## Cryptology ePrint Archive: Report 2017/040

Practical Non-Malleable Codes from $\ell$-more Extractable Hash Functions

Aggelos Kiayias and Feng-Hao Liu and Yiannis Tselekounis

Abstract: In this work, we significantly improve the efficiency of non-malleable codes in the split state model, by constructing a code with codeword length $|s|+O(k)$, where $|s|$ is the length of the message, and $k$ is the security parameter. This is a substantial improvement over previous constructions, both asymptotically and concretely.

Our construction relies on a new primitive which we define and study, called $\ell$-more extractable hash functions. This notion, which may be of independent interest, guarantees that any adversary that is given access to $\ell \in \mathbb{N}$ precomputed hash values $v_{1},\dots, v_{\ell}$, and produces a new valid hash value $\tilde v$, then it must know a pre-image of $\tilde v$. This is a stronger notion that the one by Bitansky et al. (Eprint '11) and Goldwasser et al. (ITCS '12, Eprint '14), which considers adversaries that get no access to precomputed hash values prior to producing their own value. By appropriately relaxing the extractability requirement (without hurting the applicability of the primitive) we instantiate $\ell$-more extractable hash functions under the same assumptions used for the previous extractable hash functions by Bitansky et al. and Goldwasser et al. (a variant of the Knowledge of Exponent Assumption).

Category / Keywords: Non-malleable codes, hash functions, split-state model

Original Publication (with minor differences): ACM Conference on Computer and Communications Security 2016

Date: received 17 Jan 2017, last revised 20 May 2018

Contact author: tselekounis at sians org

Available format(s): PDF | BibTeX Citation

Note: Extended abstract and minor intro changes.

Short URL: ia.cr/2017/040

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