Formal Analysis of CRT-RSA Vigilant's Countermeasure Against the BellCoRe Attack: A Pledge for Formal Methods in the Field of Implementation Security

In our paper at PROOFS 2013, we formally studied a few known countermeasures to protect CRT-RSA against the BellCoRe fault injection attack. However, we left Vigilant's countermeasure and its alleged repaired version by Coron et al. as future work, because the arithmetical framework of our tool was not sufficiently powerful. In this paper we bridge this gap and then use the same methodology to formally study both versions of the countermeasure. We obtain surprising results, which we believe demonstrate the importance of formal analysis in the field of implementation security. Indeed, the original version of Vigilant's countermeasure is actually broken, but not as much as Coron et al. thought it was. As a consequence, the repaired version they proposed can be simplified. It can actually be simplified even further as two of the nine modular verifications happen to be unnecessary. Fortunately, we could formally prove the simplified repaired version to be resistant to the BellCoRe attack, which was considered a "challenging issue" by the authors of the countermeasure themselves.Comment: arXiv admin note: substantial text overlap with arXiv:1401.817

Formal verification of a software countermeasure against instruction skip attacks

Fault attacks against embedded circuits enabled to define many new attack paths against secure circuits. Every attack path relies on a specific fault model which defines the type of faults that the attacker can perform. On embedded processors, a fault model consisting in an assembly instruction skip can be very useful for an attacker and has been obtained by using several fault injection means. To avoid this threat, some countermeasure schemes which rely on temporal redundancy have been proposed. Nevertheless, double fault injection in a long enough time interval is practical and can bypass those countermeasure schemes. Some fine-grained countermeasure schemes have also been proposed for specific instructions. However, to the best of our knowledge, no approach that enables to secure a generic assembly program in order to make it fault-tolerant to instruction skip attacks has been formally proven yet. In this paper, we provide a fault-tolerant replacement sequence for almost all the instructions of the Thumb-2 instruction set and provide a formal verification for this fault tolerance. This simple transformation enables to add a reasonably good security level to an embedded program and makes practical fault injection attacks much harder to achieve

Secure and Efficient RNS Approach for Elliptic Curve Cryptography

Scalar multiplication, the main operation in elliptic curve cryptographic protocols, is vulnerable to side-channel (SCA) and fault injection (FA) attacks. An efficient countermeasure for scalar multiplication can be provided by using alternative number systems like the Residue Number System (RNS). In RNS, a number is represented as a set of smaller numbers, where each one is the result of the modular reduction with a given moduli basis. Under certain requirements, a number can be uniquely transformed from the integers to the RNS domain (and vice versa) and all arithmetic operations can be performed in RNS. This representation provides an inherent SCA and FA resistance to many attacks and can be further enhanced by RNS arithmetic manipulation or more traditional algorithmic countermeasures. In this paper, extending our previous work, we explore the potentials of RNS as an SCA and FA countermeasure and provide an description of RNS based SCA and FA resistance means. We propose a secure and efficient Montgomery Power Ladder based scalar multiplication algorithm on RNS and discuss its SCAFA resistance. The proposed algorithm is implemented on an ARM Cortex A7 processor and its SCA-FA resistance is evaluated by collecting preliminary leakage trace results that validate our initial assumptions

Design and validation of a platform for electromagnetic fault injection

Security is acknowledged as one of the main challenges in the design and deployment of embedded circuits. Devices need to operate on-the-field safely and correctly, even when at physical reach of potential adversaries. One of the most powerful techniques to compromise the correct functioning of a device are fault injection attacks. They enable an active adversary to trigger errors on a circuit in order to bypass security features or to gain knowledge of security-sensitive information. There are several methods to induce such errors. In this work we focus on the injection of faults through the electromagnetic (EM) channel. In particular, we document our efforts towards building a suitable platform for EM pulse injection. We design a pulse injection circuit that can provide currents over 20 A to an EM injector in order to generate abrupt variations of the EM field on the vicinity of a circuit. We validate the suitability of our platform by applying a well-know attack on an embedded 8-bit microcontroller implementing the AES block cipher. In particular, we show how to extract the AES secret cryptographic keys stored in the device by careful injection of faults during the encryption operations and simple analysis of the erroneous outputs.Peer ReviewedPostprint (published version

Fault attacks on RSA and elliptic curve cryptosystems

This thesis answered how a fault attack targeting software used to program EEPROM can threaten hardware devices, for instance IoT devices. The successful fault attacks proposed in this thesis will certainly warn designers of hardware devices of the security risks their devices may face on the programming leve

Physical Fault Injection and Side-Channel Attacks on Mobile Devices:A Comprehensive Analysis

Today's mobile devices contain densely packaged system-on-chips (SoCs) with multi-core, high-frequency CPUs and complex pipelines. In parallel, sophisticated SoC-assisted security mechanisms have become commonplace for protecting device data, such as trusted execution environments, full-disk and file-based encryption. Both advancements have dramatically complicated the use of conventional physical attacks, requiring the development of specialised attacks. In this survey, we consolidate recent developments in physical fault injections and side-channel attacks on modern mobile devices. In total, we comprehensively survey over 50 fault injection and side-channel attack papers published between 2009-2021. We evaluate the prevailing methods, compare existing attacks using a common set of criteria, identify several challenges and shortcomings, and suggest future directions of research