Abstract

One important open question in side-channel analysis is to find out whether all the leakage samples in an implementation can be exploited by an adversary, as suggested by masking security proofs. For attacks exploiting a divide-and-conquer strategy, the answer is negative: only the leakages corresponding to the first/last rounds of a block cipher can be exploited. Soft Analytical Side-Channel Attacks (SASCA) have been introduced as a powerful solution to mitigate this limitation. They represent the target implementation and its leakages as a code (similar to a Low Density Parity Check code) that is decoded thanks to belief propagation. Previous works have shown the low data complexities that SASCA can reach in practice. In this paper, we revisit these attacks by modeling them with a variation of the Random Probing Model used in masking security proofs, that we denote as the Local Random Probing Model (LRPM). Our study establishes interesting connections between this model and the erasure channel used in coding theory, leading to the following benefits. First, the LRPM allows bounding the security of concrete implementations against SASCA in a fast and intuitive manner. We use it in order to confirm that the leakage of any operation in a block cipher can be exploited, although the leakages of external operations dominate in known-plaintext/ciphertext attack scenarios. Second, we show that the LRPM is a tool of choice for the (nearly worst-case) analysis of masked implementations in the noisy leakage model, taking advantage of all the operations performed, and leading to new tradeoffs between their amount of randomness and physical noise level. Third, we show that it can considerably speed up the evaluation of other countermeasures such as shuffling.

Highlights

  • A recent line of works started the investigation of masking security proofs as an ingredient of concrete side-channel security evaluations [PR13, DDF14, DFS19, GS18]

  • In order to characterize the increased amount of information that a Soft Analytical Side-Channel Attacks (SASCA) can extract from the example of Figure 1, we model an implementation with a factor graph (1), its side-channel leakages with the Random Probing Model (RPM) (2) and their exploitation with information propagation rules that can be viewed as a variation of the piling up lemma (3)

  • The section will provide a more definitive confirmation that our modeling based on the RPM can serve as an excellent predictor of the complexity of SASCA, by studying the practically-relevant case study of an AES implementation

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Summary

Introduction

A recent line of works started the investigation of masking security proofs as an ingredient of concrete side-channel security evaluations [PR13, DDF14, DFS19, GS18]. While our model already leads to considerable speed ups in the simple case of 8-bit devices investigated in previous works (due to the code size of the target implementations), these gains significantly increase if targeting a 32-bit or larger architecture In this respect, we note that it is always possible to trade time for data, by targeting only a part of the bus and considering that the untargeted bits of the architecture produce “algorithmic noise”.

Template attacks and MI metric
Soft Analytical Side-Channel Attacks
Basics in coding theory
A toy example of unprotected implementation
Target implementation
A divide-and-conquer evaluation
A SASCA evaluation with the LRPM
Discussion & definition
Factor graph generation
Analysis and results
C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14
Connections to coding theory
Protected implementations
Masked encoding
Masked multiplication
Masked S-box implementations
Shuffling
Summarizing remarks
Full Text
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