[Paper Review] Multi-Linear cryptanalysis in Power Analysis Attacks MLPA

Thomas Roche, Cédric Tavernier|ArXiv.org|Jun 1, 2009

Cryptographic Implementations and Security15 references3 citations

TL;DR

This paper introduces Multi-Linear Power Analysis (MLPA), a novel class of side-channel attacks exploiting multi-linear approximations to break embedded countermeasures against Differential Power Analysis (DPA). It demonstrates that even the 'brutal countermeasure'—a simple, efficient defense—can be broken using MLPA, with successful attacks on DES and AES using real traces from the DPA contest, achieving over 95% success probability with under 2^20 traces for 3-round DES in the Hamming Weight model.

ABSTRACT

Power analysis attacks against embedded secret key cryptosystems are widely studied since the seminal paper of Paul Kocher, Joshua Ja, and Benjamin Jun in 1998 where has been introduced the powerful Differential Power Analysis. The strength of DPA is such that it became necessary to develop sound and efficient countermeasures. Nowadays embedded cryptographic primitives usually integrate one or several of these countermeasures (e.g. masking techniques, asynchronous designs, balanced dynamic dual-rail gates designs, noise adding, power consumption smoothing, etc. ...). This document presents a simple, yet interesting, countermeasure to DPA and HO-DPA attacks, called brutal countermeasure and new power analysis attacks using multi-linear approximations (MLPA attacks) based on very recent and still unpublished results of Tavernier et al..

Motivation & Objective

• To develop a new class of side-channel attacks based on multi-linear approximations that can bypass existing countermeasures in embedded symmetric ciphers.
• To evaluate the effectiveness of the 'brutal countermeasure'—a simple, non-masked defense—against high-order power analysis attacks.
• To validate the feasibility of MLPA attacks on real-world power traces, particularly from the DPA contest.
• To explore the practicality of attacking unknown cipher implementations by directly approximating leakage functions without prior knowledge of the cipher structure.

Proposed method

• The attack uses multi-linear approximations derived from Reed-Muller codes to model the Hamming weight of intermediate data values in cryptographic implementations.
• It applies linear and multi-linear cryptanalysis techniques to power traces, focusing on the Hamming weight (HW) and Hamming distance (HD) of data during encryption.
• The method is tested on both simulated data and real power traces from the DPA contest, using a black-box model where only power consumption is observed.
• For DES, attacks target glued blocks of 1–3 rounds; for AES, the attack focuses on the last round to avoid the MixColumns transformation.
• The attack uses statistical analysis to identify linear approximations with high bias, enabling key recovery with reduced data complexity.
• The approach is extended to unknown cipher attacks by directly approximating the leakage function from power traces without requiring cipher-specific models.

Experimental results

Research questions

• RQ1 Can multi-linear approximations be used to mount effective power analysis attacks on embedded symmetric ciphers, even when traditional DPA countermeasures are applied?
• RQ2 How effective is the 'brutal countermeasure'—a simple, non-masked defense—against high-order power analysis attacks?
• RQ3 Can MLPA attacks successfully recover secret keys from real power traces, such as those from the DPA contest?
• RQ4 To what extent can MLPA be used to attack unknown cipher implementations by directly modeling leakage functions from power traces?

Key findings

• The MLPA attack successfully recovers key bits in DES with a 99% success probability using only 2^12 plaintexts in the Hamming Weight model for two rounds.
• For three rounds of DES in the Hamming Weight model, the attack achieves 99% success probability with 2^20 plaintexts, demonstrating the vulnerability of the brutal countermeasure.
• On real DPA contest traces, the attack recovered approximately 45 key bits with 20,000 traces for two rounds of DES, achieving a 99% success rate.
• The attack on AES, targeting the last round, achieved a 99% success probability with 2^11 traces, using 1410 linear approximations.
• No linear approximations were found for the first round in the Hamming Distance model, indicating potential resistance in certain configurations.
• The results validate that MLPA is a practical and powerful attack vector, especially when combined with direct leakage modeling from real power traces.