Small Stretch Problem of the DCT Scheme and How to Fix It

Authors

  • Yuchao Chen School of Cyber Science and Technology, Shandong University, Qingdao, China; Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China
  • Tingting Guo Research Center for Data Hub and Security, Zhejiang lab, Hangzhou, China
  • Lei Hu Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China; School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China
  • Lina Shang Space Star Technology Co., Ltd., Beijing, China
  • Shuping Mao Key Laboratory of Cyberspace Security Defense, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China; School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China
  • Peng Wang School of Cryptology, University of Chinese Academy of Sciences, Beijing, China

DOI:

https://doi.org/10.46586/tosc.v2024.i1.114-134

Keywords:

DCT, Deterministic Authenticated Encryption, AEAD, BRW polynomial, Forgery Attack, Stretch

Abstract

DCT is a beyond-birthday-bound (BBB) deterministic authenticated encryption (DAE) mode proposed by Forler et al. in ACISP 2016, ensuring integrity by redundancy. The instantiation of DCT employs the BRW polynomial, which is more efficient than the usual polynomial in GCM by reducing half of the multiplication operations. However, we show that DCT suffers from a small stretch problem similar to GCM. When the stretch length τ is small, choosing a special m-block message, we can reduce the number of queries required by a successful forgery to O(2τ/m). We emphasize that this attack efficiently balances space and time complexity but does not contradict the security bounds of DCT. Finally, we propose an improved scheme named Robust DCT (RDCT) with a minor change to DCT, which improves the security when τ is small and makes it resist the above attack.

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Published

2024-03-01

Issue

Section

Articles

How to Cite

Small Stretch Problem of the DCT Scheme and How to Fix It. (2024). IACR Transactions on Symmetric Cryptology, 2024(1), 114-134. https://doi.org/10.46586/tosc.v2024.i1.114-134