Paweł Lorek

Paweł Lorek, Rafał Nowak, Rafał Topolnicki et al.

Estimating the expectation of a real-valued function of a random variable from sample data is a critical aspect of statistical analysis, with far-reaching implications in various applications. Current methodologies typically assume (semi-)parametric distributions such as Gaussian or mixed Gaussian, leading to significant estimation uncertainty if these assumptions do not hold. We propose a flow-based model, integrated with stratified sampling, that leverages a parametrized neural network to offer greater flexibility in modeling unknown data distributions, thereby mitigating this limitation. Our model shows a marked reduction in estimation uncertainty across multiple datasets, including high-dimensional (30 and 128) ones, outperforming crude Monte Carlo estimators and Gaussian mixture models. Reproducible code is available at https://github.com/rnoxy/flowstrat.

Paweł Lorek, Grzegorz Łoś, Karol Gotfryd et al.

Testing the quality of pseudorandom number generators is an important issue. Security requirements become more and more demanding, weaknesses in this matter are simply not acceptable. There is a need for an in-depth analysis of statistical tests -- one has to be sure that rejecting/accepting a generator as good is not a result of errors in computations or approximations. In this paper we propose a second level statistical test based on the arcsine law for random walks. We provide a Berry-Essen type inequality for approximating the arcsine distribution, what allows us to perform a detailed error analysis of the proposed test.

Paweł Lorek, Filip Zagórski, Michał Kulis

This paper presents applicability of Strong Stationary Times (SST) techniques in the area of cryptography. The applicability is in three areas: *) Propositions of a new class of cryptographic algorithms (pseudo-random permutation generators) which do not run for the predefined number of steps. Instead, these algorithms stop according to a stopping rule defined as SST, for which one can obtain provable properties: *** results are perfect samples from uniform distribution, *** immunity to timing attacks (no information about the resulting permutation leaks through the information about the number of steps SST algorithm *) We show how one can leverage properties of SST-based algorithms to construct an implementation (of a symmetric encryption scheme) which is immune to the timing-attack by reusing implementations which are not secure against timing-attacks. In symmetric key cryptography researchers mainly focus on constant time (re)implementations. Our approach goes in a different direction and explores ideas of input masking. *) Analysis of idealized (mathematical) models of existing cryptographic schemes -- i.e., we improve a result by Mironov ((Not So) Random Shuffles of RC4; Advances in Cryptology -- CRYPTO 2002)