Tachio Terauchi

Taisei Nogami, Yoshiki Nakamura, Tachio Terauchi

The regular expression matching problem asks whether a given regular expression of length $m$ matches a given string of length $n$. As is well known, the problem can be solved in $O(nm)$ time using Thompson's algorithm. Moreover, recent studies have shown that regular expression matching extended with a practical extension called lookaround can be solved in the same time complexity. In this work, we consider four well-known extensions to regular expressions called backreference, squaring, intersection and complement. We prove a number of novel time complexity lower bounds for regular expression matching with these extensions under the Orthogonal Vectors Conjecture (OVC), $k$-OVC, $k$-Clique Hypothesis, and Combinatorial $k$-Clique Hypothesis. Some highlights of our results include the fact that none of the matching problems with the extensions can be solved in $n^{2-\varepsilon} \mathrm{poly}(m)$ time for any constant $\varepsilon > 0$ (for backreference, even when restricted to one capturing group) under OVC, and that the problem with complement, also known as extended regular expression (ERE) matching, cannot be solved in time $n^{2-\varepsilon}\mathrm{tower}(o(\sqrt{m}))$ under OVC, $n^{ω-\varepsilon}\mathrm{tower}(o(\sqrt{m}))$ under the $k$-Clique Hypothesis (where $ω$ is the matrix multiplication exponent), and $n^{3-\varepsilon}\mathrm{tower}(o(\sqrt{m}))$ under the Combinatorial $k$-Clique Hypothesis, respectively. In particular, the latter two results show that the $O(n^3 m)$-time ERE matching algorithm introduced by Hopcroft and Ullman in 1979 and recently improved by Bille, Gørtz and Jessen to run in $O(n^ωm)$ time using fast matrix multiplication was already optimal in a sense, and shed light on why the theoretical computer science community has struggled to improve the time complexity of ERE matching with respect to $n$ and $m$ for more than 45 years.

Arthur Blot, Masaki Yamamoto, Tachio Terauchi

A promising approach to defend against side channel attacks is to build programs that are leakage resilient, in a formal sense. One such formal notion of leakage resilience is the n-threshold-probing model proposed in the seminal work by Ishai et al. In a recent work, Eldib and Wang have proposed a method for automatically synthesizing programs that are leakage resilient according to this model, for the case n=1. In this paper, we show that the n-threshold-probing model of leakage resilience enjoys a certain compositionality property that can be exploited for synthesis. We use the property to design a synthesis method that efficiently synthesizes leakage-resilient programs in a compositional manner, for the general case of n > 1. We have implemented a prototype of the synthesis algorithm, and we demonstrate its effectiveness by synthesizing leakage-resilient versions of benchmarks taken from the literature.

Hirotoshi Yasuoka, Tachio Terauchi

We employ Clarkson and Schneider's "hyperproperties" to classify various verification problems of quantitative information flow. The results of this paper unify and extend the previous results on the hardness of checking and inferring quantitative information flow. In particular, we identify a subclass of liveness hyperproperties, which we call "k-observable hyperproperties", that can be checked relative to a reachability oracle via self composition.