15 Search Results for "Wee, Hoeteck"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.62
Improved Rate for Non-Malleable Codes and Time-Lock Puzzles

Authors: Cody Freitag, Ilan Komargodski, Manu Kondapaneni, and Jad Silbak

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

Abstract
Non-malleable codes allow a sender to transmit a message to a receiver, while providing a "best-possible" integrity guarantee to ensure that no attacker - who cannot already decode the message - can meaningfully tamper the message in transit. If tampered, the received message should either be invalid or unrelated to the original message. Non-malleable time-lock puzzles (TLPs) are a special case of non-malleable codes for bounded polynomial-depth tampering with very efficient encoding. In this work, we give generic techniques for constructing non-malleable codes and non-malleable TLPs with improved rate, which captures the ratio of a message’s length to its encoding length. A key contribution of our work is identifying a security notion for non-malleability, which we term "CCA-hiding", sufficient for our compilers. CCA-hiding is a relaxation of CCA-security for encryption or commitments to the fine-grained setting of codes, and requires that the encoded message remains hidden, even given a decoding oracle for any other codeword. Intriguingly, CCA-hiding does not imply non-malleability in the fine-grained setting, as is the case for encryption and commitments. Using our new techniques, we give the following constructions: - Rate-1 CCA-hiding TLPs in the plain model. - Rate-1 non-malleable codes for bounded polynomial-depth tampering in the auxiliary-input random oracle model (AI-ROM). - Rate-(1/2) non-malleable TLPs in the AI-ROM.
Cite as

Cody Freitag, Ilan Komargodski, Manu Kondapaneni, and Jad Silbak. Improved Rate for Non-Malleable Codes and Time-Lock Puzzles. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 62:1-62:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{freitag_et_al:LIPIcs.ITCS.2026.62,
  author =	{Freitag, Cody and Komargodski, Ilan and Kondapaneni, Manu and Silbak, Jad},
  title =	{{Improved Rate for Non-Malleable Codes and Time-Lock Puzzles}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{62:1--62:24},
  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.2026.62},
  URN =		{urn:nbn:de:0030-drops-253490},
  doi =		{10.4230/LIPIcs.ITCS.2026.62},
  annote =	{Keywords: Non-malleable codes, Time-lock puzzles}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.116
Decentralized Data Archival: New Definitions and Constructions

Authors: Elaine Shi, Rose Silver, and Changrui Mu

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

Abstract
We initiate the study of a new abstraction called incremental decentralized data archival (iDDA). Specifically, imagine that there is an ever-growing, massive database such as a blockchain, a comprehensive human knowledge base like Wikipedia, or the Internet archive. We want to build a decentralized archival system for such datasets to ensure long-term robustness and sustainability. We identify several important properties that an iDDA scheme should satisfy. First, to promote heterogeneity and decentralization, we want to encourage even weak nodes with limited space (e.g., users' home computers) to contribute. The minimum space requirement to contribute should be approximately independent of the data size. Second, if a collection of nodes together receive rewards commensurate with contributing a total of m blocks of space, then we want the following reassurances: 1) if m is at least the database size, we should be able to reconstruct the entire dataset; and 2) these nodes should actually be committing roughly m space in aggregate - specifically, when m is much larger than the data size, these nodes cannot store only one copy of the database, and be able to impersonate arbitrarily many pseudonyms and get unbounded rewards. We propose new definitions that mathematically formalize the aforementioned requirements of an iDDA scheme. We also devise an efficient construction in the random oracle model which satisfies the desired security requirements. Our scheme incurs only Õ(1) audit cost, as well as Õ(1) update cost for both the publisher and each node, where Õ(⋅) hides polylogarithmic factors. Further, the minimum space provisioning required to contribute is as small as polylogarithmic. Our construction exposes several interesting technical challenges. Specifically, we show that a straightforward application of the standard hierarchical data structure fails, since both our security definition and the underlying cryptographic primitives we employ lack the desired compositional guarantees. We devise novel techniques to overcome these compositional issues, resulting in a construction with provable security while still retaining efficiency. Finally, our new definitions also make a conceptual contribution, and lay the theoretical groundwork for the study of iDDA. We raise several interesting open problems along this direction.
Cite as

Elaine Shi, Rose Silver, and Changrui Mu. Decentralized Data Archival: New Definitions and Constructions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 116:1-116:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{shi_et_al:LIPIcs.ITCS.2026.116,
  author =	{Shi, Elaine and Silver, Rose and Mu, Changrui},
  title =	{{Decentralized Data Archival: New Definitions and Constructions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{116:1--116:22},
  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.2026.116},
  URN =		{urn:nbn:de:0030-drops-254037},
  doi =		{10.4230/LIPIcs.ITCS.2026.116},
  annote =	{Keywords: Decentralized Data Archival}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.15
How to Use Nondeterminism in Cryptography

Authors: Marshall Ball and Peter Crawford-Kahrl

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

Abstract
Nondeterministic reductions have yielded powerful results in the theory of computational complexity, yet are effectively useless in a cryptographic context. The reason for this is simple, a nondeterministic polynomial time adversary can trivially break almost any cryptographic primitive by simply guessing the "key." In order to use this powerful nondeterministic tool kit in the cryptographic context, we initiate the study of cryptography against adversaries with limited nondeterminism: polynomial time nondeterministic algorithms that are restricted to just a few bits of nondeterminism. We demonstrate that limited nondeterministic security is sufficient to prove two foundational results that have eluded our grasp for decades: dream hardness amplification, and extracting ω(log n) hardcore bits.
Cite as

Marshall Ball and Peter Crawford-Kahrl. How to Use Nondeterminism in Cryptography. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ball_et_al:LIPIcs.ITCS.2026.15,
  author =	{Ball, Marshall and Crawford-Kahrl, Peter},
  title =	{{How to Use Nondeterminism in Cryptography}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{15:1--15:22},
  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.2026.15},
  URN =		{urn:nbn:de:0030-drops-253024},
  doi =		{10.4230/LIPIcs.ITCS.2026.15},
  annote =	{Keywords: limited nondeterminism, cryptography, computational complexity, hardness amplification, pseudorandom generators, hardcore bits}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.76
Ideal Private Simultaneous Messages Schemes and Their Applications

Authors: Keitaro Hiwatashi and Reo Eriguchi

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

Abstract
Private Simultaneous Messages (PSM) is a minimal model for secure computation, where two parties, Alice and Bob, have private inputs x,y and a shared random string. Each of them sends a single message to an external party, Charlie, who can compute f(x,y) for a public function f but learns nothing else. The problem of narrowing the gap between upper and lower bounds on the communication complexity of PSM has been widely studied, but the gap still remains exponential. In this work, we study the communication complexity of PSM from a different perspective and introduce a special class of PSM, referred to as ideal PSM, in which each party’s message length attains the minimum, that is, their messages are taken from the same domain as inputs. We initiate a systematic study of ideal PSM with a complete characterization, several positive results, and applications. First, we provide a characterization of the class of functions that admit ideal PSM, based on permutation groups acting on the input domain. This characterization allows us to derive asymptotic upper bounds on the total number of such functions and a complete list for small domains. We also present several infinite families of functions of practical interest that admit ideal PSM. Interestingly, by simply restricting the input domains of these ideal PSM schemes, we can recover most of the existing PSM schemes that achieve the best known communication complexity in various computation models. As applications, we show that these ideal PSM schemes yield novel communication-efficient PSM schemes for functions with sparse or dense truth-tables and those with low-rank truth-tables. Furthermore, we obtain a PSM scheme for general functions that improves the constant factor in the dominant term of the best known communication complexity. An additional advantage is that our scheme simplifies the existing construction by avoiding the hierarchical design of internally invoking PSM schemes for smaller functions.
Cite as

Keitaro Hiwatashi and Reo Eriguchi. Ideal Private Simultaneous Messages Schemes and Their Applications. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 76:1-76:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hiwatashi_et_al:LIPIcs.ITCS.2026.76,
  author =	{Hiwatashi, Keitaro and Eriguchi, Reo},
  title =	{{Ideal Private Simultaneous Messages Schemes and Their Applications}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{76:1--76:23},
  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.2026.76},
  URN =		{urn:nbn:de:0030-drops-253633},
  doi =		{10.4230/LIPIcs.ITCS.2026.76},
  annote =	{Keywords: secure computation, private simultaneous messages, communication complexity}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.51
Randomized Black-Box PIT for Small Depth +-Regular Non-Commutative Circuits

Authors: G. V. Sumukha Bharadwaj and S. Raja

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
In this paper, we address the black-box polynomial identity testing (PIT) problem for non-commutative polynomials computed by +-regular circuits, a class of homogeneous circuits introduced by Arvind, Joglekar, Mukhopadhyay, and Raja (STOC 2017, Theory of Computing 2019). These circuits can compute polynomials with a number of monomials that are doubly exponential in the circuit size. They gave an efficient randomized PIT algorithm for +-regular circuits of depth 3 and posed the problem of developing an efficient black-box PIT for higher depths as an open problem. Our work makes progress on this open problem by resolving it for constant-depth +-regular circuits. We present a randomized black-box polynomial-time algorithm for +-regular circuits of any constant depth. Specifically, our algorithm runs in s^{O(d²)} time, where s and d represent the size and the depth of the +-regular circuit, respectively. Our approach combines several key techniques in a novel way. We employ a nondeterministic substitution automaton that transforms the polynomial into a structured form and utilizes polynomial sparsification along with commutative transformations to maintain non-zeroness. Additionally, we introduce matrix composition, coefficient modification via the automaton, and multi-entry outputs - methods that have not previously been applied in the context of black-box PIT. Together, these techniques enable us to effectively handle exponential degrees and doubly exponential sparsity in non-commutative settings, enabling polynomial identity testing for higher-depth circuits. In particular, we show that if f is a non-zero non-commutative polynomial in n variables over the field 𝔽, computed by a depth-d +-regular circuit of size s, then f cannot be a polynomial identity for the matrix algebra 𝕄_{N}(𝔽), where N = s^{O(d²)} and the size of the field 𝔽 depends on the degree of f. Interestingly, the size of the matrices does not depend on the degree of f. Our result can be interpreted as an Amitsur-Levitzki-type result [Amitsur and Levitzki, 1950] for polynomials computed by small-depth +-regular circuits.
Cite as

G. V. Sumukha Bharadwaj and S. Raja. Randomized Black-Box PIT for Small Depth +-Regular Non-Commutative Circuits. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 51:1-51:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sumukhabharadwaj_et_al:LIPIcs.FSTTCS.2025.51,
  author =	{Sumukha Bharadwaj, G. V. and Raja, S.},
  title =	{{Randomized Black-Box PIT for Small Depth +-Regular Non-Commutative Circuits}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{51:1--51:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.51},
  URN =		{urn:nbn:de:0030-drops-250949},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.51},
  annote =	{Keywords: Polynomial Identity Testing, Non-commutative Circuits, Algebraic Circuits, +-Regular Circuits, Black-Box}
}
Document
DOI: 10.4230/LIPIcs.ITC.2025.8
On the Definition of Malicious Private Information Retrieval

Authors: Bar Alon and Amos Beimel

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

Abstract
A multi-server private information retrieval (PIR) protocol allows a client to obtain an entry of its choice from a database, held by one or more servers, while hiding the identity of the entry from small enough coalitions of servers. In this paper, we study PIR protocols in which some of the servers are malicious and may not send messages according to the pre-described protocol. In previous papers, such protocols were defined by requiring that they are correct, private, and robust to malicious servers, i.e., by listing 3 properties that they should satisfy. However, 40 years of experience in studying secure multiparty protocols taught us that defining the security of protocols by a list of required properties is problematic. In this paper, we rectify this situation and define the security of PIR protocols with malicious servers using the real vs. ideal paradigm. We study the relationship between the property-based definition of PIR protocols and the real vs. ideal definition, showing the following results: - We prove that if we require full security from PIR protocols, e.g., the client outputs the correct value of the database entry with high probability even if a minority of the servers are malicious, then the two definitions are equivalent. This implies that constructions of such protocols that were proven secure using the property-based definition are actually secure under the "correct" definition of security. - We show that if we require security-with-abort from PIR protocols (called PIR protocols with error-detection in previous papers), i.e., protocols in which the user either outputs the correct value or an abort symbol, then there are protocols that are secure under the property-based definition; however, they do not satisfy the real vs. ideal definition, that is, they can be attacked allowing selective abort. This shows that the property-based definition of PIR protocols with security-with-abort is problematic. - We consider the compiler of Eriguchi et al. (TCC 22) that starts with a PIR protocol that is secure against semi-honest servers and constructs a PIR protocol with security-with-abort; this compiler implies the best-known PIR protocols with security-with-abort. We show that applying this compiler does not result in PIR protocols that are secure according to the real vs. ideal definition. However, we prove that a simple modification of this compiler results in PIR protocols that are secure according to the real vs. ideal definition.
Cite as

Bar Alon and Amos Beimel. On the Definition of Malicious Private Information Retrieval. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 8:1-8:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alon_et_al:LIPIcs.ITC.2025.8,
  author =	{Alon, Bar and Beimel, Amos},
  title =	{{On the Definition of Malicious Private Information Retrieval}},
  booktitle =	{6th Conference on Information-Theoretic Cryptography (ITC 2025)},
  pages =	{8:1--8:23},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-243581},
  doi =		{10.4230/LIPIcs.ITC.2025.8},
  annote =	{Keywords: Private information retrieval, secure multiparty computation}
}
Document
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.
Cite as

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}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.72
Card-Based Protocols Imply PSM Protocols

Authors: Kazumasa Shinagawa and Koji Nuida

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
Card-based cryptography is the art of cryptography using a deck of physical cards. While this area is known as a research area of recreational cryptography and is recently paid attention in educational purposes, there is no systematic study of the relationship between card-based cryptography and the other "conventional" cryptography. This paper establishes the first generic conversion from card-based protocols to private simultaneous messages (PSM) protocols, a special kind of secure multiparty computation. Our compiler supports "simple" card-based protocols, which is a natural subclass of finite-runtime protocols. The communication complexity of the resulting PSM protocol depends on how many cards are opened in total in all possible branches of the original card-based protocol. This result shows theoretical importance of such "opening complexity" of card-based protocols, which had not been focused in this area. As a consequence, lower bounds for PSM protocols imply those for simple card-based protocols. In particular, if there exists no PSM protocol with subexponential communication complexity for a function f, then there exists no simple card-based protocol with subexponential opening complexity for the same f.
Cite as

Kazumasa Shinagawa and Koji Nuida. Card-Based Protocols Imply PSM Protocols. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 72:1-72:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{shinagawa_et_al:LIPIcs.STACS.2025.72,
  author =	{Shinagawa, Kazumasa and Nuida, Koji},
  title =	{{Card-Based Protocols Imply PSM Protocols}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{72:1--72:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.72},
  URN =		{urn:nbn:de:0030-drops-228975},
  doi =		{10.4230/LIPIcs.STACS.2025.72},
  annote =	{Keywords: Card-based cryptography, private simultaneous messages}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.56
Incompressible Functional Encryption

Authors: Rishab Goyal, Venkata Koppula, Mahesh Sreekumar Rajasree, and Aman Verma

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
Incompressible encryption (Dziembowski, Crypto'06; Guan, Wichs, Zhandry, Eurocrypt'22) protects from attackers that learn the entire decryption key, but cannot store the full ciphertext. In incompressible encryption, the attacker must try to compress a ciphertext within pre-specified memory bound S before receiving the secret key. In this work, we generalize the notion of incompressibility to functional encryption. In incompressible functional encryption, the adversary can corrupt non-distinguishing keys at any point, but receives the distinguishing keys only after compressing the ciphertext to within S bits. An important efficiency measure for incompressible encryption is the ciphertext-rate (i.e., rate = |m|/|ct|). We give many new results for incompressible functional encryption for circuits, from minimal assumption of (non-incompressible) functional encryption, with 1) ct-rate-1/2 and short secret keys, 2) ct-rate-1 and large secret keys. Along the way, we also give a new incompressible attribute-based encryption for circuits from standard assumptions, with ct-rate-1/2 and short secret keys. Our results achieve optimal efficiency, as incompressible attribute-based/functional encryption with ct-rate-1 as well as short secret keys has strong barriers for provable security from standard assumptions. Moreover, our assumptions are minimal as incompressible attribute-based/functional encryption are strictly stronger than their non-incompressible counterparts.
Cite as

Rishab Goyal, Venkata Koppula, Mahesh Sreekumar Rajasree, and Aman Verma. Incompressible Functional Encryption. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 56:1-56:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goyal_et_al:LIPIcs.ITCS.2025.56,
  author =	{Goyal, Rishab and Koppula, Venkata and Rajasree, Mahesh Sreekumar and Verma, Aman},
  title =	{{Incompressible Functional Encryption}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{56:1--56:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.56},
  URN =		{urn:nbn:de:0030-drops-226849},
  doi =		{10.4230/LIPIcs.ITCS.2025.56},
  annote =	{Keywords: functional encryption, attribute-based encryption, incompressible encryption}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.6
On Identity Testing and Noncommutative Rank Computation over the Free Skew Field

Authors: V. Arvind, Abhranil Chatterjee, Utsab Ghosal, Partha Mukhopadhyay, and C. Ramya

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
The identity testing of rational formulas (RIT) in the free skew field efficiently reduces to computing the rank of a matrix whose entries are linear polynomials in noncommuting variables [Hrubeš and Wigderson, 2015]. This rank computation problem has deterministic polynomial-time white-box algorithms [Ankit Garg et al., 2016; Ivanyos et al., 2018] and a randomized polynomial-time algorithm in the black-box setting [Harm Derksen and Visu Makam, 2017]. In this paper, we propose a new approach for efficient derandomization of black-box RIT. Additionally, we obtain results for matrix rank computation over the free skew field and construct efficient linear pencil representations for a new class of rational expressions. More precisely, we show: - Under the hardness assumption that the ABP (algebraic branching program) complexity of every polynomial identity for the k×k matrix algebra is 2^Ω(k) [Andrej Bogdanov and Hoeteck Wee, 2005], we obtain a subexponential-time black-box RIT algorithm for rational formulas of inversion height almost logarithmic in the size of the formula. This can be seen as the first "hardness implies derandomization" type theorem for rational formulas. - We show that the noncommutative rank of any matrix over the free skew field whose entries have small linear pencil representations can be computed in deterministic polynomial time. While an efficient rank computation was known for matrices with noncommutative formulas as entries [Ankit Garg et al., 2020], we obtain the first deterministic polynomial-time algorithms for rank computation of matrices whose entries are noncommutative ABPs or rational formulas. - Motivated by the definition given by Bergman [George M Bergman, 1976], we define a new class of rational functions where a rational function of inversion height at most h is defined as a composition of a noncommutative r-skewed circuit (equivalently an ABP) with inverses of rational functions of this class of inversion height at most h-1 which are also disjoint. We obtain a polynomial-size linear pencil representation for this class which gives a white-box deterministic polynomial-time identity testing algorithm for the class.
Cite as

V. Arvind, Abhranil Chatterjee, Utsab Ghosal, Partha Mukhopadhyay, and C. Ramya. On Identity Testing and Noncommutative Rank Computation over the Free Skew Field. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{arvind_et_al:LIPIcs.ITCS.2023.6,
  author =	{Arvind, V. and Chatterjee, Abhranil and Ghosal, Utsab and Mukhopadhyay, Partha and Ramya, C.},
  title =	{{On Identity Testing and Noncommutative Rank Computation over the Free Skew Field}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.6},
  URN =		{urn:nbn:de:0030-drops-175093},
  doi =		{10.4230/LIPIcs.ITCS.2023.6},
  annote =	{Keywords: Algebraic Complexity, Identity Testing, Non-commutative rank}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.28
Lattice-Inspired Broadcast Encryption and Succinct Ciphertext-Policy ABE

Authors: Zvika Brakerski and Vinod Vaikuntanathan

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
Broadcast encryption remains one of the few remaining central cryptographic primitives that are not yet known to be achievable under a standard cryptographic assumption (excluding obfuscation-based constructions, see below). Furthermore, prior to this work, there were no known direct candidates for post-quantum-secure broadcast encryption. We propose a candidate ciphertext-policy attribute-based encryption (CP-ABE) scheme for circuits, where the ciphertext size depends only on the depth of the policy circuit (and not its size). This, in particular, gives us a Broadcast Encryption (BE) scheme where the size of the keys and ciphertexts have a poly-logarithmic dependence on the number of users. This goal was previously only known to be achievable assuming ideal multilinear maps (Boneh, Waters and Zhandry, Crypto 2014) or indistinguishability obfuscation (Boneh and Zhandry, Crypto 2014) and in a concurrent work from generic bilinear groups and the learning with errors (LWE) assumption (Agrawal and Yamada, Eurocrypt 2020). Our construction relies on techniques from lattice-based (and in particular LWE-based) cryptography. We analyze some attempts at cryptanalysis, but we are unable to provide a security proof.
Cite as

Zvika Brakerski and Vinod Vaikuntanathan. Lattice-Inspired Broadcast Encryption and Succinct Ciphertext-Policy ABE. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{brakerski_et_al:LIPIcs.ITCS.2022.28,
  author =	{Brakerski, Zvika and Vaikuntanathan, Vinod},
  title =	{{Lattice-Inspired Broadcast Encryption and Succinct Ciphertext-Policy ABE}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{28:1--28:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.28},
  URN =		{urn:nbn:de:0030-drops-156243},
  doi =		{10.4230/LIPIcs.ITCS.2022.28},
  annote =	{Keywords: Theoretical Cryptography, Broadcast Encryption, Attribute-Based Encryption, Lattice-Based Cryptography}
}
Document
DOI: 10.4230/LIPIcs.ITC.2021.12
Linear Threshold Secret-Sharing with Binary Reconstruction

Authors: Marshall Ball, Alper Çakan, and Tal Malkin

Published in: LIPIcs, Volume 199, 2nd Conference on Information-Theoretic Cryptography (ITC 2021)

Abstract
Motivated in part by applications in lattice-based cryptography, we initiate the study of the size of linear threshold (`t-out-of-n') secret-sharing where the linear reconstruction function is restricted to coefficients in {0,1}. We also study the complexity of such schemes with the additional requirement that the joint distribution of the shares of any unauthorized set of parties is not only independent of the secret, but also uniformly distributed. We prove upper and lower bounds on the share size of such schemes, where the size is measured by the total number of field elements distributed to the parties. We prove our results by defining and investigating an equivalent variant of Karchmer and Wigderson’s Monotone Span Programs [CCC, 1993]. One ramification of our results is that a natural variant of Shamir’s classic scheme [Comm. of ACM, 1979], where bit-decomposition is applied to each share, is optimal for when the underlying field has characteristic 2. Another ramification is that schemes obtained from monotone formulae are optimal for certain threshold values when the field’s characteristic is any constant. For schemes with the uniform distribution requirement, we show that they must use Ω(nlog n) field elements, for all thresholds 2 < t < n and regardless of the field. Moreover, this is tight up to constant factors for the special cases where any t = n-1 parties can reconstruct, as well as for any threshold when the field characteristic is 2.
Cite as

Marshall Ball, Alper Çakan, and Tal Malkin. Linear Threshold Secret-Sharing with Binary Reconstruction. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ball_et_al:LIPIcs.ITC.2021.12,
  author =	{Ball, Marshall and \c{C}akan, Alper and Malkin, Tal},
  title =	{{Linear Threshold Secret-Sharing with Binary Reconstruction}},
  booktitle =	{2nd Conference on Information-Theoretic Cryptography (ITC 2021)},
  pages =	{12:1--12:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-197-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{199},
  editor =	{Tessaro, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.12},
  URN =		{urn:nbn:de:0030-drops-143313},
  doi =		{10.4230/LIPIcs.ITC.2021.12},
  annote =	{Keywords: Secret sharing, Span programs, Lattice-based cryptography}
}
Document
DOI: 10.4230/LIPIcs.ITC.2020.13
One-One Constrained Pseudorandom Functions

Authors: Naty Peter, Rotem Tsabary, and Hoeteck Wee

Published in: LIPIcs, Volume 163, 1st Conference on Information-Theoretic Cryptography (ITC 2020)

Abstract
We define and study a new cryptographic primitive, named One-One Constrained Pseudorandom Functions. In this model there are two parties, Alice and Bob, that hold a common random string K, where Alice in addition holds a predicate f:[N] → {0,1} and Bob in addition holds an input x ∈ [N]. We then let Alice generate a key K_f based on f and K, and let Bob evaluate a value K_x based on x and K. We consider a third party that sees the values (x,f,K_f) and the goal is to allow her to reconstruct K_x whenever f(x)=1, while keeping K_x pseudorandom whenever f(x)=0. This primitive can be viewed as a relaxation of constrained PRFs, such that there is only a single key query and a single evaluation query. We focus on the information-theoretic setting, where the one-one cPRF has perfect correctness and perfect security. Our main results are as follows. 1) A Lower Bound. We show that in the information-theoretic setting, any one-one cPRF for punctured predicates is of exponential complexity (and thus the lower bound meets the upper bound that is given by a trivial construction). This stands in contrast with the well known GGM-based punctured PRF from OWF, which is in particular a one-one cPRF. This also implies a similar lower bound for all NC1. 2) New Constructions. On the positive side, we present efficient information-theoretic constructions of one-one cPRFs for a few other predicate families, such as equality predicates, inner-product predicates, and subset predicates. We also show a generic AND composition lemma that preserves complexity. 3) An Amplification to standard cPRF. We show that all of our one-one cPRF constructions can be amplified to a standard (single-key) cPRF via any key-homomorphic PRF that supports linear computations. More generally, we suggest a new framework that we call the double-key model which allows to construct constrained PRFs via key-homomorphic PRFs. 4) Relation to CDS. We show that one-one constrained PRFs imply conditional disclosure of secrets (CDS) protocols. We believe that this simple model can be used to better understand constrained PRFs and related cryptographic primitives, and that further applications of one-one constrained PRFs and our double-key model will be found in the future, in addition to those we show in this paper.
Cite as

Naty Peter, Rotem Tsabary, and Hoeteck Wee. One-One Constrained Pseudorandom Functions. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{peter_et_al:LIPIcs.ITC.2020.13,
  author =	{Peter, Naty and Tsabary, Rotem and Wee, Hoeteck},
  title =	{{One-One Constrained Pseudorandom Functions}},
  booktitle =	{1st Conference on Information-Theoretic Cryptography (ITC 2020)},
  pages =	{13:1--13:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-151-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{163},
  editor =	{Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020.13},
  URN =		{urn:nbn:de:0030-drops-121188},
  doi =		{10.4230/LIPIcs.ITC.2020.13},
  annote =	{Keywords: Constrained pseudorandom functions, function secret-sharing, conditional disclosure of secrets}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2020.68
Pseudorandomness and the Minimum Circuit Size Problem

Authors: Rahul Santhanam

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

Abstract
We explore the possibility of basing one-way functions on the average-case hardness of the fundamental Minimum Circuit Size Problem (MCSP[s]), which asks whether a Boolean function on n bits specified by its truth table has circuits of size s(n). 1) (Pseudorandomness from Zero-Error Average-Case Hardness) We show that for a given size function s, the following are equivalent: Pseudorandom distributions supported on strings describable by s(O(n))-size circuits exist; Hitting sets supported on strings describable by s(O(n))-size circuits exist; MCSP[s(O(n))] is zero-error average-case hard. Using similar techniques, we show that Feige’s hypothesis for random k-CNFs implies that there is a pseudorandom distribution (with constant error) supported entirely on satisfiable formulas. Underlying our results is a general notion of semantic sampling, which might be of independent interest. 2) (A New Conjecture) In analogy to a known universal construction of succinct hitting sets against arbitrary polynomial-size adversaries, we propose the Universality Conjecture: there is a universal construction of succinct pseudorandom distributions against arbitrary polynomial-size adversaries. We show that under the Universality Conjecture, the following are equivalent: One-way functions exist; Natural proofs useful against sub-exponential size circuits do not exist; Learning polynomial-size circuits with membership queries over the uniform distribution is hard; MCSP[2^(ε n)] is zero-error hard on average for some ε > 0; Cryptographic succinct hitting set generators exist. 3) (Non-Black-Box Results) We show that for weak circuit classes ℭ against which there are natural proofs [Alexander A. Razborov and Steven Rudich, 1997], pseudorandom functions secure against poly-size circuits in ℭ imply superpolynomial lower bounds in P against poly-size circuits in ℭ. We also show that for a certain natural variant of MCSP, there is a polynomial-time reduction from approximating the problem well in the worst case to solving it on average. These results are shown using non-black-box techniques, and in the first case we show that there is no black-box proof of the result under standard crypto assumptions.
Cite as

Rahul Santhanam. Pseudorandomness and the Minimum Circuit Size Problem. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 68:1-68:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{santhanam:LIPIcs.ITCS.2020.68,
  author =	{Santhanam, Rahul},
  title =	{{Pseudorandomness and the Minimum Circuit Size Problem}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{68:1--68:26},
  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.2020.68},
  URN =		{urn:nbn:de:0030-drops-117532},
  doi =		{10.4230/LIPIcs.ITCS.2020.68},
  annote =	{Keywords: Minimum Circuit Size Problem, Pseudorandomness, Average-case Complexity, Natural Proofs, Universality Conjecture}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2018.41
On the Inner Product Predicate and a Generalization of Matching Vector Families

Authors: Balthazar Bauer, Jevgenijs Vihrovs, and Hoeteck Wee

Published in: LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

Abstract
Motivated by cryptographic applications such as predicate encryption, we consider the problem of representing an arbitrary predicate as the inner product predicate on two vectors. Concretely, fix a Boolean function P and some modulus q. We are interested in encoding x to x_vector and y to y_vector so that P(x,y) = 1 <=> <x_vector,y_vector> = 0 mod q, where the vectors should be as short as possible. This problem can also be viewed as a generalization of matching vector families, which corresponds to the equality predicate. Matching vector families have been used in the constructions of Ramsey graphs, private information retrieval (PIR) protocols, and more recently, secret sharing. Our main result is a simple lower bound that allows us to show that known encodings for many predicates considered in the cryptographic literature such as greater than and threshold are essentially optimal for prime modulus q. Using this approach, we also prove lower bounds on encodings for composite q, and then show tight upper bounds for such predicates as greater than, index and disjointness.
Cite as

Balthazar Bauer, Jevgenijs Vihrovs, and Hoeteck Wee. On the Inner Product Predicate and a Generalization of Matching Vector Families. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 41:1-41:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bauer_et_al:LIPIcs.FSTTCS.2018.41,
  author =	{Bauer, Balthazar and Vihrovs, Jevgenijs and Wee, Hoeteck},
  title =	{{On the Inner Product Predicate and a Generalization of Matching Vector Families}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{41:1--41:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Ganguly, Sumit and Pandya, Paritosh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.41},
  URN =		{urn:nbn:de:0030-drops-99400},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.41},
  annote =	{Keywords: Predicate Encryption, Inner Product Encoding, Matching Vector Families}
}
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