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Revision #2 to TR18-070 | 6th April 2019 15:22

Non-Malleable Codes, Extractors and Secret Sharing for Interleaved Tampering and Composition of Tampering

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Revision #2
Authors: Eshan Chattopadhyay, Xin Li
Accepted on: 6th April 2019 15:22
Downloads: 49
Keywords: 


Abstract:

Abstract
Non-malleable codes were introduced by Dziembowski, Pietrzak, and Wichs (JACM 2018) as a generalization of standard error correcting codes to handle severe forms of tampering on codewords. This notion has attracted a lot of recent research, resulting in various explicit constructions, which have found applications in tamper-resilient cryptography and connections to other pseudorandom objects in theoretical computer science.

We continue the line of investigation on explicit constructions of non-malleable codes in the information theoretic setting, and give explicit constructions for several new classes of tampering functions. These classes strictly generalize several previously studied classes of tampering functions, and in particular extend the well studied split-state model which is a ``compartmentalized" model in the sense that the codeword is partitioned a prior into disjoint intervals for tampering. Specifically, we give explicit non-malleable codes for the following classes of tampering functions.

(1) Interleaved split-state tampering: Here the codeword is partitioned in an unknown way by an adversary, and then tampered with by a split-state tampering function.

(2) Affine tampering composed with split-state tampering: In this model, the codeword is first tampered with by a split-state adversary, and then the whole tampered codeword is further tampered with by an affine function. In fact our results are stronger, and we can handle affine tampering composed with interleaved split-state tampering.

Our results are the first explicit constructions of non-malleable codes in any of these tampering models. As applications, they also directly give non-malleable secret sharing schemes with binary shares in the split-state joint tampering model and the stronger model of affine tampering composed with split-state joint tampering. We derive all these results from explicit constructions of seedless non-malleable extractors, which we believe are of independent interest.


Using our techniques, we also give an improved seedless extractor for an unknown interleaving of two independent sources.



Changes to previous version:

added results on non-malleable secret sharing; changes in presentation.


Revision #1 to TR18-070 | 2nd November 2018 18:35

Non-Malleable Extractors and Codes for Composition of Tampering, Interleaved Tampering and More





Revision #1
Authors: Eshan Chattopadhyay, Xin Li
Accepted on: 2nd November 2018 18:35
Downloads: 139
Keywords: 


Abstract:

Non-malleable codes were introduced by Dziembowski, Pietrzak, and Wichs (JACM 2018) as a generalization of standard error correcting codes to handle severe forms of tampering on codewords. This notion has attracted a lot of recent research, resulting in various explicit constructions, which have found applications in tamper-resilient cryptography and connections to other pseudorandom objects in theoretical computer science.

We continue the line of investigation on explicit constructions of non-malleable codes in the information theoretic setting, and give explicit constructions for several new classes of tampering functions. These classes strictly generalize several previously studied classes of tampering functions, and in particular extend the well studied split-state model which is a "compartmentalized" model in the sense that the codeword is partitioned a prior into disjoint intervals for tampering. Specifically, we give explicit non-malleable codes for the following classes of tampering functions.

(1) Interleaved split-state tampering: Here the codeword is partitioned in an unknown way by an adversary, and then tampered with by a split-state tampering function.

(2) Linear function composed with split-state tampering: In this model, the codeword is first tampered with by a split-state adversary, and then the whole tampered codeword is further tampered with by a linear function. In fact our results are stronger, and we can handle linear function composed with interleaved split-state tampering.

(3) Bounded communication split-state tampering: In this model, the two split-state tampering adversaries are allowed to participate in a communication protocol with a bounded communication budget.

Our results are the first explicit constructions of non-malleable codes in any of these tampering models. We derive all these results from explicit constructions of seedless non-malleable extractors, which we believe are of independent interest.

Using our techniques, we also give an improved seedless extractor for an unknown interleaving of two independent sources.



Changes to previous version:

Includes stronger results compared to previous version (which unifies results); major change in presentation.


Paper:

TR18-070 | 13th April 2018 00:39

Non-Malleable Extractors and Codes in the Interleaved Split-State Model and More





TR18-070
Authors: Eshan Chattopadhyay, Xin Li
Publication: 15th April 2018 12:04
Downloads: 341
Keywords: 


Abstract:

We present explicit constructions of non-malleable codes with respect to the following tampering classes. (i) Linear functions composed with split-state adversaries: In this model, the codeword is first tampered by a split-state adversary, and then the whole tampered codeword is further tampered by a linear function. (ii) Interleaved split-state adversary: Here the codeword is partitioned in an unknown (but fixed) way, and then tampered by a split-state adversary. (iii) Bounded communication split-state model: In this model, the split-state adversaries are allowed to participate in a communication protocol (with bounded communication budget) to tamper the codeword. Our results are the first explicit constructions of non-malleable codes in any of these tampering models.

We derive all our non-malleable codes from explicit constructions of seedless non-malleable extractors. We believe that our results on seedless non-malleable extractors and the techniques developed are of independent interest. Using our techniques, we also give an improved extractor for an unknown interleaving of two independent sources.



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