Loop-Abort Faults on Lattice-Based Fiat–Shamir and Hash-and-Sign Signatures

As the advent of general-purpose quantum computers appears to be drawing closer, agencies and advisory bodies have started recommending that we prepare the transition away from factoring and discrete logarithm-based cryptography, and towards postquantum secure constructions, such as lattice- based schemes. Almost all primitives of classical cryptography (and more!) can be realized with lattices, and the efficiency of primitives like encryption and signatures has gradually improved to the point that key sizes are competitive with RSA at similar security levels, and fast performance can be achieved both in soft- ware and hardware. However, little research has been conducted on physical attacks targeting concrete implementations of postquantum cryptography in general and lattice-based schemes in particular, and such research is essential if lattices are going to replace RSA and elliptic curves in our devices and smart cards. In this paper, we look in particular at fault attacks against implementations of lattice-based signature schemes, looking both at Fiat–Shamir type constructions (particularly BLISS, but also GLP, PASSSing and Ring-TESLA) and at hash-and-sign schemes (particularly the GPV-based scheme of Ducas–Prest– Lyubashevsky). These schemes include essentially all practical lattice-based signatures, and achieve the best efficiency to date in both software and hardware. We present several fault attacks against those schemes yielding a full key recovery with only a few or even a single faulty signature, and discuss possible countermeasures to protect against these attacks

Side-channel Assisted Existential Forgery Attack on Dilithium - A NIST PQC candidate

The recent lattice-based signature scheme Dilithium, submitted as part of the CRYSTALS (Cryptographic Suite for Algebraic Lattices) package, is one of a number of strong candidates submitted for the NIST standardisation process of post-quantum cryptography. The Dilithium signature scheme is based on the Fiat-Shamir paradigm and can be seen as a variant of the Bai-Galbraith scheme (BG) combined with several improvements from previous ancestor lattice-based schemes like GLP and BLISS signature schemes. One of the main features of Dilithium is the compressed public-key, which is a rounded version of the LWE instance. This implies that Dilithium is not breakable with the knowledge of only the secret or the error of the LWE instance, unlike its ancestor lattice-based signature schemes. In this paper, we investigate the security of Dilithium against a combination of side-channel and classical attacks. Side-channel attacks on schoolbook and optimised polynomial multiplication algorithms in the signing procedure are shown to extract the secret component of the LWE instance, which is just one among the multiple components of the secret-key of Dilithium. We then propose an alternative signing procedure, through which it is possible to forge signatures with only the extracted portion of the secret-key, without requiring the knowledge of all its elements. Thus showing that Dilithium too breaks on just knowing the secret portion of the LWE instance, similar to previous lattice-based schemes

Number Not Used Once - Practical fault attack on pqm4 implementations of NIST candidates

In this paper, we demonstrate practical fault attacks over a number of lattice based schemes, in particular NewHope, Kyber, Frodo, Dilithium which are based on the hardness of the Learning with Errors (LWE) problem. One of the common traits of all the considered LWE schemes is the use of nonces as domain separators to sample the secret components of the LWE instance. We show that simple faults targeting the usage of nonce can result in a nonce-reuse scenario which allows key recovery and message recovery attacks. To the best of our knowledge, we propose the first practical fault attack on lattice-based Key encapsulation schemes secure in the CCA model. We perform experimental validation of our attack using Electromagnetic fault injection on reference implementations of the aforementioned schemes taken from the pqm4 library, a benchmarking and testing framework for post quantum cryptographic implementations for the ARM Cortex-M4. We use the instruction skip fault model, which is very practical and popular in microcontroller based implementations. Our attack requires to inject a very few number of faults (numbering less than 10 for recommended parameter sets) and can be repeated with a 100% accuracy with our Electromagnetic fault injection setup

Fault Attacks Sensitivity of Public Parameters in the Dilithium Verification

This paper presents a comprehensive analysis of the verification algorithm of the CRYSTALS-Dilithium, focusing on a C reference implementation. Limited research has been conducted on its susceptibility to fault attacks, despite its critical role in ensuring the scheme’s security. To fill this gap, we investigate three distinct fault models - randomizing faults, zeroizing faults, and skipping faults - to identify vulnerabilities within the verification process. Based on our analysis, we propose a methodology for forging CRYSTALS-Dilithium signatures without knowledge of the secret key. Instead, we leverage specific types of faults during the verification phase and some properties about public parameters to make these signatures accepted. Additionally, we compared different attack scenarios after identifying sensitive operations within the verification algorithm. The most effective requires potentially fewer fault injections than targeting the verification check itself. Finally, we introduce a set of countermeasures designed to thwart all the identified scenarios rendering the verification algorithm intrinsically resistant to the presented attacks

From MLWE to RLWE: A Differential Fault Attack on Randomized & Deterministic Dilithium

The post-quantum digital signature scheme CRYSTALS-Dilithium has been recently selected by the NIST for standardization. Implementing CRYSTALS-Dilithium, and other post-quantum cryptography schemes, on embedded devices raises a new set of challenges, including ones related to performance in terms of speed and memory requirements, but also related to side-channel and fault injection attacks security. In this work, we investigated the latter and describe a differential fault attack on the randomized and deterministic versions of CRYSTALS-Dilithium. Notably, the attack requires a few instructions skips and is able to reduce the MLWE problem that Dilithium is based on to a smaller RLWE problem which can be practically solved with lattice reduction techniques. Accordingly, we demonstrated key recoveries using hints extracted on the secret keys from the same faulted signatures using the LWE with side-information framework introduced by Dachman-Soled et al. at CRYPTO’20. As a final contribution, we proposed algorithmic countermeasures against this attack and in particular showed that the second one can be parameterized to only induce a negligible overhead over the signature generation

Grafting Trees: a Fault Attack against the SPHINCS framework

Because they require no assumption besides the preimage or collision resistance of hash functions, hash-based signatures are a unique and very attractive class of post-quantum primitives. Among them, the schemes of the SPHINCS family are arguably the most practical stateless schemes, and can be implemented on embedded devices such as FPGAs or smart cards. This naturally raises the question of their resistance to implementation attacks. In this paper, we propose the first fault attack against the framework underlying SPHINCS, Gravity-SPHINCS and SPHINCS+. Our attack allows to forge any message signature at the cost of a single faulted message. Furthermore, the fault model is very reasonable and the faulted signatures remain valid, which renders our attack both stealthy and practical. As the attack involves a non-negligible computational cost, we propose a fine-grained trade-off allowing to lower this cost by slightly increasing the number of faulted messages. Our attack is generic in the sense that it does not depend on the underlying hash function(s) used

A Differential Fault Attack against Deterministic Falcon Signatures

We describe a fault attack against the deterministic variant of the Falcon signature scheme. It is the first fault attack that exploits specific properties of deterministic Falcon. The attack works under a very liberal and realistic single fault random model. The main idea is to inject a fault into the pseudo-random generator of the pre-image trapdoor sampler, generate different signatures for the same input, find reasonably short lattice vectors this way, and finally use lattice reduction techniques to obtain the private key. We investigate the relationship between fault location, the number of faults, computational effort for a possibly remaining exhaustive search step and success probability

PCD

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Page 96 blank. Cataloged from PDF version of thesis.Includes bibliographical references (p. 87-95).The security of systems can often be expressed as ensuring that some property is maintained at every step of a distributed computation conducted by untrusted parties. Special cases include integrity of programs running on untrusted platforms, various forms of confidentiality and side-channel resilience, and domain-specific invariants. We propose a new approach, proof-carrying data (PCD), which sidesteps the threat of faults and leakage by reasoning about properties of a computation's output data, regardless of the process that produced it. In PCD, the system designer prescribes the desired properties of a computation's outputs. Corresponding proofs are attached to every message flowing through the system, and are mutually verified by the system's components. Each such proof attests that the message's data and all of its history comply with the prescribed properties. We construct a general protocol compiler that generates, propagates, and verifies such proofs of compliance, while preserving the dynamics and efficiency of the original computation. Our main technical tool is the cryptographic construction of short non-interactive arguments (computationally-sound proofs) for statements whose truth depends on "hearsay evidence": previous arguments about other statements. To this end, we attain a particularly strong proof-of-knowledge property. We realize the above, under standard cryptographic assumptions, in a model where the prover has blackbox access to some simple functionality - essentially, a signature card.by Alessandro Chiesa.M.Eng