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**Published in:** LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Current protocols for Multi-Party Computation (MPC) consider the setting where all parties have access to similar resources. For example, all parties have access to channels bounded by the same worst-case delay upper bound Δ, and all channels have the same cost of communication. As a consequence, the overall protocol performance (resp. the communication cost) may be heavily affected by the slowest (resp. the most expensive) channel, even when most channels are fast (resp. cheap). Given the state of affairs, we initiate a systematic study of asymmetric MPC. In asymmetric MPC, the parties are divided into two categories: fast and slow parties, depending on whether they have access to high-end or low-end resources.
We investigate two different models. In the first, we consider asymmetric communication delays: Fast parties are connected via channels with small delay δ among themselves, while channels connected to (at least) one slow party have a large delay Δ ≫ δ. In the second model, we consider asymmetric communication costs: Fast parties benefit from channels with cheap communication, while channels connected to a slow party have an expensive communication. We provide a wide range of positive and negative results exploring the trade-offs between the achievable number of tolerated corruptions t and slow parties s, versus the round complexity and communication cost in each of the models. Among others, we achieve the following results. In the model with asymmetric communication delays, focusing on the information-theoretic (i-t) setting:
- An i-t asymmetric MPC protocol with security with abort as long as t+s < n and t < n/2, in a constant number of slow rounds.
- We show that achieving an i-t asymmetric MPC protocol for t+s = n and with number of slow rounds independent of the circuit size implies an i-t synchronous MPC protocol with round complexity independent of the circuit size, which is a major problem in the field of round-complexity of MPC.
- We identify a new primitive, asymmetric broadcast, that allows to consistently distribute a value among the fast parties, and at a later time the same value to slow parties. We completely characterize the feasibility of asymmetric broadcast by showing that it is possible if and only if 2t + s < n.
- An i-t asymmetric MPC protocol with guaranteed output delivery as long as t+s < n and t < n/2, in a number of slow rounds independent of the circuit size.
In the model with asymmetric communication cost, we achieve an asymmetric MPC protocol for security with abort for t+s < n and t < n/2, based on one-way functions (OWF). The protocol communicates a number of bits over expensive channels that is independent of the circuit size. We conjecture that assuming OWF is needed and further provide a partial result in this direction.

Vipul Goyal, Chen-Da Liu-Zhang, and Rafail Ostrovsky. Asymmetric Multi-Party Computation. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 6:1-6:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{goyal_et_al:LIPIcs.ITC.2023.6, author = {Goyal, Vipul and Liu-Zhang, Chen-Da and Ostrovsky, Rafail}, title = {{Asymmetric Multi-Party Computation}}, booktitle = {4th Conference on Information-Theoretic Cryptography (ITC 2023)}, pages = {6:1--6:25}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-271-6}, ISSN = {1868-8969}, year = {2023}, volume = {267}, editor = {Chung, Kai-Min}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.6}, URN = {urn:nbn:de:0030-drops-183342}, doi = {10.4230/LIPIcs.ITC.2023.6}, annote = {Keywords: multiparty computation, asymmetric, delays, communication} }

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**Published in:** LIPIcs, Volume 266, 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)

Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties in such a way that certain authorized subsets can reconstruct the secret, while unauthorized subsets obtain no information about it. Previous works on QSS for general access structures focused solely on the existence of perfectly secure schemes, and the share size of the known schemes is necessarily exponential even in cases where the access structure is computed by polynomial size monotone circuits. This stands in stark contrast to the classical setting, where polynomial-time computationally-secure secret sharing schemes have been long known for all access structures computed by polynomial-size monotone circuits under standard hardness assumptions, and one can even obtain shares which are much shorter than the secret (which is impossible with perfect security).
While QSS was introduced over twenty years ago, previous works only considered information-theoretic privacy. In this work, we initiate the study of computationally-secure QSS and show that computational assumptions help significantly in building QSS schemes, just as in the classical case. We present a simple compiler and use it to obtain a large variety results: We construct polynomial-time computationally-secure QSS schemes under standard hardness assumptions for a rich class of access structures. This includes many access structures for which previous results in QSS necessarily required exponential share size. In fact, we can go even further: We construct QSS schemes for which the size of the quantum shares is significantly smaller than the size of the secret. As in the classical setting, this is impossible with perfect security.
We also apply our compiler to obtain results beyond computational QSS. In the information-theoretic setting, we improve the share size of perfect QSS schemes for a large class of n-party access structures to 1.5^{n+o(n)}, improving upon best known schemes and matching the best known result for general access structures in the classical setting. Finally, among other things, we study the class of access structures which can be efficiently implemented when the quantum secret sharing scheme has access to a given number of copies of the secret, including all such functions in 𝖯 and NP.

Alper Çakan, Vipul Goyal, Chen-Da Liu-Zhang, and João Ribeiro. Computational Quantum Secret Sharing. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 4:1-4:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cakan_et_al:LIPIcs.TQC.2023.4, author = {\c{C}akan, Alper and Goyal, Vipul and Liu-Zhang, Chen-Da and Ribeiro, Jo\~{a}o}, title = {{Computational Quantum Secret Sharing}}, booktitle = {18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)}, pages = {4:1--4:26}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-283-9}, ISSN = {1868-8969}, year = {2023}, volume = {266}, editor = {Fawzi, Omar and Walter, Michael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2023.4}, URN = {urn:nbn:de:0030-drops-183144}, doi = {10.4230/LIPIcs.TQC.2023.4}, annote = {Keywords: Quantum secret sharing, quantum cryptography} }

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

Multi-party quantum computation (MPQC) allows a set of parties to securely compute a quantum circuit over private quantum data. Current MPQC protocols rely on the fact that the network is synchronous, i.e., messages sent are guaranteed to be delivered within a known fixed delay upper bound, and unfortunately completely break down even when only a single message arrives late.
Motivated by real-world networks, the seminal work of Ben-Or, Canetti and Goldreich (STOC'93) initiated the study of multi-party computation for classical circuits over asynchronous networks, where the network delay can be arbitrary. In this work, we begin the study of asynchronous multi-party quantum computation (AMPQC) protocols, where the circuit to compute is quantum.
Our results completely characterize the optimal achievable corruption threshold: we present an n-party AMPQC protocol secure up to t < n/4 corruptions, and an impossibility result when t ≥ n/4 parties are corrupted. Remarkably, this characterization differs from the analogous classical setting, where the optimal corruption threshold is t < n/3.

Vipul Goyal, Chen-Da Liu-Zhang, Justin Raizes, and João Ribeiro. Asynchronous Multi-Party Quantum Computation. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 62:1-62:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{goyal_et_al:LIPIcs.ITCS.2023.62, author = {Goyal, Vipul and Liu-Zhang, Chen-Da and Raizes, Justin and Ribeiro, Jo\~{a}o}, title = {{Asynchronous Multi-Party Quantum Computation}}, booktitle = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, pages = {62:1--62:22}, 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.2023.62}, URN = {urn:nbn:de:0030-drops-175655}, doi = {10.4230/LIPIcs.ITCS.2023.62}, annote = {Keywords: Quantum Cryptography, Multiparty Computation, Asynchronous} }

Document

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

In this work we consider the following question: What is the cost of security for multi-party protocols? Specifically, given an insecure protocol where parties exchange (in the worst case) Γ bits in N rounds, is it possible to design a secure protocol with communication complexity close to Γ and N rounds? We systematically study this problem in a variety of settings and we propose solutions based on the intractability of different cryptographic problems.
For the case of two parties we design an interaction-preserving compiler where the number of bits exchanged in the secure protocol approaches Γ and the number of rounds is exactly N, assuming the hardness of standard problems over lattices. For the more general multi-party case, we obtain the same result assuming either (i) an additional round of interaction or (ii) the existence of extractable witness encryption and succinct non-interactive arguments of knowledge. As a contribution of independent interest, we construct the first multi-key fully homomorphic encryption scheme with message-to-ciphertext ratio (i.e., rate) of 1 - o(1), assuming the hardness of the learning with errors (LWE) problem.
We view our work as a support for the claim that, as far as interaction and communication are concerned, one does not need to pay a significant price for security in multi-party protocols.

Nico Döttling, Vipul Goyal, Giulio Malavolta, and Justin Raizes. Interaction-Preserving Compilers for Secure Computation. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 57:1-57:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dottling_et_al:LIPIcs.ITCS.2022.57, author = {D\"{o}ttling, Nico and Goyal, Vipul and Malavolta, Giulio and Raizes, Justin}, title = {{Interaction-Preserving Compilers for Secure Computation}}, booktitle = {13th Innovations in Theoretical Computer Science Conference (ITCS 2022)}, pages = {57:1--57:18}, 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.2022.57}, URN = {urn:nbn:de:0030-drops-156534}, doi = {10.4230/LIPIcs.ITCS.2022.57}, annote = {Keywords: Multiparty Computation, Communication Complexity, Fully Homomorphic Encryption} }

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

Blockchain technology has the potential of transforming cryptography. We study the problem of round-complexity of zero-knowledge, and more broadly, of secure computation in the blockchain-hybrid model, where all parties can access the blockchain as an oracle.
We study zero-knowledge and secure computation through the lens of a new security notion where the simulator is given the ability to "time-travel” or more accurately, to look into the future states of the blockchain and use this information to perform simulation. Such a time-traveling simulator gives a novel security guarantee of the following form: whatever the adversary could have learnt from an interaction, it could have computed on its own shortly into the future (e.g., a few hours from now).
We exhibit the power of time-traveling simulators by constructing round-efficient protocols in the blockchain-hybrid model. In particular, we construct:
1) Three-round zero-knowledge (ZK) argument for NP with a polynomial-time black-box time-traveling simulator.
2) Three-round secure two-party computation (2PC) for any functionality with a polynomial-time black-box time-traveling simulator for both parties.
In addition to standard cryptographic assumptions, we rely on natural hardness assumptions for Proof-of-Work based blockchains. In comparison, in the plain model, three-round protocols with black-box simulation are impossible, and constructions with non-black-box simulation for ZK require novel cryptographic assumptions while no construction for three-round 2PC is known. Our three-round 2PC result relies on a new, two-round extractable commitment that admits a time-traveling extractor.

Vipul Goyal, Justin Raizes, and Pratik Soni. Time-Traveling Simulators Using Blockchains and Their Applications. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 81:1-81:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{goyal_et_al:LIPIcs.ITCS.2022.81, author = {Goyal, Vipul and Raizes, Justin and Soni, Pratik}, title = {{Time-Traveling Simulators Using Blockchains and Their Applications}}, booktitle = {13th Innovations in Theoretical Computer Science Conference (ITCS 2022)}, pages = {81:1--81:19}, 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.2022.81}, URN = {urn:nbn:de:0030-drops-156770}, doi = {10.4230/LIPIcs.ITCS.2022.81}, annote = {Keywords: Cryptography, Zero Knowledge, Secure Two-Party Computation, Blockchain} }

Document

**Published in:** LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

Functional encryption provides fine-grained access control for encrypted data, allowing each user to learn only specific functions of the encrypted data. We study the notion of hierarchical functional encryption, which augments functional encryption with delegation capabilities, offering significantly more expressive access control.
We present a generic transformation that converts any general-purpose public-key functional encryption scheme into a hierarchical one without relying on any additional assumptions. This significantly refines our understanding of the power of functional encryption, showing that the existence of functional encryption is equivalent to that of its hierarchical generalization.
Instantiating our transformation with the existing functional encryption schemes yields a variety of hierarchical schemes offering various trade-offs between their delegation capabilities (i.e., the depth and width of their hierarchical structures) and underlying assumptions. When starting with a scheme secure against an unbounded number of collusions, we can support arbitrary hierarchical structures. In addition, even when starting with schemes that are secure against a bounded number of collusions (which are known to exist under rather minimal assumptions such as the existence of public-key encryption and shallow pseudorandom generators), we can support hierarchical structures of bounded depth and width.

Zvika Brakerski, Nishanth Chandran, Vipul Goyal, Aayush Jain, Amit Sahai, and Gil Segev. Hierarchical Functional Encryption. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 8:1-8:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{brakerski_et_al:LIPIcs.ITCS.2017.8, author = {Brakerski, Zvika and Chandran, Nishanth and Goyal, Vipul and Jain, Aayush and Sahai, Amit and Segev, Gil}, title = {{Hierarchical Functional Encryption}}, booktitle = {8th Innovations in Theoretical Computer Science Conference (ITCS 2017)}, pages = {8:1--8:27}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-029-3}, ISSN = {1868-8969}, year = {2017}, volume = {67}, editor = {Papadimitriou, Christos H.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.8}, URN = {urn:nbn:de:0030-drops-81992}, doi = {10.4230/LIPIcs.ITCS.2017.8}, annote = {Keywords: Functional Encryption, Delegatable Encryption, Cryptography} }

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**Published in:** LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

We study the cryptographic complexity of two-party differentially-private protocols for a large natural class of boolean functionalities. Information theoretically, McGregor et al. [FOCS 2010] and Goyal et al. [Crypto 2013] demonstrated several functionalities for which the maximal possible accuracy in the distributed setting is significantly lower than that in the client-server setting. Goyal et al. [Crypto 2013] further showed that "highly accurate" protocols in the distributed setting for any non-trivial functionality in fact imply the existence of one-way functions. However, it has remained an open problem to characterize the exact cryptographic complexity of this class. In particular, we know that semi-honest oblivious transfer helps obtain optimally accurate distributed differential privacy. But we do not know whether the reverse is true. We study the following question: Does the existence of optimally accurate distributed differentially private protocols for any class of functionalities imply the existence of oblivious transfer (or equivalently secure multi-party computation)? We resolve this question in the affirmative for the class of boolean functionalities that contain an XOR embedded on adjacent inputs. We give a reduction from oblivious transfer to:
- Any distributed optimally accurate epsilon-differentially private protocol with epsilon > 0 computing a functionality with a boolean XOR embedded on adjacent inputs.
- Any distributed non-optimally accurate epsilon-differentially private protocol with epsilon > 0, for a constant range of non-optimal accuracies and constant range of values of epsilon, computing a functionality with a boolean XOR embedded on adjacent inputs.
Enroute to proving these results, we demonstrate a connection between optimally-accurate twoparty differentially-private protocols for functions with a boolean XOR embedded on adjacent inputs, and noisy channels, which were shown by Crépeau and Kilian [FOCS 1988] to be sufficient for oblivious transfer.

Vipul Goyal, Dakshita Khurana, Ilya Mironov, Omkant Pandey, and Amit Sahai. Do Distributed Differentially-Private Protocols Require Oblivious Transfer?. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{goyal_et_al:LIPIcs.ICALP.2016.29, author = {Goyal, Vipul and Khurana, Dakshita and Mironov, Ilya and Pandey, Omkant and Sahai, Amit}, title = {{Do Distributed Differentially-Private Protocols Require Oblivious Transfer?}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {29:1--29:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-013-2}, ISSN = {1868-8969}, year = {2016}, volume = {55}, editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.29}, URN = {urn:nbn:de:0030-drops-63080}, doi = {10.4230/LIPIcs.ICALP.2016.29}, annote = {Keywords: Oblivious Transfer, Distributed Differential Privacy, Noisy Channels, Weak Noisy Channels} }

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**Published in:** LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Non-malleable codes, introduced by Dziembowski, Pietrzak, and Wichs (ICS'10) provide the guarantee that if a codeword c of a message m, is modified by a tampering function f to c', then c' either decodes to m or to "something unrelated" to m. In recent literature, a lot of focus has been on explicitly constructing such codes against a large and natural class of tampering functions such as split-state model in which the tampering function operates on different parts of the codeword independently.
In this work, we consider a stronger adversarial model called block-wise tampering model, in which we allow tampering to depend on more than one block: if a codeword consists of two blocks c = (c1, c2), then the first tampering function f1 could produce a tampered part c'_1 = f1(c1) and the second tampering function f2 could produce c'_2 = f2(c1, c2) depending on both c2 and c1. The notion similarly extends to multiple blocks where tampering of block ci could happen with the knowledge of all cj for j <= i. We argue this is a natural notion where, for example, the blocks are sent one by one and the adversary must send the tampered block before it gets the next block.
A little thought reveals that it is impossible to construct such codes that are non-malleable (in the standard sense) against such a powerful adversary: indeed, upon receiving the last block, an adversary could decode the entire codeword and then can tamper depending on the message. In light of this impossibility, we consider a natural relaxation called non-malleable codes with replacement which requires the adversary to produce not only related but also a valid codeword in order to succeed. Unfortunately, we show that even this relaxed definition is not achievable in the information-theoretic setting (i.e., when the tampering functions can be unbounded) which implies that we must turn our attention towards computationally bounded adversaries.
As our main result, we show how to construct a block-wise non-malleable code (BNMC) from sub-exponentially hard one-way permutations. We provide an interesting connection between BNMC and non-malleable commitments. We show that any BNMC can be converted into a nonmalleable
(w.r.t. opening) commitment scheme. Our techniques, quite surprisingly, give rise to a non-malleable commitment scheme (secure against so-called synchronizing adversaries), in which only the committer sends messages. We believe this result to be of independent interest. In the other direction, we show that any non-interactive non-malleable (w.r.t. opening) commitment can be used to construct BNMC only with 2 blocks. Unfortunately, such commitment scheme exists only under highly non-standard assumptions (adaptive one-way functions) and hence can not substitute our main construction.

Nishanth Chandran, Vipul Goyal, Pratyay Mukherjee, Omkant Pandey, and Jalaj Upadhyay. Block-Wise Non-Malleable Codes. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{chandran_et_al:LIPIcs.ICALP.2016.31, author = {Chandran, Nishanth and Goyal, Vipul and Mukherjee, Pratyay and Pandey, Omkant and Upadhyay, Jalaj}, title = {{Block-Wise Non-Malleable Codes}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {31:1--31:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-013-2}, ISSN = {1868-8969}, year = {2016}, volume = {55}, editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.31}, URN = {urn:nbn:de:0030-drops-63102}, doi = {10.4230/LIPIcs.ICALP.2016.31}, annote = {Keywords: Non-malleable codes, Non-malleable commitments, Block-wise Tampering, Complexity-leveraging} }

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