Efficient Message Authentication Codes with Combinatorial Group Testing

Kazuhiko Minematsu

Paper 2019/404

Efficient Message Authentication Codes with Combinatorial Group Testing

Kazuhiko Minematsu

Abstract

Message authentication code, MAC for short, is a symmetric-key cryptographic function for authenticity. A standard MAC verification only tells whether the message is valid or invalid, and thus we can not identify which part is corrupted in case of invalid message. In this paper we study a class of MAC functions that enables to identify the part of corruption, which we call group testing MAC (GTM). This can be seen as an application of a classical (non-adaptive) combinatorial group testing to MAC. Although the basic concept of GTM (or its keyless variant) has been proposed in various application areas, such as data forensics and computer virus testing, they rather treat the underlying MAC function as a black box, and exact computation cost for GTM seems to be overlooked. In this paper, we study the computational aspect of GTM, and show that a simple yet non-trivial extension of parallelizable MAC (PMAC) enables $O(m+t)$ computation for $m$ data items and $t$ tests, irrespective of the underlying test matrix we use, under a natural security model. This greatly improves efficiency from naively applying a black-box MAC for each test, which requires $O(mt)$ time. Based on existing group testing methods, we also present experimental results of our proposal and observe that ours runs as fast as taking single MAC tag, with speed-up from the conventional method by factor around 8 to 15 for $m=10^4$ to $10^5$ items.

Note: Minor corrections on technical backgrounds, tables and figures.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Minor revision. ESORICS 2015
Keywords: Message authentication code Combinatorial group testing Data corruption Provable security.
Contact author(s): k-minematsu @ ah jp nec com
History: 2019-04-25: revised; 2019-04-22: received; See all versions
Short URL: https://ia.cr/2019/404
License: CC BY

BibTeX

@misc{cryptoeprint:2019/404,
      author = {Kazuhiko Minematsu},
      title = {Efficient Message Authentication Codes with Combinatorial Group Testing},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/404},
      year = {2019},
      url = {https://eprint.iacr.org/2019/404}
}