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Paper: Explicit Rate-1 Non-malleable Codes for Local Tampering

Authors:
Divya Gupta
Hemanta K. Maji
Mingyuan Wang
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DOI: 10.1007/978-3-030-26948-7_16
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Abstract: This paper constructs high-rate non-malleable codes in the information-theoretic plain model against tampering functions with bounded locality. We consider $$\delta $$-local tampering functions; namely, each output bit of the tampering function is a function of (at most) $$\delta $$ input bits. This work presents the first explicit and efficient rate-1 non-malleable code for $$\delta $$-local tampering functions, where $$\delta =\xi \lg n$$ and $$\xi <1$$ is any positive constant. As a corollary, we construct the first explicit rate-1 non-malleable code against NC$$^0$$ tampering functions.Before our work, no explicit construction for a constant-rate non-malleable code was known even for the simplest 1-local tampering functions. Ball et al. (EUROCRYPT–2016), and Chattopadhyay and Li (STOC–2017) provided the first explicit non-malleable codes against $$\delta $$-local tampering functions. However, these constructions are rate-0 even when the tampering functions have 1-locality. In the CRS model, Faust et al. (EUROCRYPT–2014) constructed efficient rate-1 non-malleable codes for $$\delta = O(\log n)$$ local tampering functions.Our main result is a general compiler that bootstraps a rate-0 non-malleable code against leaky input and output local tampering functions to construct a rate-1 non-malleable code against $$\xi \lg n$$-local tampering functions, for any positive constant $$\xi < 1$$. Our explicit construction instantiates this compiler using an appropriate encoding by Ball et al. (EUROCRYPT–2016).
BibTeX
@article{crypto-2019-29869,
  title={Explicit Rate-1 Non-malleable Codes for Local Tampering},
  booktitle={Advances in Cryptology – CRYPTO 2019},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={11692},
  pages={435-466},
  doi={10.1007/978-3-030-26948-7_16},
  author={Divya Gupta and Hemanta K. Maji and Mingyuan Wang},
  year=2019
}