Limits of Preprocessing for Single-Server PIR

We present a lower bound for the static cryptographic data structure problem of single-server private information retrieval (PIR). PIR considers the setting where a server holds a database of $n$ entries and a client wishes to privately retrieve the $i$-th entry without revealing the index $i$ to the server. In our work, we focus on PIR with preprocessing where an $r$-bit hint may be computed in a preprocessing stage and stored by the server to be used to perform private queries in expected time $t$. We consider the public preprocessing setting of Beimel et al. [JoC, 2004] where the hint is publicly available to everyone including the adversary. We prove that for any single-server computationally secure PIR with preprocessing it must be that $tr = \Omega(n \log n)$ when $r = \Omega(\log n)$. If $r = O(\log n)$, we show that $t = \Omega(n)$. Our lower bound holds even when the scheme errs with probability $1/n^2$ and the adversary’s distinguishing advantage is $1/n$. Our work improves upon the $tr = \Omega(n)$ lower bound of Beimel et al. [JoC, 2004]. We prove our lower bound in a variant of the cell probe model where only accesses to the memory are charged cost and computation and accesses to the hint are free. Our main technical contribution is a novel use of the cell sampling technique (also known as the incompressibility technique) used to obtain lower bounds on data structures. In previous works, this technique only leveraged the correctness guarantees to prove lower bounds even when used for cryptographic primitives. Our work combines the cell sampling technique with the privacy guarantees of PIR to construct a powerful, polynomial-time adversary that is critical to proving our higher lower bounds

The Roles of Polyploidy, Climate, and Genetic Architecture in the Evolution of Leaf Form in Viburnum (Adoxaceae)

Plants exhibit extensive variation in leaf form, but the evolutionary drivers of this variation are not well understood. This dissertation leverages the wide diversity of leaf form and instances of leaf syndrome convergence in Viburnum to investigate trends in leaf trait evolution across the group. First, I explore how changes in chromosome number and genome size influence leaf characters of ecophysiological importance. It appears that even with extensive variation in chromosome number and genome size across Viburnum, nucleotypic changes largely do not constrain leaf traits related to ecophysiological function. I then look into a case of convergent evolution for leaf syndromes in a radiation of Central and South American cloud forest species. First, I studied whether or not different species with the same leaf syndromes occupied similar climatic niches and found that though all leaf syndromes occupied largely overlapping climatic zones, some leaf syndromes do seem to sort by a couple select climate variables. I then uncover hybridization between two Mexican species with different leaf syndromes and use this underlying genetic diversity to identify genetic markers associated with leaf trait differences. I find that some leaf traits are associated with many genomic regions while others are associated with only a few and that some significant regions are associated with multiple traits. Overall, there are many factors, from genetic to environmental, shaping the evolution of leaf form in Viburnum

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum