International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Algebraic Meet-in-the-Middle Attack on LowMC

Fukang Liu , University of Hyogo
Santanu Sarkar , Indian Institute of Technology Madras
Gaoli Wang , East China Normal University; Shandong University
Willi Meier , FHNW
Takanori Isobe , University of Hyogo; NICT; PRESTO
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Conference: ASIACRYPT 2022
Abstract: By exploiting the feature of partial nonlinear layers, we propose a new technique called algebraic meet-in-the-middle (MITM) attack to analyze the security of LowMC, which can reduce the memory complexity of the simple difference enumeration attack over the state-of-the-art. Moreover, while an efficient algebraic technique to retrieve the full key from a differential trail of LowMC has been proposed at CRYPTO 2021, its time complexity is still exponential in the key size. In this work, we show how to reduce it to constant time when there are a sufficiently large number of active S-boxes in the trail. With the above new techniques, the attacks on LowMC and LowMC-M published at CRYPTO 2021 are further improved, and some LowMC instances could be broken for the first time. Our results seem to indicate that partial nonlinear layers are still not well-understood.
Video from ASIACRYPT 2022
  title={Algebraic Meet-in-the-Middle Attack on LowMC},
  author={Fukang Liu and Santanu Sarkar and Gaoli Wang and Willi Meier and Takanori Isobe},