Formal Analysis of the Entropy / Security Trade-off in First-Order Masking Countermeasures against Side-Channel Attacks

Abstract

Abstract. Several types of countermeasures against side-channel attacks are known. The one called masking is of great interest since it can be applied to any protocol and/or algorithm, without nonetheless requiring special care at the implementation level. Masking countermeasures are usually studied with the maximal possible entropy for the masks. However, in practice, this requirement can be viewed as too costly. It is thus relevant to study how the security evolves when the number of mask values decreases. In this article, we study a first-order masking scheme, that makes use of one n-bit mask taking values in a strict subset of F n 2 . For a given entropy budget, we show that the security does depend on the choice of the mask values. More specifically, we explore the space of mask sets that resist first-and second-order correlation analysis (CPA and 2O-CPA), using exhaustive search for word size n 5 bit and a SAT-solver for n up to 8 bit. We notably show that it is possible to protect algorithms against both CPA and 2O-CPA such as AES with only 12 mask values. If the general trend is that more entropy means less leakage, some particular mask subsets can leak less (or on the contrary leak remarkably more). Additionally, we exhibit such mask subsets that allows for a minimal leakage.

Attacking Suggest Boxes in Web Applications Over HTTPS Using Side-Channel Stochastic Algorithms

“…Even though the randomization of packet lengths makes it harder to infer a search query, it is still possible to guess the target correctly in many cases. There have been numerous attempts to mitigate side-channel leaks in general [13,14], but it is generally considered that preventing every side-channel leak source is very difficult [15]. However, for the particular leak exploited in this paper, it would be easy to implement an efficient countermeasure by sending only packets of a given, fixed size (e.g., the size of the longest possible packet in response of a request).…”

Analysis of Software Implemented Low Entropy Masking Schemes

“…However, if the mask is drawn randomly from 2 possible masks, too much memory is required to keep all the possible masked S-Boxes. To offer a reasonable solution to balance the security protection and the performance of implementations, Low Entropy Masking Schemes (LEMS) [10,11] are designed by limiting the amount of mask entropy.…”

“…Another aspect is the chosen mask set which plays significant roles in security. Some research studied how to select them for hardware implemented LEMS [11,18]. The selection criterion of the mask sets considered finding secure mask sets under two important assumptions [19].…”

“…(i) We find that the mask sets selected according to selection criteria in [11,18] have the vulnerabilities based on the absolute difference measurements on software LEMS. Such vulnerabilities make the software LEMS implementations insecure when the leakages corresponding to the masked values could be exploited.…”

Detecting Hidden Leakages

“…However, each of these heuristics has a drawback which may lead to a seriously vulnerable implementation (see [10]). Instead, reducing the entropy of the mask is the idea followed by [30,31]. Use of fewer mask values allows precomputing all masked look-up tables and fit them to the small-size platforms, e.g., smartcards or microcontrollers with a few Kilobytes of flash memory.…”