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  4. Optimal Computational Split-state Non-malleable Codes
 
conference paper

Optimal Computational Split-state Non-malleable Codes

Aggarwal, Divesh  
•
Agrawal, Shashank
•
Gupta, Divya
Show more
Kushilevitz, E
•
Malkin, T
2016
Theory Of Cryptography, Pt Ii
13th International Theory of Cryptography Conference (TCC)

Non-malleable codes are a generalization of classical error-correcting codes where the act of "corrupting" a codeword is replaced by a "tampering" adversary. Non-malleable codes guarantee that the message contained in the tampered codeword is either the original message m, or a completely unrelated one. In the common split-state model, the codeword consists of multiple blocks (or states) and each block is tampered with independently. The central goal in the split-state model is to construct high rate non-malleable codes against all functions with only two states (which are necessary). Following a series of long and impressive line of work, constant rate, two-state, non-malleable codes against all functions were recently achieved by Aggarwal et al. [2]. Though constant, the rate of all known constructions in the split state model is very far from optimal (even with more than two states). In this work, we consider the question of improving the rate of splitstate non-malleable codes. In the "information theoretic" setting, it is not possible to go beyond rate 1/2. We therefore focus on the standard computational setting. In this setting, each tampering function is required to be efficiently computable, and the message in the tampered codeword is required to be either the original message m or a "computationally" independent one. In this setting, assuming only the existence of one-way functions, we present a compiler which converts any poor rate, two-state, (sufficiently strong) non-malleable code into a rate-1, two-state, computational non-malleable code. These parameters are asymptotically optimal. Furthermore, for the qualitative optimality of our result, we generalize the result of Cheraghchi and Guruswami [10] to show that the existence of one-way functions is necessary to achieve rate > 1/2 for such codes. Our compiler requires a stronger form of non-malleability, called augmented non-malleability. This notion requires a stronger simulation guarantee for non-malleable codes and simplifies their modular usage in cryptographic settings where composition occurs. Unfortunately, this form of non-malleability is neither straightforward nor generally guaranteed by known results. Nevertheless, we prove this stronger form of non-malleability for the two-state construction of Aggarwal et al. [3]. This result is of independent interest.

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Type
conference paper
DOI
10.1007/978-3-662-49099-0_15
Web of Science ID

WOS:000375380000015

Author(s)
Aggarwal, Divesh  
Agrawal, Shashank
Gupta, Divya
Maji, Hemanta K.
Pandey, Omkant
Prabhakaran, Manoj
Editors
Kushilevitz, E
•
Malkin, T
Date Issued

2016

Publisher

Springer Int Publishing Ag

Publisher place

Cham

Published in
Theory Of Cryptography, Pt Ii
ISBN of the book

978-3-662-49099-0

978-3-662-49098-3

Total of pages

25

Series title/Series vol.

Lecture Notes in Computer Science

Volume

9563

Start page

393

End page

417

Subjects

Non-malleable codes

•

Split-state

•

Explicit construction

•

Computational setting

•

One-way functions

•

Pseudorandom generators

•

Authenticated encryption schemes

•

Rate 1

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LASEC  
Event nameEvent placeEvent date
13th International Theory of Cryptography Conference (TCC)

Tel Aviv, ISRAEL

JAN 10-13, 2016

Available on Infoscience
July 19, 2016
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/127956
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