A Bit-fixing PRF with O(1) Collusion-Resistance from LWE

Constrained pseudorandom functions (CPRFs) allow learning modified PRF keys that can evaluate the PRF on a subset of the input space, or based on some sort of predicate. First introduced by Boneh and Waters [Asiacrypt 2013], they have been shown to be a useful cryptographic primitive with many applications. The full security definition of CPRFs requires the adversary to learn multiple constrained keys, a requirement for all of these applications. Unfortunately, existing constructions of CPRFs satisfying this security notion are only known from exceptionally strong cryptographic assumptions, such as indistinguishability obfuscation and the existence of multilinear maps, even for very weak predicates. CPRFs from more standard assumptions only satisfy security when one key is learnt. In this work, we give the first construction of a CPRF that can issue a constant number of constrained keys for bit-fixing predicates, from learning with errors (LWE). It also satisfies $1$-key privacy (otherwise known as constraint-hiding). Finally, our construction achieves fully adaptive security with polynomial security loss; the only construction to achieve such security under a standard assumption. Our technique represents a noted departure existing for CPRF constructions. We hope that it may lead to future constructions that can expose a greater number of keys, or consider more expressive predicates (such as circuit-based constraints)

Constrained PRFs for Bit-fixing (and More) from OWFs with Adaptive Security and Constant Collusion Resistance

Constrained pseudorandom functions (CPRFs) allow learning constrained PRF keys that can evaluate the PRF on a subset of the input space, or based on some sort of predicate. First introduced by Boneh and Waters [AC\u2713], Kiayias et al. [CCS\u2713] and Boyle et al. [PKC\u2714], they have been shown to be a useful cryptographic primitive with many applications. The full security definition of CPRFs requires the adversary to learn multiple constrained keys in an arbitrary order, a requirement for many of these applications. Unfortunately, existing constructions of CPRFs satisfying this security notion are only known from exceptionally strong cryptographic assumptions, such as indistinguishability obfuscation (IO) and the existence of multilinear maps, even for very weak constraints. CPRFs from more standard assumptions only satisfy selective security for a single constrained key query. In this work, we give the first construction of a CPRF that can adaptively issue a constant number of constrained keys for bit-fixing predicates (or more generally $t$-conjunctive normal form predicates), only requiring the existence of one-way functions (OWFs). This is a much weaker assumption compared with all previous constructions. In addition, we prove that the new scheme satisfies 1-key privacy (otherwise known as constraint-hiding). This is the only construction for any non-trivial predicates to achieve adaptive security and collusion-resistance outside of the random oracle model or relying on strong cryptographic assumptions. Our technique represents a noted departure from existing CPRF constructions

Note on Constructing Constrained PRFs from OWFs with Constant Collusion Resistance

Constrained pseudorandom functions (CPRFs) are a type of PRFs that allows one to derive a constrained key $\mathsf{K}_C$ from the master key $\mathsf{K}$. While the master key $\mathsf{K}$ allows one to evaluate on any input as a standard PRF, the constrained key $\mathsf{K}_C$ only allows one to evaluate on inputs $x$ such that $C(x) = 1$. Since the introduction of CPRFs by Boneh and Waters (ASIACRYPT\u2713), Kiayias et al. (CCS\u2713), and Boyle et al. (PKC\u2714), there have been various constructions of CPRFs. However, thus far, almost all constructions (from standard assumptions and non-trivial constraints) are only proven to be secure if at most one constrained key $\mathsf{K}_C$ is known to the adversary, excluding the very recent work of Davidson and Nishimaki (EPRINT\u2718). Considering the interesting applications of CPRFs such as ID-based non-interactive key exchange, we desire CPRFs that are collusion resistance with respect to the constrained keys. In this work, we make progress in this direction and construct a CPRF for the bit-fixing predicates that are collusion resistance for a constant number of constrained keys. Surprisingly, compared to the heavy machinery that was used by previous CPRF constructions, our construction only relies on the existence of one-way functions

Privately Puncturing PRFs from Lattices: Adaptive Security and Collusion Resistant Pseudorandomness

A private puncturable pseudorandom function (PRF) enables one to create a constrained version of a PRF key, which can be used to evaluate the PRF at all but some punctured points. In addition, the constrained key reveals no information about the punctured points and the PRF values on them. Existing constructions of private puncturable PRFs are only proven to be secure against a restricted adversary that must commit to the punctured points before viewing any information. It is an open problem to achieve the more natural adaptive security, where the adversary can make all its choices on-the-fly. In this work, we solve the problem by constructing an adaptively secure private puncturable PRF from standard lattice assumptions. To achieve this goal, we present a new primitive called explainable hash, which allows one to reprogram the hash function on a given input. The new primitive may find further applications in constructing more cryptographic schemes with adaptive security. Besides, our construction has collusion resistant pseudorandomness, which requires that even given multiple constrained keys, no one could learn the values of the PRF at the punctured points. Private puncturable PRFs with collusion resistant pseudorandomness were only known from multilinear maps or indistinguishability obfuscations in previous works, and we provide the first solution from standard lattice assumptions

Fully Secure Attribute-Based Encryption for tt-CNF from LWE

Attribute-based Encryption (ABE), first introduced by [SW05,GPSW06], is a public key encryption system that can support multiple users with varying decryption permissions. One of the main properties of such schemes is the supported function class of policies. While there are fully secure constructions from bilinear maps for a fairly large class of policies, the situation with lattice-based constructions is less satisfactory and many efforts were made to close this gap. Prior to this work the only known fully secure lattice construction was for the class of point functions (also known as IBE). In this work we construct for the first time a lattice-based (ciphertext-policy) ABE scheme for the function class $t$-CNF, which consists of CNF formulas where each clause depends on at most $t$ bits of the input, for any constant $t$. This class includes NP-verification policies, bit-fixing policies and $t$-threshold policies. Towards this goal we also construct a fully secure single-key constrained PRF from OWF for the same function class, which might be of independent interest

Keeping your Friends Secret: Improving the Security, Effciency and Usability of Private Set Intersection

Private set intersection (PSI) allows two parties, who each hold a set of items, to compute the intersection of those sets without revealing anything about other items. Recent advances in PSI have significantly improved its performance for the case of semi-honest security, making semi-honest PSI a practical alternative to insecure methods for computing intersections. However, these protocols have two major drawbacks: 1) the amount of data required to be communicated can be orders of magnitude larger than an insecure solution and 2) when in the presence of malicious parties the security of these protocols breaks down. In this work, four malicious secure PSI protocols are introduced along with three semi-honest protocols which have sublinear communication. These protocols are based on a combination of fast symmetric-key primitives and fully homomorphic encryption. Three of these protocols represent the current state of the art for their respective settings. The practicality of these protocols are demonstrated with prototype implementations. To securely compute the intersection of two sets of size 2²⁰ in the malicious setting requires only 13 seconds, which is ~ 450x faster than the previous best malicious-secure protocol (De Cristofaro et al, Asiacrypt 2010), and only 3x slower than the best semi-honest protocol (Kolesnikov et al., CCS 2016). Alternatively, when computing the intersection between set sizes of 2¹⁰ and 2²⁸, our fastest protocol require just 6 seconds and 5MB of communication