# Single Trace Analysis against HyMES by Exploitation of Joint Distributions of Leakages
## 2 Related Works
### Code-Based Cryptography
#### 2.2.1 McEliece Cryptosystem
The noise standard deviation was increased by 0.1. The analysis was conducted 10000 times for each noise standard deviation. The analysis performed for each trace is the maximum likelihood when using four variables. We performed a maximum likelihood analysis for each trace and used four random variables. The attack success rate remains at 1 up to a noise standard deviation of 2.1, and then begins to decrease from 2.2. In this paper, we experimented with 10 traces, but we can obtain better experimental results by using more traces. Figure 6: Success rate according to noise standard deviation (\(\alpha_{0}=999\)). ## 5 Conclusions

In this paper, we analyzed HyMES by exploiting the joint distributions of leakages. We exploited the nonlinearity of the precomputation table used in calculating the column vector \(h_{i}\) of the parity check matrix \(H\) in the decryption process. Previously, the side-channel analysis by exploiting the joint distributions of leakages was only investigated for the symmetric key cryptography. To the best of our knowledge, this is the first to analyze the public-key cryptosystem exploiting the joint distributions of leakages. The experimental results using a single simulated power trace show a success rate of 100% up to a noise standard deviation 1.3. We demonstrated that the proposed attack can be applied to all code-based cryptosystems that calculate \(h_{i}\) in the manner proposed in Reference [6]. All authors have contributed to this work. [PERSON] and S.K. analyzed the algorithm and drafted and revised the manuscript. [PERSON] and S.K. performed the experiment and analyzed the result. [PERSON] and [PERSON] devised a methodology of additional experiment. H.K.K. and S.C.S. verified the analytical methods and supervised this work. All authors have read and agreed to the published version of the manuscript. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2019R1A2C2088960). The authors declare no conflict of interest. ## References

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