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Title:
Coefficient Grouping: Breaking Chaghri and More
Authors: Fukang Liu, Ravi Anand, Libo Wang, Willi Meier, Takanori Isobe
Abstract:We propose an efficient technique called coefficient grouping to evaluate the algebraic degree of the FHE-friendly cipher Chaghri, which has been accepted for ACM CCS 2022. It is found that the algebraic degree increases linearly rather than exponentially. As a consequence, we can construct a 13-round distinguisher with time and data complexity of 2^{63} and mount a 13.5-round key-recovery attack with time complexity of about 2^{119.6}. In particular, a higher-order differential attack on 8 rounds of Chaghri can be achieved with time and data complexity of 2^{38}. Hence, it indicates that the full 8 rounds are far from being secure. Furthermore, we also demonstrate the application of our coefficient grouping technique to the design of secure cryptographic components. As a result, a countermeasure is found for Chaghri and it has little overhead compared with the original design. Since more and more symmetric primitives defined over a large finite field are emerging, we believe our new technique can have more applications in the future research.
ePrint: https://eprint.iacr.org/2022/991
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