Paper 2019/404

Efficient Message Authentication Codes with Combinatorial Group Testing

Kazuhiko Minematsu


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.

Available format(s)
Secret-key cryptography
Publication info
Published elsewhere. MINOR revision.ESORICS 2015
Message authentication codeCombinatorial group testingData corruptionProvable security.
Contact author(s)
k-minematsu @ ah jp nec com
2019-04-25: revised
2019-04-22: received
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Creative Commons Attribution


      author = {Kazuhiko Minematsu},
      title = {Efficient Message Authentication Codes with Combinatorial Group Testing},
      howpublished = {Cryptology ePrint Archive, Paper 2019/404},
      year = {2019},
      note = {\url{}},
      url = {}
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