Optimality and Efficiency of Higher-Order Rank-Based Side-Channel Attacks against Inner Product Masking Schemes

Haitao Zhan; Wei Cheng; Yuejun Liu; Jingdian Ming; Sylvain Guilley; Yongbin Zhou

Paper 2026/2676

Optimality and Efficiency of Higher-Order Rank-Based Side-Channel Attacks against Inner Product Masking Schemes

Haitao Zhan

, Nanjing University of Science and Technology

Wei Cheng

, Nanjing University of Science and Technology, Télécom Paris, Institut Polytechnique de Paris

Yuejun Liu

, Nanjing University of Science and Technology

Jingdian Ming

, Nanjing University of Science and Technology

Sylvain Guilley

, Secure-IC S.A.S., Télécom Paris, Institut Polytechnique de Paris

Yongbin Zhou

, Nanjing University of Science and Technology

Abstract

Higher-Order Spearman Coefficient Analysis (HO-SPA) is of particular interest in non-profiling Side-Channel Attacks (SCA) due to its effectiveness against monotonic nonlinear leakage. However, the optimal form, effective order combinations, and performance of HO-SPA (or its variants) remain underexplored. This work systematically revisits HO-SPA in the presence of Boolean Masking (BM) and Inner Product Masking (IPM). Specifically, we propose a new variant of HO-SPA, called HO-ASPA (Higher-Order Adjusted Spearman Coefficient Analysis), and derive the optimal form of HO-ASPA for two-share BM and IPM across a wide range of order combinations under the Hamming weight (HW) leakage model. We first derive the optimal form of HO-ASPA by extending the Spearman Coefficient Analysis to higher-order moments, while preserving the centered-product combination of the share leakages. We then establish an upper bound on the maximal correlation induced by the rank transformation and characterize the relationship between the signal-to-noise ratio and the optimal correlation coefficient in the rank-domain, and extend these analyses to IPM. To enable a fair comparison, we also derive the optimal forms of Higher-Order Correlation Power Analysis (HO-CPA) and HO-ASPA for both BM and IPM under the Least-Significant-Bit (LSB) leakage model. Our analysis highlights a key distinction: unlike HO-CPA, where higher orders often outperform the lowest feasible order, HO-ASPA shows no significant performance gap between higher-order and lower-order attacks. Moreover, under the HW leakage model, our HO-ASPA not only aligns with existing results and succeeds in counteracting the security order amplification, but also significantly outperforms Kruskal-Wallis Analysis (KWA)-based attacks at various order combinations. We further validate the effectiveness of the proposed HO-ASPA through simulated and real-world experimental evaluations.

Note: This is the authors' version of the paper accepted for publication in the IEEE Transactions on Information Forensics and Security (TIFS).

Metadata

Available format(s): PDF
Category: Applications
Publication info: Published elsewhere. Minor revision. IEEE TIFS
Keywords: Side-Channel Attacks Non-profiling Distinguishers Higher-Order Correlation Analysis Inner Product Masking.
Contact author(s): zhanhaitao @ njust edu cn
wei cheng @ njust edu cn
liuyuejun @ njust edu cn
mingjingdian @ njust edu cn
sylvain guilley @ secure-ic com
zhouyongbin @ njust edu cn
History: 2026-10-31: approved; 2026-10-29: received; See all versions
Short URL: https://ia.cr/2026/2676
License: CC BY-NC

BibTeX

@misc{cryptoeprint:2026/2676,
      author = {Haitao Zhan and Wei Cheng and Yuejun Liu and Jingdian Ming and Sylvain Guilley and Yongbin Zhou},
      title = {Optimality and Efficiency of Higher-Order Rank-Based Side-Channel Attacks against Inner Product Masking Schemes},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/2676},
      year = {2026},
      url = {https://eprint.iacr.org/2026/2676}
}