Higher-Order Cryptanalysis of LowMC
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LowMC is a family of block ciphers developed particularly for use in multi-party computations and fully homomorphic encryption schemes, where the main performance penalty comes from non-linear operations. Thus, LowMC has been designed to minimize the total quantity of logical “and” operations, as well as the “and” depth. To achieve this, the LowMC designers opted for an incomplete S-box layer that does not cover the complete state, and compensate for it with a very dense, randomly chosen linear layer. In this work, we exploit this design strategy in a cube-like key-recovery attack. We are able to recover the secret key of a round-reduced variant of LowMC with 80-bit security, where the number of rounds is reduced from 11 to 9. Our attacks are independent of the actual instances of the used linear layers and therefore, do not exploit possible weak choices of them. From our results, we conclude that the resulting security margin of 2 rounds is smaller than expected.
KeywordsCryptanalysis LowMC Higher-order cryptanalysis Key recovery Zero-sum distinguisher
The work has been supported in part by the Austrian Science Fund (project P26494-N15) and by the Austrian Research Promotion Agency (FFG) and the Styrian Business Promotion Agency (SFG) under grant number 836628 (SeCoS).
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