## CryptoDB

### George Lu

#### Publications

**Year**

**Venue**

**Title**

2024

PKC

Dynamic Collusion Functional Encryption and Multi-Authority Attribute-Based Encryption
Abstract

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function can be computed by a polynomial-size monotone circuit under the existence of one-way functions [Yao89, unpublished].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.

2024

CRYPTO

Reducing the CRS Size in Registered ABE Systems
Abstract

Attribute-based encryption (ABE) is a generalization of public-key encryption that enables fine-grained access control to encrypted data. In (ciphertext-policy) ABE, a central trusted authority issues decryption keys for attributes $x$ to users. In turn, ciphertexts are associated with a decryption policy $\mathcal{P}$. Decryption succeeds and recovers the encrypted message whenever $\mathcal{P}(x) = 1$. Recently, Hohenberger, Lu, Waters, and Wu (Eurocrypt 2023) introduced the notion of registered ABE, which is an ABE scheme without a trusted central authority. Instead, users generate their own public/secret keys (just like in public-key encryption) and then register their keys (and attributes) with a key curator. The key curator is a transparent and untrusted entity.
Currently, the best pairing-based registered ABE schemes support monotone Boolean formulas and an a priori bounded number of users $L$. A major limitation of existing schemes is that they require a (structured) common reference string (CRS) of size $L^2 \cdot |\mathcal{U}|$ where $|\mathcal{U}|$ is the size of the attribute universe. In other words, the size of the CRS scales quadratically with the number of users and multiplicatively with the size of the attribute universe. The large CRS makes these schemes expensive in practice and limited to a small number of users and a small universe of attributes.
In this work, we give two ways to reduce the CRS size in pairing-based registered ABE schemes. First, we introduce a combinatoric technique based on progression-free sets that enables registered ABE for the same class of policies but with a CRS whose size is sub-quadratic in the number of users. Asymptotically, we obtain a scheme where the CRS size is nearly linear in the number of users $L$ (i.e., $L^{1 + o(1)}$). If we take a more concrete-efficiency-oriented focus, we can instantiate our framework to obtain a construction with a CRS of size $L^{\log_2 3} \approx L^{1.6}$. For instance, in a scheme for 100,000 users, our approach reduces the CRS by a factor of over $115\times$ compared to previous approaches (and without incurring any overhead in encryption/decryption time). Our second approach for reducing the CRS size is to rely on a partitioning-based argument when arguing security of the registered ABE scheme. Previous approaches took a dual-system approach. Using a partitioning-based argument yields a registered ABE scheme where the size of the CRS is independent of the size of the attribute universe. The cost is the resulting scheme satisfies a weaker notion of static security. Our techniques for reducing the CRS size can be combined, and taken together, we obtain a pairing-based registered ABE scheme that supports monotone Boolean formulas with a CRS size of $L^{1 + o(1)}$. Notably, this is the first pairing-based registered ABE scheme that does not require imposing a bound on the size of the attribute universe during setup time.
As an additional application, we also show how to apply our techniques based on progression-free sets to the batch argument (BARG) for $\mathsf{NP}$ scheme of Waters and Wu (Crypto 2022) to obtain a scheme with a nearly-linear CRS without needing to rely on non-black-box bootstrapping techniques.

2024

CRYPTO

Limits on the Power of Prime-Order Groups: Separating Q-Type from Static Assumptions
Abstract

Subgroup decision techniques on cryptographic groups and pairings have been critical for numerous applications. Originally conceived in the composite-order setting, there is a large body of work showing how to instantiate subgroup decision techniques in the prime-order setting as well. In this work, we demonstrate the first barrier to this research program, by demonstrating an important setting where composite-order techniques cannot be replicated in the prime-order setting.
In particular, we focus on the case of q-type assumptions, which are ubiquitous in group- and pairing-based cryptography, but unfortunately are less desirable than the more well-understood static assumptions. Subgroup decision techniques have had great success in removing q-type assumptions, even allowing q-type assumptions to be generically based on static assumptions on composite-order groups. Our main result shows that the same likely does \emph{not} hold in the prime order setting. Namely, we show that a large class of q-type assumptions, including the security definition of a number of cryptosystems, cannot be proven secure in a black box way from any static assumption.

2023

EUROCRYPT

Registered Attribute-Based Encryption
Abstract

Attribute-based encryption (ABE) generalizes public-key encryption and enables fine-grained control to encrypted data. However, ABE upends the traditional trust model of public-key encryption by requiring a single trusted authority to issue decryption keys. If an adversary compromises the central authority and exfiltrates its secret key, then the adversary can decrypt every ciphertext in the system.
This work introduces registered ABE, a primitive that allows users to generate secret keys on their own and then register the associated public key with a "key curator" along with their attributes. The key curator aggregates the public keys from the different users into a single compact master public key. To decrypt, users occasionally need to obtain helper decryption keys from the key curator which they combine with their own secret keys. We require that the size of the aggregated public key, the helper decryption keys, the ciphertexts, as well as the encryption/decryption times to be polylogarithmic in the number of registered users. Moreover, the key curator is entirely transparent and maintains no secrets. Registered ABE generalizes the notion of registration-based encryption (RBE) introduced by Garg et al. (TCC 2018), who focused on the simpler setting of identity-based encryption.
We construct a registered ABE scheme that supports an a priori bounded number of users and policies that can be described by a linear secret sharing scheme (e.g., monotone Boolean formulas) from assumptions on composite-order pairing groups. Our approach deviates sharply from previous techniques for constructing RBE and only makes black-box use of cryptography. All existing RBE constructions (a weaker notion than registered ABE) rely on heavy non-black-box techniques. The encryption and decryption costs of our construction are comparable to those of vanilla pairing-based ABE. Two limitations of our scheme are that it requires a structured reference string whose size scales quadratically with the number of users (and linearly with the size of the attribute universe) and the running time of registration scales linearly with the number of users.
Finally, as a feasibility result, we construct a registered ABE scheme that supports general policies and an arbitrary number of users from indistinguishability obfuscation and somewhere statistically binding hash functions.

2023

EUROCRYPT

On Non-uniform Security for Black-box Non-Interactive CCA Commitments
Abstract

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.

2022

EUROCRYPT

Dynamic Collusion Bounded Functional Encryption from Identity-Based Encryption
📺
Abstract

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

2022

TCC

How to Sample a Discrete Gaussian (and more) from a Random Oracle
Abstract

The random oracle methodology is central to the design of many practical cryptosystems. A common challenge faced in several systems is the need to have a random oracle that outputs from a structured distribution D, even though most heuristic implementations such as SHA-3 are best suited for outputting bitstrings.
Our work explores the problem of sampling from discrete Gaussian (and related) distributions in a manner that they can be programmed into random oracles. We make the following contributions:
- We provide a definitional framework for our results. We say that a sampling algorithm Sample() for a distribution is explainable if there exists an algorithm Explain(), where, for a x in the domain, we have that Explain(x) -> r \in {0,1}^n such that Sample(r)=x. Moreover, if x is sampled from D the explained distribution is statistically close to choosing r uniformly at random. We consider a variant of this definition that allows the statistical closeness to be a "precision parameter" given to the Explain() algorithm. We show that sampling algorithms which satisfy our `explainability' property can be programmed as a random oracle.
- We provide a simple algorithm for explaining any sampling algorithm that works over distributions with polynomial sized ranges. This includes discrete Gaussians with small standard deviations.
- We show how to transform a (not necessarily explainable) sampling algorithm Sample() for a distribution into a new Sample'() that is explainable. The requirements for doing this is that (1) the probability density function is efficiently computable (2) it is possible to efficiently uniformly sample from all elements that have a probability density above a given threshold p, showing the equivalence of random oracles to these distributions and random oracles to uniform bitstrings. This includes a large class of distributions, including all discrete Gaussians.
- A potential drawback of the previous approach is that the transformation requires an additional computation of the density function. We provide a more customized approach that shows the Miccancio-Walter discrete Gaussian sampler is explainable as is. This suggests that other discrete Gaussian samplers in a similar vein might also be explainable as is.

2021

EUROCRYPT

Black-Box Non-Interactive Non-Malleable Commitments
📺
Abstract

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.

2020

TCC

New Techniques in Replica Encodings with Client Setup
📺
Abstract

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.

#### Coauthors

- Rachit Garg (6)
- Rishab Goyal (2)
- Susan Hohenberger (1)
- Dakshita Khurana (2)
- George Lu (9)
- Brent Waters (7)
- David J. Wu (2)
- Mark Zhandry (1)