for Black-box Non-Interactive CCA Commitments
We obtain a black-box construction of non-interactive CCA commitments against non-uniform adversaries. This makes black-box use of an appropriate base commitment scheme for small tag spaces, variants of sub-exponential hinting PRG (Koppula and Waters, Crypto 2019) and variants of keyless sub-exponentially collision-resistant hash function with security against non-uniform adversaries (Bitansky, Kalai and Paneth, STOC 2018 and Bitansky and Lin, TCC 2018). All prior works on non-interactive non-malleable or CCA commitments without setup first construct a ``base'' scheme for a relatively small identity/tag space, and then build a tag amplification compiler to obtain commitments for an exponential-sized space of identities. Prior black-box constructions either add multiple rounds of interaction (Goyal, Lee, Ostrovsky and Visconti, FOCS 2012) or only achieve security against uniform adversaries (Garg, Khurana, Lu and Waters, Eurocrypt 2021). Our key technical contribution is a novel tag amplification compiler for CCA commitments that replaces the non-interactive proof of consistency required in prior work. Our construction satisfies the strongest known definition of non-malleability, i.e., CCA2 (chosen commitment attack) security. In addition to only making black-box use of the base scheme, our construction replaces sub-exponential NIWIs with sub-exponential hinting PRGs, which can be obtained based on assumptions such as (sub-exponential) CDH or LWE.
Dynamic Collusion Bounded Functional Encryption from Identity-Based Encryption 📺
Functional Encryption is a powerful notion of encryption in which each decryption key is associated with a function f such that decryption recovers the function evaluation f(m). Informally, security states that a user with access to function keys sk_f1,sk_f2,..., (and so on) can only learn f1(m), f2(m),... (and so on) but nothing more about the message. The system is said to be q-bounded collusion resistant if the security holds as long as an adversary gets access to at most q = q(λ) function keys. A major drawback of such statically bounded collusion systems is that the collusion bound q must be declared at setup time and is fixed for the entire lifetime of the system. We initiate the study of dynamically bounded collusion resistant functional encryption systems which provide more flexibility in terms of selecting the collusion bound, while reaping the benefits of statically bounded collusion FE systems (such as quantum resistance, simulation security, and general assumptions). Briefly, the virtues of a dynamically bounded scheme can be summarized as: -Fine-grained individualized selection: It lets each encryptor select the collusion bound by weighing the trade-off between performance overhead and the amount of collusion resilience. -Evolving encryption strategies: Since the system is no longer tied to a single collusion bound, thus it allows to dynamically adjust the desired collusion resilience based on any number of evolving factors such as the age of the system, or a number of active users, etc. -Ease and simplicity of updatability: None of the system parameters have to be updated when adjusting the collusion bound. That is, the same key skf can be used to decrypt ciphertexts for collusion bound q = 2 as well as q = 2^λ. We construct such a dynamically bounded functional encryption scheme for the class of all polynomial-size circuits under the general assumption of Identity-Based Encryption
Fully Succinct Batch Arguments for NP from Indistinguishability Obfuscation
Non-interactive batch arguments for $\mathsf{NP}$ provide a way to amortize the cost of $\mathsf{NP}$ verification across multiple instances. In particular, they allow a prover to convince a verifier of multiple $\mathsf{NP}$ statements with communication that scales sublinearly in the number of instances. In this work, we study fully succinct batch arguments for $\mathsf{NP}$ in the common reference string (CRS) model where the length of the proof scales not only sublinearly in the number of instances $T$, but also sublinearly with the size of the $\mathsf{NP}$ relation. Batch arguments with these properties are special cases of succinct non-interactive arguments (SNARGs); however, existing constructions of SNARGs either rely on idealized models or strong non-falsifiable assumptions. The one exception is the Sahai-Waters SNARG based on indistinguishability obfuscation. However, when applied to the setting of batch arguments, we must impose an a priori bound on the number of instances. Moreover, the size of the common reference string scales linearly with the number of instances. In this work, we give a direct construction of a fully succinct batch argument for $\mathsf{NP}$ that supports an unbounded number of statements from indistinguishability obfuscation and one-way functions. Then, by additionally relying on a somewhere statistically-binding (SSB) hash function, we show how to extend our construction to obtain a fully succinct and updatable batch argument. In the updatable setting, a prover can take a proof $\pi$ on $T$ statements $(x_1, \ldots, x_T)$ and "update" it to obtain a proof $\pi'$ on $(x_1, \ldots, x_T, x_{T + 1})$. Notably, the update procedure only requires knowledge of a (short) proof for $(x_1, \ldots, x_T)$ along with a single witness $w_{T + 1}$ for the new instance $x_{T + 1}$. Importantly, the update does not require knowledge of witnesses for $x_1, \ldots, x_T$.
Black-Box Non-Interactive Non-Malleable Commitments 📺
There has been recent exciting progress in building non-interactive non-malleable commitments from judicious assumptions. All proposed approaches proceed in two steps. First, obtain simple “base” commitment schemes for very small tag/identity spaces based on a various sub-exponential hardness assumptions. Next, assuming sub-exponential non-interactive witness indistinguishable proofs (NIWIs), and variants of keyless collision-resistant hash functions, construct non-interactive compilers that convert tag-based non-malleable commitments for a small tag space into tag-based non-malleable commitments for a larger tag space. We propose the first black-box construction of non-interactive non-malleable commitments. Our key technical contribution is a novel implementation of the non-interactive proof of consistency required for tag amplification. Prior to our work, the only known approach to tag amplification without setup and with black-box use of the base scheme (Goyal, Lee, Ostrovsky, and Visconti, FOCS 2012) added multiple rounds of interaction. Our construction satisfies the strongest known definition of non-malleability, i.e., CCA (chosen commitment attack) security. In addition to being black-box, our approach dispenses with the need for sub-exponential NIWIs, that was common to all prior work. Instead of NIWIs, we rely on sub-exponential hinting PRGs which can be obtained based on a broad set of assumptions such as sub-exponential CDH or LWE.
New Techniques in Replica Encodings with Client Setup 📺
Rachit Garg George Lu Brent Waters
A proof of replication system is a cryptographic primitive that allows a server (or group of servers) to prove to a client that it is dedicated to storing multiple copies or replicas of a file. Until recently, all such protocols required fined-grained timing assumptions on the amount of time it takes for a server to produce such replicas. Damgard, Ganesh, and Orlandi [DGO19] proposed a novel notion that we will call proof of replication with client setup. Here, a client first operates with secret coins to generate the replicas for a file. Such systems do not inherently have to require fine-grained timing assumptions. At the core of their solution to building proofs of replication with client setup is an abstraction called replica encodings. Briefly, these comprise a private coin scheme where a client algorithm given a file m can produce an encoding \sigma. The encodings have the property that, given any encoding \sigma, one can decode and retrieve the original file m. Secondly, if a server has significantly less than n·|m| bit of storage, it cannot reproduce n encodings. The authors give a construction of encodings from ideal permutations and trapdoor functions. In this work, we make three central contributions: 1) Our first contribution is that we discover and demonstrate that the security argument put forth by [DGO19] is fundamentally flawed. Briefly, the security argument makes assumptions on the attacker's storage behavior that does not capture general attacker strategies. We demonstrate this issue by constructing a trapdoor permutation which is secure assuming indistinguishability obfuscation, serves as a counterexample to their claim (for the parameterization stated). 2) In our second contribution we show that the DGO construction is actually secure in the ideal permutation model from any trapdoor permutation when parameterized correctly. In particular, when the number of rounds in the construction is equal to \lambda·n·b where \lambda is the security parameter, n is the number of replicas and b is the number of blocks. To do so we build up a proof approach from the ground up that accounts for general attacker storage behavior where we create an analysis technique that we call "sequence-then-switch". 3) Finally, we show a new construction that is provably secure in the random oracle (or random function) model. Thus requiring less structure on the ideal function.