Thomas Espitau

Bio: Thomas Espitau is an academic researcher from Pierre-and-Marie-Curie University. The author has contributed to research in topics: Probabilistic logic & Cryptography. The author has an hindex of 12, co-authored 42 publications receiving 450 citations. Previous affiliations of Thomas Espitau include Centre national de la recherche scientifique & University of Paris.

Side-Channel Attacks on BLISS Lattice-Based Signatures: Exploiting Branch Tracing against strongSwan and Electromagnetic Emanations in Microcontrollers

Abstract: In this paper, we investigate the security of the BLISS lattice-based signature scheme, one of the most promising candidates for postquantum-secure signatures, against side-channel attacks. Several works have been devoted to its efficient implementation on various platforms, from desktop CPUs to microcontrollers and FPGAs, and more recent papers have also considered its security against certain types of physical attacks, notably fault injection and cache attacks. We turn to more traditional side-channel analysis, and describe several attacks that can yield a full key recovery. We first identify a serious source of leakage in the rejection sampling algorithm used during signature generation. Existing implementations of that rejection sampling step, which is essential for security, actually leak the "relative norm" of the secret key. We show how an extension of an algorithm due to Howgrave-Graham and Szydlo can be used to recover the key from that relative norm, at least when the absolute norm is easy to factor (which happens for a significant fraction of secret keys). We describe how this leakage can be exploited in practice both on an embedded device (an 8-bit AVR microcontroller) using electromagnetic analysis (EMA), and a desktop computer (recent Intel CPU running Linux) using branch tracing. The latter attack has been mounted against the open source VPN software strongSwan. We also show that other parts of the BLISS signing algorithm can leak secrets not just for a subset of secret keys, but for 100% of them. The BLISS Gaussian sampling algorithm in strongSwan is intrinsically variable time. This would be hard to exploit using a noisy source of leakage like EMA, but branch tracing allows to recover the entire randomness and hence the key: we show that a single execution of the strongSwan signature algorithm is actually sufficient for full key recovery. We also describe a more traditional side-channel attack on the sparse polynomial multiplications carried out in BLISS: classically, multiplications can be attacked using DPA; however, our target 8-bit AVR target implementation uses repeated shifted additions instead. Surprisingly, we manage to obtain a full key recovery in that setting using integer linear programming from a single EMA trace.

Synthesizing Probabilistic Invariants via Doob’s Decomposition

Abstract: When analyzing probabilistic computations, a powerful approach is to first find a martingale—an expression on the program variables whose expectation remains invariant—and then apply the optional stopping theorem in order to infer properties at termination time. One of the main challenges, then, is to systematically find martingales.

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

Abstract: Although postquantum cryptography is of growing practical concern, not many works have been devoted to implementation security issues related to postquantum schemes.

LWE Without Modular Reduction and Improved Side-Channel Attacks Against BLISS

Abstract: This paper is devoted to analyzing the variant of Regev’s learning with errors (LWE) problem in which modular reduction is omitted: namely, the problem (ILWE) of recovering a vector \(\mathbf {s}\in \mathbb {Z}^n\) given polynomially many samples of the form \((\mathbf {a},\langle \mathbf {a},\mathbf {s}\rangle + e)\in \mathbb {Z}^{n+1}\) where \(\mathbf { a}\) and e follow fixed distributions. Unsurprisingly, this problem is much easier than LWE: under mild conditions on the distributions, we show that the problem can be solved efficiently as long as the variance of e is not superpolynomially larger than that of \(\mathbf { a}\). We also provide almost tight bounds on the number of samples needed to recover \(\mathbf {s}\).

GALACTICS: Gaussian Sampling for Lattice-Based Constant- Time Implementation of Cryptographic Signatures, Revisited

Abstract: In this paper, we propose a constant-time implementation of the BLISS lattice-based signature scheme. BLISS is possibly the most efficient lattice-based signature scheme proposed so far, with a level of performance on par with widely used pre-quantum primitives like ECDSA. It is only one of the few postquantum signatures to have seen real-world deployment, as part of the strongSwan VPN software suite. The outstanding performance of the BLISS signature scheme stems in large part from its reliance on discrete Gaussian distributions, which allow for better parameters and security reductions. However, that advantage has also proved to be its Achilles' heel, as discrete Gaussians pose serious challenges in terms of secure implementations. Implementations of BLISS so far have included secret-dependent branches and memory accesses, both as part of the discrete Gaussian sampling and of the essential rejection sampling step in signature generation. These defects have led to multiple devastating timing attacks, and were a key reason why BLISS was not submitted to the NIST postquantum standardization effort. In fact, almost all of the actual candidates chose to stay away from Gaussians despite their efficiency advantage, due to the serious concerns surrounding implementation security. Moreover, naive countermeasures will often not cut it: we show that a reasonable-looking countermeasure suggested in previous work to protect the BLISS rejection sampling can again be defeated using novel timing attacks, in which the timing information is fed to phase retrieval machine learning algorithm in order to achieve a full key recovery. Fortunately, we also present careful implementation techniques that allow us to describe an implementation of BLISS with complete timing attack protection, achieving the same level of efficiency as the original unprotected code, without resorting on floating point arithmetic or platform-specific optimizations like AVX intrinsics. These techniques, including a new approach to the polynomial approximation of transcendental function, can also be applied to the masking of the BLISS signature scheme, and will hopefully make more efficient and secure implementations of lattice-based cryptography possible going forward.

CRYSTALS-Dilithium: A lattice-based digital signature scheme

Abstract: In this paper, we present the lattice-based signature scheme Dilithium, which is a component of the CRYSTALS (Cryptographic Suite for Algebraic Lattices) suite that was submitted to NIST’s call for post-quantum cryptographic standards. The design of the scheme avoids all uses of discrete Gaussian sampling and is easily implementable in constant-time. For the same security levels, our scheme has a public key that is 2.5X smaller than the previously most efficient lattice-based schemes that did not use Gaussians, while having essentially the same signature size. In addition to the new design, we significantly improve the running time of the main component of many lattice-based constructions – the number theoretic transform. Our AVX2-based implementation results in a speed-up of roughly a factor of 2 over the previously best algorithms that appear in the literature. The techniques for obtaining this speed-up also have applications to other lattice-based schemes.

E fficient Identity-Based Encryption over NTRU Lattices.

Abstract: Efficient implementations of lattice-based cryptographic schemes have been limited to only the most basic primitives like encryption and digital signatures. The main reason for this limitation is that at the core of many advanced lattice primitives is a trapdoor sampling algorithm (Gentry, Peikert, Vaikuntanathan, STOC 2008) that produced outputs that were too long for practical applications. In this work, we show that using a particular distribution over NTRU lattices can make GPV-based schemes suitable for practice. More concretely, we present the first lattice-based IBE scheme with practical parameters – key and ciphertext sizes are between two and four kilobytes, and all encryption and decryption operations take approximately one millisecond on a moderately-powered laptop. As a by-product, we also obtain digital signature schemes which are shorter than the previously most-compact ones of Ducas, Durmus, Lepoint, and Lyubashevsky from Crypto 2013.

Side-Channel Attacks on BLISS Lattice-Based Signatures: Exploiting Branch Tracing against strongSwan and Electromagnetic Emanations in Microcontrollers

Abstract: In this paper, we investigate the security of the BLISS lattice-based signature scheme, one of the most promising candidates for postquantum-secure signatures, against side-channel attacks. Several works have been devoted to its efficient implementation on various platforms, from desktop CPUs to microcontrollers and FPGAs, and more recent papers have also considered its security against certain types of physical attacks, notably fault injection and cache attacks. We turn to more traditional side-channel analysis, and describe several attacks that can yield a full key recovery. We first identify a serious source of leakage in the rejection sampling algorithm used during signature generation. Existing implementations of that rejection sampling step, which is essential for security, actually leak the "relative norm" of the secret key. We show how an extension of an algorithm due to Howgrave-Graham and Szydlo can be used to recover the key from that relative norm, at least when the absolute norm is easy to factor (which happens for a significant fraction of secret keys). We describe how this leakage can be exploited in practice both on an embedded device (an 8-bit AVR microcontroller) using electromagnetic analysis (EMA), and a desktop computer (recent Intel CPU running Linux) using branch tracing. The latter attack has been mounted against the open source VPN software strongSwan. We also show that other parts of the BLISS signing algorithm can leak secrets not just for a subset of secret keys, but for 100% of them. The BLISS Gaussian sampling algorithm in strongSwan is intrinsically variable time. This would be hard to exploit using a noisy source of leakage like EMA, but branch tracing allows to recover the entire randomness and hence the key: we show that a single execution of the strongSwan signature algorithm is actually sufficient for full key recovery. We also describe a more traditional side-channel attack on the sparse polynomial multiplications carried out in BLISS: classically, multiplications can be attacked using DPA; however, our target 8-bit AVR target implementation uses repeated shifted additions instead. Surprisingly, we manage to obtain a full key recovery in that setting using integer linear programming from a single EMA trace.

A Concrete Treatment of Fiat-Shamir Signatures in the Quantum Random-Oracle Model

Abstract: The Fiat-Shamir transform is a technique for combining a hash function and an identification scheme to produce a digital signature scheme. The resulting scheme is known to be secure in the random oracle model (ROM), which does not, however, imply security in the scenario where the adversary also has quantum access to the oracle. The goal of this current paper is to create a generic framework for constructing tight reductions in the QROM from underlying hard problems to Fiat-Shamir signatures.

A Concrete Treatment of Fiat-Shamir Signatures in the Quantum Random-Oracle Model.

Abstract: The Fiat-Shamir transform is a technique for combining a hash function and an identification scheme to produce a digital signature scheme. The resulting scheme is known to be secure in the random oracle model (ROM), which does not, however, imply security in the scenario where the adversary also has quantum access to the oracle. The goal of this current paper is to create a generic framework for constructing tight reductions in the QROM from underlying hard problems to Fiat-Shamir signatures.