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Documents authored by Weber, Daniel

Document
DOI: 10.4230/LIPIcs.ITCS.2026.71
Lower Bounds on FSS from Dynamic Data Structures

Authors: Niv Gilboa and Daniel Weber

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
In Function Secret Sharing (FSS), a dealer with a given function f: {0,1}ⁿ → 𝔾 from n bits to a commutative group 𝔾 such that f is in a function class ℱ shares succinct keys with two properties. Evaluating each key separately on a common input x results in additive shares of f(x) and any subset of the keys does not provide information on f. Two-party FSS schemes which are reducible to One-way Functions (OWF) have applications in cryptography, complexity, and in practical data security systems. We establish a two-way transformation between a two-party FSS scheme for a function class ℱ, which is black-box reducible to an OWF, or even black-box reducible to a family of Pseudo-Random Functions (PRF) and a dynamic data structure that supports range queries on ℱ. A data structure of this type enables dynamically adding functions to a multiset of functions F ⊆ ℱ, and answering range queries on the output of F, i.e., returning ∑_{f ∈ F} f(x) for a query x. The data structures are defined in one of several models which abstract RAM. The correspondence together with known lower bounds on the update time and the query time in data structures leads to the first non-trivial lower bounds on FSS schemes which are black-box reducible to PRF. These lower bounds apply to FSS schemes with polynomial key size and include: - For ℱ^d_{box}, the class of all functions which assign a constant group element β ∈ 𝔾 to any input in a specified d-dimensional box and 0 to all other inputs: if the key sharing function, Gen, runs in time polynomial in n and the evaluation function is Eval then: - If d ≥ 2 and 𝔾 = ℤ₂ then Eval’s running time is Ω ((n^{3/2})/(log³ n)). - If d ≥ 2 and 𝔾 is cyclic such that log |𝔾| = (1 + ε) n then Eval’s running time is Ω ((n/(log n)) ²). - If d > 2 is a constant and further, Gen and Eval correspond to operations on data structures in the Oblivious Group Model (this includes all known FSS from OWF techniques), then the product of Eval’s time and the key size is Ω(n^{d-1}). - For ℱ_{mono}, the class of all monomials ax^b ∈ 𝔽_{2ⁿ}[X] such that b ≤ B, assuming n^{ω(1)} ≤ B ≤ 2^{n/4}: if Gen runs in polynomial time, then Eval’s running time is Ω ((n √{log B})/(log² n)).
Cite as

Niv Gilboa and Daniel Weber. Lower Bounds on FSS from Dynamic Data Structures. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 71:1-71:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gilboa_et_al:LIPIcs.ITCS.2026.71,
  author =	{Gilboa, Niv and Weber, Daniel},
  title =	{{Lower Bounds on FSS from Dynamic Data Structures}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{71:1--71:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.71},
  URN =		{urn:nbn:de:0030-drops-253585},
  doi =		{10.4230/LIPIcs.ITCS.2026.71},
  annote =	{Keywords: FSS, Data Structures, Lower Bounds, Black-Box Reductions}
}
Document
DOI: 10.4230/OASIcs.iPMVM.2020.11
Finite Element Simulation Combination to Predict the Distortion of Thin Walled Milled Aluminum Workpieces as a Result of Machining Induced Residual Stresses

Authors: Daniel Weber, Benjamin Kirsch, Christopher R. Chighizola, Julianne E. Jonsson, Christopher R. D’Elia, Barbara S. Linke, Michael R. Hill, and Jan C. Aurich

Published in: OASIcs, Volume 89, 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020)

Abstract
Machining induced residual stresses (MIRS) are a main driver for distortion of monolithic thin walled aluminum workpieces. A typical machining process for manufacturing such geometries for the aerospace industry is milling. In order to avoid high costs due to remanufacturing or part rejection, a simulation combination, consisting of two different finite element method (FEM) models, is developed to predict the part distortion due to MIRS. First, a 3D FEM cutting simulation is developed to predict the residual stresses due to machining. This simulation avoids cost intensive residual stress measurements. The milling process of the aluminum alloy AA7050-T7451 with a regular end mill is simulated. The simulation output, MIRS, forces and temperatures, is validated by face milling experiments on aluminum. The model takes mechanical dynamic effects, thermomechanical coupling, material properties and a damage law into account. Second, a subsequent finite element simulation, characterized by a static, linear elastic model, where the simulated MIRS from the cutting model are used as an input and the distortion of the workpiece is calculated, is presented. The predicted distortion is compared to an additional experiment, where a 1 mm thick wafer was removed at the milled surface of the aluminum workpiece. Furthermore, a thin walled component that represents a down scaled version of an aerospace component is manufactured and its distortion is analyzed. The results show that MIRS could be forecasted with moderate accuracy, which leads to the conclusion that the FEM cutting model needs to be improved in order to use the MIRS for a correct prediction of the distortion with the help of the linear elastic FEM model. The linear elastic model on the other hand is able to predict the part distortion with higher accuracy when using measured data instead of MIRS from the cutting simulation.
Cite as

Daniel Weber, Benjamin Kirsch, Christopher R. Chighizola, Julianne E. Jonsson, Christopher R. D’Elia, Barbara S. Linke, Michael R. Hill, and Jan C. Aurich. Finite Element Simulation Combination to Predict the Distortion of Thin Walled Milled Aluminum Workpieces as a Result of Machining Induced Residual Stresses. In 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020). Open Access Series in Informatics (OASIcs), Volume 89, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{weber_et_al:OASIcs.iPMVM.2020.11,
  author =	{Weber, Daniel and Kirsch, Benjamin and Chighizola, Christopher R. and Jonsson, Julianne E. and D’Elia, Christopher R. and Linke, Barbara S. and Hill, Michael R. and Aurich, Jan C.},
  title =	{{Finite Element Simulation Combination to Predict the Distortion of Thin Walled Milled Aluminum Workpieces as a Result of Machining Induced Residual Stresses}},
  booktitle =	{2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020)},
  pages =	{11:1--11:21},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-183-2},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{89},
  editor =	{Garth, Christoph and Aurich, Jan C. and Linke, Barbara and M\"{u}ller, Ralf and Ravani, Bahram and Weber, Gunther H. and Kirsch, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.iPMVM.2020.11},
  URN =		{urn:nbn:de:0030-drops-137604},
  doi =		{10.4230/OASIcs.iPMVM.2020.11},
  annote =	{Keywords: Machining induced residual stresses, distortion, Finite element method simulation}
}
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