Paper 2023/1750

A Statistical Verification Method of Random Permutations for Hiding Countermeasure Against Side-Channel Attacks

Jong-Yeon Park, Samsung (South Korea), Kyushu University
Jang-Won Ju, Samsung (South Korea)
Wonil Lee, Samsung (South Korea)
Bo-Gyeong Kang, Samsung (South Korea)
Yasuyuki Kachi, University of Aizu
Kouichi Sakurai, Kyushu University

As NIST is putting the final touches on the standardization of PQC (Post Quantum Cryptography) public key algorithms, it is a racing certainty that peskier cryptographic attacks undeterred by those new PQC algorithms will surface. Such a trend in turn will prompt more follow-up studies of attacks and countermeasures. As things stand, from the attackers’ perspective, one viable form of attack that can be implemented thereupon is the so-called “side-channel attack”. Two best-known countermeasures heralded to be durable against side-channel attacks are: “masking” and “hiding”. In that dichotomous picture, of particular note are successful single-trace attacks on some of the NIST’s PQC then-candidates, which worked to the detriment of the former: “masking”. In this paper, we cast an eye over the latter: “hiding”. Hiding proves to be durable against both side-channel attacks and another equally robust type of attacks called “fault injection attacks”, and hence is deemed an auspicious countermeasure to be implemented. Mathematically, the hiding method is fundamentally based on random permutations. There has been a cornucopia of studies on generating random permutations. However, those are not tied to implementation of the hiding method. In this paper, we propose a reliable and efficient verification of permutation implementation, through employing Fisher–Yates’ shuffling method. We introduce the concept of an 𝑛-th order permutation and explain how it can be used to verify that our implementation is more efficient than its previous-gen counterparts for hiding countermeasures.

Note: Some of the content covered in this paper includes pure mathematical insights.

Available format(s)
Publication info
Side Channel AttackHiding methodRandom PermutationPost-Quantum Cryptography
Contact author(s)
pjy8499 @ gmail com
jangwon95 ju @ samsung com
wonil01 lee @ samsung com
bogyeong kang @ samsung com
kachi @ u-aizu ac jp
sakurai @ inf kyushu-u ac jp
2023-11-13: approved
2023-11-13: received
See all versions
Short URL
Creative Commons Attribution


      author = {Jong-Yeon Park and Jang-Won Ju and Wonil Lee and Bo-Gyeong Kang and Yasuyuki Kachi and Kouichi Sakurai},
      title = {A Statistical Verification Method of Random Permutations for Hiding Countermeasure Against Side-Channel Attacks},
      howpublished = {Cryptology ePrint Archive, Paper 2023/1750},
      year = {2023},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.