Kolmogorov Complexity Characterizes Statistical Zero Knowledge

We show that a decidable promise problem has a non-interactive statistical zero-knowledge proof system if and only if it is randomly reducible via an honest polynomial-time reduction to a promise problem for Kolmogorov-random strings, with a superlogarithmic additive approximation term. This extends recent work by Saks and Santhanam (CCC 2022). We build on this to give new characterizations of Statistical Zero Knowledge SZK, as well as the related classes NISZK_L and SZK_L

Robustness for Space-Bounded Statistical Zero Knowledge

We show that the space-bounded Statistical Zero Knowledge classes SZK_L and NISZK_L are surprisingly robust, in that the power of the verifier and simulator can be strengthened or weakened without affecting the resulting class. Coupled with other recent characterizations of these classes [Eric Allender et al., 2023], this can be viewed as lending support to the conjecture that these classes may coincide with the non-space-bounded classes SZK and NISZK, respectively

One-Way Functions and a Conditional Variant of MKTP

One-way functions (OWFs) are central objects of study in cryptography and computational complexity theory. In a seminal work, Liu and Pass (FOCS 2020) proved that the average-case hardness of computing time-bounded Kolmogorov complexity is equivalent to the existence of OWFs. It remained an open problem to establish such an equivalence for the average-case hardness of some natural NP-complete problem. In this paper, we make progress on this question by studying a conditional variant of the Minimum KT-complexity Problem (MKTP), which we call McKTP, as follows. 1) First, we prove that if McKTP is average-case hard on a polynomial fraction of its instances, then there exist OWFs. 2) Then, we observe that McKTP is NP-complete under polynomial-time randomized reductions. 3) Finally, we prove that the existence of OWFs implies the nontrivial average-case hardness of McKTP. Thus the existence of OWFs is inextricably linked to the average-case hardness of this NP-complete problem. In fact, building on recently-announced results of Ren and Santhanam [Rahul Ilango et al., 2021], we show that McKTP is hard-on-average if and only if there are logspace-computable OWFs

Effect of Geometry, Loading and Elastic Moduli on Critical Parameters in a Nanoindentation Test in Polymeric Matrix Composites with a Nonhomogeneous Interphase

Fiber nanoindentation models are developed for polymeric matrix composites with nonhomogeneous interphases. Using design of experiments, the effects of geometry, loading and material parameters on the critical parameters of the indentation test such as the load-displacement curve, the maximum interfacial shear and normal stresses are studied. The sensitivity analysis shows that the initial load-displacement curve is dependent only on the indenter type, and not on parameters such as fiber volume fraction, interphase type, thickness of interphase, and boundary conditions. The interfacial tensile radial stresses are not sensitive to indenter type, or to type and thickness of interphase, while the interfacial compressive radial stresses are sensitive mainly to boundary conditions and thickness of interphase; however, the influence of these factors on the interfacial radial stresses can be large. In contrast, the interfacial shear stress is sensitive to all factors, but the influence of the factors is relatively small