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Documents authored by Vasudevan, Prashant Nalini

Document
DOI: 10.4230/LIPIcs.ITCS.2026.23
Decoding Balanced Linear Codes with Preprocessing

Authors: Andrej Bogdanov, Rohit Chatterjee, Yunqi Li, and Prashant Nalini Vasudevan

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

Abstract
Prange’s information set algorithm is a well-known decoding algorithm for linear codes. It decodes corrupted codewords of most 𝔽₂-linear codes C of message length n up to relative error rate O(log n / n) in poly(n) time. We show that the error rate can be improved to O((log n)² / n), provided: (1) the decoder has access to a polynomial-length advice string that depends on C only, and (2) C is n^{-Ω(1)}-balanced. As a consequence we improve the error tolerance in decoding random linear codes if inefficient preprocessing of the code is allowed. This reveals potential vulnerabilities in cryptographic applications of Learning Noisy Parities with low noise rate. Our main technical result is that the Hamming weight of Hw, where the rows of H are a random sample of short dual codewords, measures the proximity of a received word w to the code in the regime of interest. Given such H as advice, our algorithm corrects errors by locally minimizing this measure. We show that for most codes, the error rate tolerated by our decoder is asymptotically optimal among all algorithms whose decision is based on thresholding Hw for an arbitrary polynomial-size advice matrix H.
Cite as

Andrej Bogdanov, Rohit Chatterjee, Yunqi Li, and Prashant Nalini Vasudevan. Decoding Balanced Linear Codes with Preprocessing. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 23:1-23:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bogdanov_et_al:LIPIcs.ITCS.2026.23,
  author =	{Bogdanov, Andrej and Chatterjee, Rohit and Li, Yunqi and Vasudevan, Prashant Nalini},
  title =	{{Decoding Balanced Linear Codes with Preprocessing}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{23:1--23:23},
  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.2026.23},
  URN =		{urn:nbn:de:0030-drops-253107},
  doi =		{10.4230/LIPIcs.ITCS.2026.23},
  annote =	{Keywords: Linear codes, nearest codeword problem, learning parity with noise}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.2
Hardness Amplification for Real-Valued Functions

Authors: Yunqi Li and Prashant Nalini Vasudevan

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
Given an integer-valued function f:{0,1}ⁿ → {0,1,… , m-1} that is mildly hard to compute on instances drawn from some distribution D over {0,1}ⁿ, we show that the function g(x_1, … , x_t) = f(x_1) + ⋯ + f(x_t) is strongly hard to compute on instances (x_1,… ,x_t) drawn from the product distribution D^t. We also show the same for the task of approximately computing real-valued functions f:{0,1}ⁿ → [0,m). Our theorems immediately imply hardness self-amplification for several natural problems including Max-Clique and Max-SAT, Approximate #SAT, Entropy Estimation, etc..
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Yunqi Li and Prashant Nalini Vasudevan. Hardness Amplification for Real-Valued Functions. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 2:1-2:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{li_et_al:LIPIcs.CCC.2025.2,
  author =	{Li, Yunqi and Vasudevan, Prashant Nalini},
  title =	{{Hardness Amplification for Real-Valued Functions}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{2:1--2:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.2},
  URN =		{urn:nbn:de:0030-drops-236967},
  doi =		{10.4230/LIPIcs.CCC.2025.2},
  annote =	{Keywords: Average-case complexity, hardness amplification}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.81
Cryptography from Information Loss

Authors: Marshall Ball, Elette Boyle, Akshay Degwekar, Apoorvaa Deshpande, Alon Rosen, Vinod Vaikuntanathan, and Prashant Nalini Vasudevan

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
Reductions between problems, the mainstay of theoretical computer science, efficiently map an instance of one problem to an instance of another in such a way that solving the latter allows solving the former. The subject of this work is "lossy" reductions, where the reduction loses some information about the input instance. We show that such reductions, when they exist, have interesting and powerful consequences for lifting hardness into "useful" hardness, namely cryptography. Our first, conceptual, contribution is a definition of lossy reductions in the language of mutual information. Roughly speaking, our definition says that a reduction C is t-lossy if, for any distribution X over its inputs, the mutual information I(X;C(X)) ≤ t. Our treatment generalizes a variety of seemingly related but distinct notions such as worst-case to average-case reductions, randomized encodings (Ishai and Kushilevitz, FOCS 2000), homomorphic computations (Gentry, STOC 2009), and instance compression (Harnik and Naor, FOCS 2006). We then proceed to show several consequences of lossy reductions: 1. We say that a language L has an f-reduction to a language L' for a Boolean function f if there is a (randomized) polynomial-time algorithm C that takes an m-tuple of strings X = (x_1,…,x_m), with each x_i ∈ {0,1}^n, and outputs a string z such that with high probability, L'(z) = f(L(x_1),L(x_2),…,L(x_m)). Suppose a language L has an f-reduction C to L' that is t-lossy. Our first result is that one-way functions exist if L is worst-case hard and one of the following conditions holds: - f is the OR function, t ≤ m/100, and L' is the same as L - f is the Majority function, and t ≤ m/100 - f is the OR function, t ≤ O(m log n), and the reduction has no error This improves on the implications that follow from combining (Drucker, FOCS 2012) with (Ostrovsky and Wigderson, ISTCS 1993) that result in auxiliary-input one-way functions. 2. Our second result is about the stronger notion of t-compressing f-reductions - reductions that only output t bits. We show that if there is an average-case hard language L that has a t-compressing Majority reduction to some language for t=m/100, then there exist collision-resistant hash functions. This improves on the result of (Harnik and Naor, STOC 2006), whose starting point is a cryptographic primitive (namely, one-way functions) rather than average-case hardness, and whose assumption is a compressing OR-reduction of SAT (which is now known to be false unless the polynomial hierarchy collapses). Along the way, we define a non-standard one-sided notion of average-case hardness, which is the notion of hardness used in the second result above, that may be of independent interest.
Cite as

Marshall Ball, Elette Boyle, Akshay Degwekar, Apoorvaa Deshpande, Alon Rosen, Vinod Vaikuntanathan, and Prashant Nalini Vasudevan. Cryptography from Information Loss. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 81:1-81:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ball_et_al:LIPIcs.ITCS.2020.81,
  author =	{Ball, Marshall and Boyle, Elette and Degwekar, Akshay and Deshpande, Apoorvaa and Rosen, Alon and Vaikuntanathan, Vinod and Vasudevan, Prashant Nalini},
  title =	{{Cryptography from Information Loss}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{81:1--81:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.81},
  URN =		{urn:nbn:de:0030-drops-117667},
  doi =		{10.4230/LIPIcs.ITCS.2020.81},
  annote =	{Keywords: Compression, Information Loss, One-Way Functions, Reductions, Generic Constructions}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2019.4
Placing Conditional Disclosure of Secrets in the Communication Complexity Universe

Authors: Benny Applebaum and Prashant Nalini Vasudevan

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
In the conditional disclosure of secrets (CDS) problem (Gertner et al., J. Comput. Syst. Sci., 2000) Alice and Bob, who hold n-bit inputs x and y respectively, wish to release a common secret z to Carol (who knows both x and y) if and only if the input (x,y) satisfies some predefined predicate f. Alice and Bob are allowed to send a single message to Carol which may depend on their inputs and some shared randomness, and the goal is to minimize the communication complexity while providing information-theoretic security. Despite the growing interest in this model, very few lower-bounds are known. In this paper, we relate the CDS complexity of a predicate f to its communication complexity under various communication games. For several basic predicates our results yield tight, or almost tight, lower-bounds of Omega(n) or Omega(n^{1-epsilon}), providing an exponential improvement over previous logarithmic lower-bounds. We also define new communication complexity classes that correspond to different variants of the CDS model and study the relations between them and their complements. Notably, we show that allowing for imperfect correctness can significantly reduce communication - a seemingly new phenomenon in the context of information-theoretic cryptography. Finally, our results show that proving explicit super-logarithmic lower-bounds for imperfect CDS protocols is a necessary step towards proving explicit lower-bounds against the class AM, or even AM cap coAM - a well known open problem in the theory of communication complexity. Thus imperfect CDS forms a new minimal class which is placed just beyond the boundaries of the "civilized" part of the communication complexity world for which explicit lower-bounds are known.
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Benny Applebaum and Prashant Nalini Vasudevan. Placing Conditional Disclosure of Secrets in the Communication Complexity Universe. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 4:1-4:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{applebaum_et_al:LIPIcs.ITCS.2019.4,
  author =	{Applebaum, Benny and Vasudevan, Prashant Nalini},
  title =	{{Placing Conditional Disclosure of Secrets in the Communication Complexity Universe}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{4:1--4:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.4},
  URN =		{urn:nbn:de:0030-drops-100976},
  doi =		{10.4230/LIPIcs.ITCS.2019.4},
  annote =	{Keywords: Conditional Disclosure of Secrets, Information-Theoretic Security}
}
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