Abstract
Profiled DPA is an important and powerful type of side-channel attacks (SCAs). Thanks to its profiling phase that learns the leakage features from a controlled device, profiled DPA outperforms many other types of SCA and are widely used in the security evaluation of cryptographic devices. Typical profiling methods (such as linear regression based ones) suffer from the overfitting issue which is often neglected in previous works, i.e., the model characterizes details that are specific to the dataset used to build it (and not the distribution we want to capture). In this paper, we propose a novel profiling method based on ridge regression and investigate its generalization ability (to mitigate the overfitting issue) theoretically and by experiments. Further, based on cross-validation, we present a parameter optimization method that finds out the most suitable parameter for our ridge-based profiling. Finally, the simulation-based and practical experiments show that ridge-based profiling not only outperforms ‘classical’ and linear regression-based ones (especially for nonlinear leakage functions), but also is a good candidate for the robust profiling.
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Notes
- 1.
We often omit the superscript ‘j’ in \(\mathrm {L}^j\), \(\mathrm {M}^j\) and \(\varepsilon ^j\) for succinctness.
- 2.
We shall not confuse K with k in online exploitation phase, where K is a parameter as in the “K-fold cross-validation” and k is a subkey hypothesis.
- 3.
We use the coefficient of determination to measure the goodness-of-fit in this paper, i.e., \(R = \sum _{i=1}^{N_t}(\hat{T}_i-T_i)^2/\sum _{i=1}^{N_t}(T_i-\sum _{i=1}^{N_t}T_i)^2\), where \(\hat{T}\) is the estimated power consumption and \(N_t\) is the trace number in \(\mathcal {C}_i\).
- 4.
We apply the averaged goodness-of-fit for normalization, i.e., \(\mathrm {norm}(R_{\lambda })=(R_{\lambda }-\mathrm {mean}(R)/(\mathrm {max}(R)-\mathrm {min}(R)))\), where \(\mathrm {mean}(R)\) is the average of \(\{R_{\lambda }\}_{\lambda \in \varLambda }\) and \(\mathrm {norm}(\cdot )\) is the normalization function.
- 5.
We shall not confuse the ‘averaged trace’ with the ‘256 mean power traces’, where the former one is the mean of all the power traces which is only for the presentation of the measurements. And the latter one, as the result of pre-processing, is the means of the traces of same corresponding plaintext.
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Acknowledgments
This work has been funded in parts by Major State Basic Research Development Program (973 Plan), the European Commission through the ERC project NANOSEC and by the INNOVIRIS project SCAUT. Yu Yu was supported by the National Natural Science Foundation of China Grant (Nos. 61472249, 61572192, 61572149), Science and Technology on Communication Security Laboratory (9140C110203140C11049), and International Science & Technology Cooperation & Exchange Projects of Shaanxi Province (2016KW-038). François-Xavier Standaert is a research associate of the Belgian Fund for Scientific Research (FNRS-F.R.S.). Dawu Gu was supported by National Natural Science Foundation of China (No. 61472250).
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Wang, W., Yu, Y., Standaert, FX., Gu, D., Sen, X., Zhang, C. (2017). Ridge-Based Profiled Differential Power Analysis. In: Handschuh, H. (eds) Topics in Cryptology – CT-RSA 2017. CT-RSA 2017. Lecture Notes in Computer Science(), vol 10159. Springer, Cham. https://doi.org/10.1007/978-3-319-52153-4_20
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