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DOI: 10.4230/LIPIcs.ITC.2025.4

Time-Space Tradeoffs of Truncation with Preprocessing

Authors: Krzysztof Pietrzak and Pengxiang Wang

Published in: LIPIcs, Volume 343, 6th Conference on Information-Theoretic Cryptography (ITC 2025)

Abstract

Truncation of cryptographic outputs is a technique that was recently introduced in Baldimtsi et al. [Foteini Baldimtsi et al., 2022]. The general idea is to try out many inputs to some cryptographic algorithm until the output (e.g. a public-key or some hash value) falls into some sparse set and thus can be compressed: by trying out an expected 2^k different inputs one will find an output that starts with k zeros. Using such truncation one can for example save substantial gas fees on Blockchains where storing values is very expensive. While [Foteini Baldimtsi et al., 2022] show that truncation preserves the security of the underlying primitive, they only consider a setting without preprocessing. In this work we show that lower bounds on the time-space tradeoff for inverting random functions and permutations also hold with truncation, except for parameters ranges where the bound fails to hold for "trivial" reasons. Concretely, it’s known that any algorithm that inverts a random function or permutation with range N making T queries and using S bits of auxiliary input must satisfy S⋅ T ≥ Nlog N. This lower bound no longer holds in the truncated setting where one must only invert a challenge from a range of size N/2^k, as now one can simply save the replies to all N/2^k challenges, which requires S = log N⋅ N /2^k bits and allows to invert with T = 1 query. We show that with truncation, whenever S is somewhat smaller than the log N⋅ N /2^k bits required to store the entire truncated function table, the known S⋅ T ≥ Nlog N lower bound applies.

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Krzysztof Pietrzak and Pengxiang Wang. Time-Space Tradeoffs of Truncation with Preprocessing. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 4:1-4:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pietrzak_et_al:LIPIcs.ITC.2025.4,
  author =	{Pietrzak, Krzysztof and Wang, Pengxiang},
  title =	{{Time-Space Tradeoffs of Truncation with Preprocessing}},
  booktitle =	{6th Conference on Information-Theoretic Cryptography (ITC 2025)},
  pages =	{4:1--4:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-385-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{343},
  editor =	{Gilboa, Niv},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2025.4},
  URN =		{urn:nbn:de:0030-drops-243544},
  doi =		{10.4230/LIPIcs.ITC.2025.4},
  annote =	{Keywords: Time-Space Lower Bounds, Blockchains}
}

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RANDOM

DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.56

Robustness for Space-Bounded Statistical Zero Knowledge

Authors: Eric Allender, Jacob Gray, Saachi Mutreja, Harsha Tirumala, and Pengxiang Wang

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract

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.

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Eric Allender, Jacob Gray, Saachi Mutreja, Harsha Tirumala, and Pengxiang Wang. Robustness for Space-Bounded Statistical Zero Knowledge. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 56:1-56:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{allender_et_al:LIPIcs.APPROX/RANDOM.2023.56,
  author =	{Allender, Eric and Gray, Jacob and Mutreja, Saachi and Tirumala, Harsha and Wang, Pengxiang},
  title =	{{Robustness for Space-Bounded Statistical Zero Knowledge}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{56:1--56:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.56},
  URN =		{urn:nbn:de:0030-drops-188815},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.56},
  annote =	{Keywords: Interactive Proofs}
}

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Documents authored by Wang, Pengxiang

Time-Space Tradeoffs of Truncation with Preprocessing

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Robustness for Space-Bounded Statistical Zero Knowledge

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