International Association
for Cryptologic Research

We present two new constructions for private information retrieval (PIR) in the classical setting where the clients do not need to do any preprocessing or store any database dependent information, and the server does not need to store any client-dependent information. Our first construction (HintlessPIR) eliminates the client preprocessing step from the recent LWE-based SimplePIR (Henzinger et. al., USENIX Security 2023) by outsourcing the ``hint'' related computation to the server, leveraging a new concept of \emph{homomorphic encryption with composable preprocessing}. We realize this concept with RLWE encryption schemes, and by leveraging the composibility of this technique we are able to preprocess almost all the expensive parts of the homomorphic computation and reuse them across multiple protocol executions. As a concrete application, we propose highly efficient matrix vector multiplication that allows us to build HintlessPIR. For a database of size 8GB, HintlessPIR achieves throughput about 6.37GB/s without requiring transmission of any client or server state. We additionally formalize the matrix vector multiplication protocol as a novel primitive that we call LinPIR, which may be of independent interest. In our second construction (TensorPIR) we reduce the communication of HintlessPIR from square root to cubic root in the database size. We show how to use RLWE encryption with preprocessing to outsource LWE decryption for ciphertexts generated by homomorphic multiplications. This allows the server to do more complex processing using a more compact query under LWE. We implement and benchmark HintlessPIR which achieves better concrete costs than TensorPIR for a large set of databases of interest. We show that it improves the communication of recent preprocessing constructions when clients do not have large numbers of queries or the database updates frequently. The computation cost for removing the hint is small and decreases as the database becomes larger, and it is always more efficient than other constructions with client hints such as Spiral PIR (Menon and Wu, S&P 2022). In the setting of anonymous queries we also improve on Spiral's communication.

We introduce a new primitive called \emph{anonymous counting tokens} (ACTs) which allows clients to obtain blind signatures or MACs (aka tokens) on messages of their choice, while at the same time enabling issuers to enforce rate limits on the number of tokens that a client can obtain for each message. Our constructions enforce that each client will be able to obtain only one token per message and we show a generic transformation to support other rate limiting as well. We achieve this new property while maintaining the unforgeability and unlinkability properties required for anonymous tokens schemes. We present four ACT constructions with various trade-offs for their efficiency and underlying security assumptions. One construction uses factorization-based primitives and a cyclic group. It is secure in the random oracle model under the q-DDHI assumption (in a cyclic group) and the DCR assumption. Our three other constructions use bilinear maps: one is secure in the standard model under q-DDHI and SXDH, one is secure in the random oracle model under SXDH, and the most efficient of the three is secure in the random oracle model and generic bilinear group model.

We present an algorithm solving the ROS ( R andom inhomogeneities in a O verdetermined S olvable system of linear equations) problem mod p in polynomial time for $$\ell > \log p$$ ℓ > log p dimensions. Our algorithm can be combined with Wagner’s attack, and leads to a sub-exponential solution for any dimension $$\ell $$ ℓ with the best complexity known so far. When concurrent executions are allowed, our algorithm leads to practical attacks against unforgeability of blind signature schemes such as Schnorr and Okamoto–Schnorr blind signatures, threshold signatures such as GJKR and the original version of FROST, multisignatures such as CoSI and the two-round version of MuSig, partially blind signatures such as Abe–Okamoto, and conditional blind signatures such as ZGP17. Schemes for e-cash (such as Brands’ signature) and anonymous credentials (such as Anonymous Credentials Light) inspired from the above are also affected.

We present an algorithm solving the ROS (Random inhomogeneities in a Overdetermined Solvable system of linear equations) problem mod p in polynomial time for $l > log p$ dimensions. Our algorithm can be combined with Wagner's attack, and leads to a sub-exponential solution for any dimension $l$ with best complexity known so far. When concurrent executions are allowed, our algorithm leads to practical attacks against unforgeability of blind signature schemes such as Schnorr and Okamoto--Schnorr blind signatures, threshold signatures such as GJKR and the original version of FROST, multisignatures such as CoSI and the two-round version of MuSig, partially blind signatures such as Abe--Okamoto, and conditional blind signatures such as ZGP17. Schemes for e-cash and anonymous credentials (such as Anonymous Credentials Light) inspired from the above are also affected.

The private join and compute (PJC) functionality enables secure computation over data distributed across different databases, and is applicable to a wide range of applications, many of which address settings where the input databases are of significantly different sizes. We introduce the notion of private information retrieval (PIR) with default, which enables two-party PJC functionalities in a way that hides the size of the intersection of the two databases and incurs sublinear communication cost in the size of the bigger database. We provide two constructions for this functionality, one of which requires offline linear communication, which can be amortized across queries, and one that provides sublinear cost for each query but relies on more computationally expensive tools. We construct inner-product PJC, which has applications to ads conversion measurement and contact tracing, relying on an extension of PIR with default. We evaluate the efficiency of our constructions, which can enable $\mathbf{2^{8}}$ PIR with default lookups on a database of size $\mathbf{2^{25}}$ (or inner-product PJC on databases with such sizes) with the communication of $\mathbf{44}$MB, which costs less than $\mathbf{0.17}$c. for the client and $\mathbf{26.48}$c. for the server.

Private intersection-sum with cardinality allows two parties, where each party holds a private set and one of the parties additionally holds a private integer value associated with each element in her set, to jointly compute the cardinality of the intersection of the two sets as well as the sum of the associated integer values for all the elements in the intersection, and nothing beyond that. We present a new construction for private intersection sum with cardinality that provides malicious security with abort and guarantees that both parties receive the output upon successful completion of the protocol. A central building block for our constructions is a primitive called shuffled distributed oblivious PRF (DOPRF), which is a PRF that offers oblivious evaluation using a secret key shared between two parties, and in addition to this allows obliviously permuting the PRF outputs of several parallel oblivious evaluations. We present the first construction for shuffled DOPRF with malicious security. We further present several new sigma proof protocols for relations across Pedersen commitments, ElGamal encryptions, and Camenisch-Shoup encryptions that we use in our main construction, for which we develop new batching techniques to reduce communication. We implement and evaluate the efficiency of our protocol and show that we can achieve communication cost that is only 4-5x greater than the most efficient semi-honest protocol. When measuring monetary cost of executing the protocol in the cloud, our protocol is 25x more expensive than the semi-honest protocol. Our construction also allows for different parameter regimes that enable trade-offs between communication and computation.

We present a cryptographic construction for anonymous tokens with private metadata bit, called PMBTokens. This primitive enables an issuer to provide a user with a lightweight, single-use anonymous trust token that can embed a single private bit, which is accessible only to the party who holds the secret authority key and is private with respect to anyone else. Our construction generalizes and extends the functionality of Privacy Pass (PETS’18) with this private metadata bit capability. It provides unforgeability, unlinkability, and privacy for the metadata bit properties based on the DDH and CTDH assumptions in the random oracle model. Both Privacy Pass and PMBTokens rely on non-interactive zero-knowledge proofs (NIZKs). We present new techniques to remove the need for NIZKs, while still achieving unlinkability. We implement our constructions and we report their efficiency costs.

We construct public-key function-private predicate encryption for the “small superset functionality,” recently introduced by Beullens and Wee (PKC 2019). This functionality captures several important classes of predicates:Point functions. For point function predicates, our construction is equivalent to public-key function-private anonymous identity-based encryption.Conjunctions. If the predicate computes a conjunction, our construction is a public-key function-private hidden vector encryption scheme. This addresses an open problem posed by Boneh, Raghunathan, and Segev (ASIACRYPT 2013).d-CNFs and read-once conjunctions of d-disjunctions for constant-size d. Our construction extends the group-based obfuscation schemes of Bishop et al. (CRYPTO 2018), Beullens and Wee (PKC 2019), and Bartusek et al. (EUROCRYPT 2019) to the setting of public-key function-private predicate encryption. We achieve an average-case notion of function privacy, which guarantees that a decryption key $$\mathsf {sk} _f$$ reveals nothing about f as long as f is drawn from a distribution with sufficient entropy. We formalize this security notion as a generalization of the (enhanced) real-or-random function privacy definition of Boneh, Raghunathan, and Segev (CRYPTO 2013). Our construction relies on bilinear groups, and we prove security in the generic bilinear group model.

We give a simple and efficient method for obfuscating pattern matching with wildcards. In other words, we construct a way to check an input against a secret pattern, which is described in terms of prescribed values interspersed with unconstrained “wildcard” slots. As long as the support of the pattern is sufficiently sparse and the pattern itself is chosen from an appropriate distribution, we prove that a polynomial-time adversary cannot find a matching input, except with negligible probability. We rely upon the generic group heuristic (in a regular group, with no multilinearity). Previous work [9, 10, 32] provided less efficient constructions based on multilinear maps or LWE.