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

TL;DR

This paper presents new explicit constructions of non-malleable codes capable of resisting complex tampering functions, including interleaved split-state, linear, and communication-bounded models, advancing the field of tamper-resilient coding.

Contribution

It introduces the first explicit non-malleable codes for several advanced tampering models, derived from novel seedless non-malleable extractors, expanding the scope of tamper-resilient coding techniques.

Findings

First explicit constructions for interleaved split-state tampering

New non-malleable codes for linear function composed tampering

Improved seedless extractor for interleaved sources

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. (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.