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Encrypt or Decrypt? To Make a Single-Key Beyond Birthday Secure Nonce-Based MAC

  • Nilanjan Datta
  • Avijit Dutta
  • Mridul Nandi
  • Kan Yasuda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10991)

Abstract

At CRYPTO 2016, Cogliati and Seurin have proposed a highly secure nonce-based MAC called Encrypted Wegman-Carter with Davies-Meyer (\(\textsf {EWCDM}\)) construction, as \(\textsf {E}_{K_2}\bigl (\textsf {E}_{K_1}(N)\oplus N\oplus \textsf {H}_{K_h}(M)\bigr )\) for a nonce N and a message M. This construction achieves roughly \(2^{2n/3}\) bit MAC security with the assumption that \(\textsf {E}\) is a PRP secure n-bit block cipher and \(\textsf {H}\) is an almost xor universal n-bit hash function. In this paper we propose Decrypted Wegman-Carter with Davies-Meyer (\(\textsf {DWCDM}\)) construction, which is structurally very similar to its predecessor \(\textsf {EWCDM}\) except that the outer encryption call is replaced by decryption. The biggest advantage of \(\textsf {DWCDM}\) is that we can make a truly single key MAC: the two block cipher calls can use the same block cipher key \(K=K_1=K_2\). Moreover, we can derive the hash key as \(K_h=\textsf {E}_K(1)\), as long as \(|K_h|=n\). Whether we use encryption or decryption in the outer layer makes a huge difference; using the decryption instead enables us to apply an extended version of the mirror theory by Patarin to the security analysis of the construction. \(\textsf {DWCDM}\) is secure beyond the birthday bound, roughly up to \(2^{2n/3}\) MAC queries and \(2^n\) verification queries against nonce-respecting adversaries. \(\textsf {DWCDM}\) remains secure up to \(2^{n/2}\) MAC queries and \(2^n\) verification queries against nonce-misusing adversaries.

Keywords

\(\textsf {EDM}\) \(\textsf {EWCDM}\) Mirror theory Extended mirror theory H-Coefficient 

Notes

Acknowledgments

Initial part of this work was done in NTT Lab, Japan when Avijit Dutta was visiting there. Mridul Nandi is supported by R.C.Bose Centre for Cryptology and Security. The authors would like to thank all the anonymous reviewers of CRYPTO 2018 for their invaluable comments and suggestions and also to Eik List and Yaobin Shen for pointing out some minor issues in the paper.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Nilanjan Datta
    • 1
  • Avijit Dutta
    • 2
  • Mridul Nandi
    • 2
  • Kan Yasuda
    • 3
  1. 1.Indian Institute of Technology, KharagpurKharagpurIndia
  2. 2.Indian Statistical InstituteKolkataIndia
  3. 3.NTT Secure Platform LaboratoriesNTT CorporationTokyoJapan

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