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In this talk, we present two new results on private information retrieval (PIR), each playing with a trade between time and space. 

Our first result spends some extra space to greatly shrink the PIR servers' time. We present the first "doubly-efficient", information-theoretic PIR scheme with any constant number of servers (in our case, two) that has quasilinear server storage n^{1 + o(1)} and polynomially-sublinear server time n^{1 - \Omega(1)}. Concretely, on a database of n > 10^6 bits, the PIR servers store a preprocessed data structure of size 1.5 * sqrt(log_2 n) * n bits and then answer each PIR query by probing 12 n^{0.82} bits in this data structure. The key ingredient in our scheme is a compact data structure for evaluating a multivariate polynomial and its derivatives, leveraging the fact that Hasse derivatives can be efficiently computed on-the-fly by taking finite differences between the polynomial's evaluations.

Our second result uses PIR techniques to obtain new time-space tradeoffs for simulating arbitrary Turing machines. To this end, we give a new low-space algorithm for the tree-evaluation task, when operating in a catalytic-computation model: the algorithm is given access to a large, full hard drive (catalytic space), which it may overwrite---as long as the hard drive is ultimately returned to its initial state. Combined with the landmark reduction of Williams (STOC 2025), our work implies that any time T Turing-machine computation can be simulated with O(sqrt(T)) free space, 2^{O(sqrt(T))} time, and 2^{T^epsilon} catalytic space (for any epsilon > 0). For comparison, the original result of Williams did not require any catalytic space but required O(sqrt(T log T)) free space.

Based on work at Eurocrypt 2026 (ePrint:2025/2008) and a manuscript with Edward Pyne (ePrint:2026/265).

Interactive Oracle Proofs (IOPs) enable probabilistic verification of NP statements in sublinear time, and have been intensively researched since their introduction a decade ago. Zero-Knowledge IOPs (ZK-IOPs) additionally guarantee a query-bounded verifier learns nothing about the NP witness. Such IOPs are often constructed by composing smaller building blocks, and require a tedious proof to show ZK is preserved under such composition.
In this talk, I will present a framework for ZK-IOP composition. Using this framework, we’ll see that ZK is preserved when composing IOPs in the natural setting of perfect black-box straight-line ZK, and public-coin honest verifiers. I will also demonstrate how to use the composition framework by discussing several applications.