Data Structure Lower Bounds for Document Indexing Problems

We study data structure problems related to document indexing and pattern matching queries and our main contribution is to show that the pointer machine model of computation can be extremely useful in proving high and unconditional lower bounds that cannot be obtained in any other known model of computation with the current techniques. Often our lower bounds match the known space-query time trade-off curve and in fact for all the problems considered, there is a very good and reasonable match between the our lower bounds and the known upper bounds, at least for some choice of input parameters. The problems that we consider are set intersection queries (both the reporting variant and the semi-group counting variant), indexing a set of documents for two-pattern queries, or forbidden- pattern queries, or queries with wild-cards, and indexing an input set of gapped-patterns (or two-patterns) to find those matching a document given at the query time.Comment: Full version of the conference version that appeared at ICALP 2016, 25 page

Fully leakage-resilient signatures revisited: Graceful degradation, noisy leakage, and construction in the bounded-retrieval model

We construct new leakage-resilient signature schemes. Our schemes remain unforgeable against an adversary leaking arbitrary (yet bounded) information on the entire state of the signer (sometimes known as fully leakage resilience), including the random coin tosses of the signing algorithm. The main feature of our constructions is that they offer a graceful degradation of security in situations where standard existential unforgeability is impossible

The Implied-Realized Volatility Relation with Jumps in Underlying Asset Prices

Recent developments allow a nonparametric separation of the continuous sample path component and the jump component of realized volatility. The jump component has very different time series properties than the continuous component, and accounting for this allows improved forecasting of future realized volatility. We investigate the potential forecasting role of implied volatility backed out from option prices in the presence of these new separate realized volatility components. We show that implied volatility has incremental information relative to both the continuous and jump components of realized volatility when forecasting subsequently realized return volatility, and it appears to be an unbiased forecast. Furthermore, implied volatility has predictive power for future values of each component of realized volatility separately, showing in particular that even the jump component of realized volatility is, to some extent, predictable.Bipower variation, implied volatility, instrumental variables, jumps, options, realized volatility, stock prices, vector autoregressive model, volatility forecasting

Determinantal point process models on the sphere

We consider determinantal point processes on the $d$-dimensional unit sphere $\mathbb S^d$. These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified by a so-called kernel which we assume is a complex covariance function defined on $\mathbb S^d\times\mathbb S^d$. We review the appealing properties of such processes, including their specific moment properties, density expressions and simulation procedures. Particularly, we characterize and construct isotropic DPPs models on $\mathbb{S}^d$, where it becomes essential to specify the eigenvalues and eigenfunctions in a spectral representation for the kernel, and we figure out how repulsive isotropic DPPs can be. Moreover, we discuss the shortcomings of adapting existing models for isotropic covariance functions and consider strategies for developing new models, including a useful spectral approach

Continuously non-malleable codes with split-state refresh

Non-malleable codes for the split-state model allow to encode a message into two parts, such that arbitrary independent tampering on each part, and subsequent decoding of the corresponding modified codeword, yields either the same as the original message, or a completely unrelated value. Continuously non-malleable codes further allow to tolerate an unbounded (polynomial) number of tampering attempts, until a decoding error happens. The drawback is that, after an error happens, the system must self-destruct and stop working, otherwise generic attacks become possible. In this paper we propose a solution to this limitation, by leveraging a split-state refreshing procedure. Namely, whenever a decoding error happens, the two parts of an encoding can be locally refreshed (i.e., without any interaction), which allows to avoid the self-destruct mechanism. An additional feature of our security model is that it captures directly security against continual leakage attacks. We give an abstract framework for building such codes in the common reference string model, and provide a concrete instantiation based on the external Diffie-Hellman assumption. Finally, we explore applications in which our notion turns out to be essential. The first application is a signature scheme tolerating an arbitrary polynomial number of split-state tampering attempts, without requiring a self-destruct capability, and in a model where refreshing of the memory happens only after an invalid output is produced. This circumvents an impossibility result from a recent work by Fuijisaki and Xagawa (Asiacrypt 2016). The second application is a compiler for tamper-resilient RAM programs. In comparison to other tamper-resilient compilers, ours has several advantages, among which the fact that, for the first time, it does not rely on the self-destruct feature