International Association for Cryptologic Research

International Association
for Cryptologic Research


Sihang Pu


Multiparty Cardinality Testing for Threshold Private Set Intersection
Threshold Private Set Intersection (PSI) allows multiple parties to compute the intersection of their input sets if and only if the intersection is larger than $n-t$, where $n$ is the size of the sets and $t$ is some threshold. The main appeal of this primitive is that, in contrast to standard PSI, known upper-bounds on the communication complexity only depend on the threshold $t$ and not on the sizes of the input sets. Current Threshold PSI protocols split themselves into two components: A Cardinality Testing phase, where parties decide if the intersection is larger than some threshold; and a PSI phase, where the intersection is computed. The main source of inefficiency of Threshold PSI is the former part. In this work, we present a new Cardinality Testing protocol that allows $N$ parties to check if the intersection of their input sets is larger than $n-t$. The protocol incurs in $\tilde{ \mathcal{O}} (Nt^2)$ communication complexity. We thus obtain a Threshold PSI scheme for $N$ parties with communication complexity $\tilde{ \mathcal{O}}(Nt^2)$.
A Combinatorial Approach to Quantum Random Functions 📺
Quantum pseudorandom functions (QPRFs) extend the classical security of a PRF by allowing the adversary to issue queries on input superpositions. Zhandry [Zhandry, FOCS 2012] showed a separation between the two notions and proved that common construction paradigms are also quantum secure, albeit with a new ad-hoc analysis. In this work, we revisit the question of constructing QPRFs and propose a new method starting from small-domain (classical) PRFs: At the heart of our approach is a new domain-extension technique based on bipartite expanders. Interestingly, our analysis is almost entirely classical. As a corollary of our main theorem, we obtain the first (approximate) key-homomorphic quantum PRF based on the quantum intractability of the learning with errors problem.