arXiv subjects

Guillaume Hanrot

Publications and source records attributed to Guillaume Hanrot.

9 recordsLinked to original sources

arXiv2026

Private Iris Recognition with High-Performance FHE

Among biometric verification systems, irises stand out because they offer high accuracy even in large-scale databases. For example, the World ID project aims to provide authentication to all humans via iris recognition, with millions already registered. Storing such biometric data raises privacy concerns, which can be addressed using privacy-enhancing techniques. Bloemen et al. describe a solution based on 2-out-of-3 Secret-Sharing Multiparty Computation (SS-MPC), for the World ID setup. In terms of security, unless an adversary corrupts 2~servers, the iris codes remain confidential and nothing leaks beyond the result of the computation. Their solution is able to match~$32$ users against a database of~$2^{22}$ iris codes in~$\approx 2$s , using~24 H100 GPUs, more than 40~communication rounds and $81$GB/party of data transferred (the timing assumes a network speed above~3Tb/s). In the present work, we explore the use of Threshold Fully Homomorphic Encryption (ThFHE) for the same task. The ThFHE solution brings a number of security advantages: no trusted setup, the encrypted database and queries can be public, the secret can be distributed among many parties, and active security can be added without significant performance degradation. Our proof-of-concept implementation of the computation phase handles $32$~eyes against a database of $7\cdot 2^{14}$ iris codes in~$\approx 1.8$s ($\approx 0.33s$ for 4 eyes against the same database), using 8 RTX-5090 GPUs. To this, one should add~2 to 3 rounds of communication (depending on deployment choice). We perform the matching using the CKKS (Th)FHE scheme. Our main technical ingredients are the use of recent progress on FHE-based linear algebra boosted using int8 GPU operations, and the introduction of a technique reducing the number of ciphertexts to be processed as early as possible.

cs.CR↗

arXiv2026

Scaling up FHE-based Privacy-Preserving ML: Higher Throughput, Longer Inputs for LLama-3-8B

As large language models (LLMs) become ubiquitous, privacy concerns pertaining to inference keep growing. Fully homomorphic encryption (FHE) has emerged as a primary cryptographic solution for non-interactive confidential LLM inference. However, existing solutions scale poorly with input token length, focusing on small models or input sizes. They also suffer from large outlier values, which strongly impact the evaluation of non-linear layers, leading to heavy polynomial approximation costs. We scale up FHE-based LLM inference in two directions. First, we accelerate FHE-based inference for 128 encrypted tokens. We adopt ML techniques (token prepending and orthogonal rotations) to mitigate outlier impacts on the FHE evaluation of non-linear layers. Separately, we devise a novel polynomial evaluation method for sparsely-packed ciphertexts to speed up our homomorphic SoftMax implementation. We combine these with recent fast homomorphic linear algebra techniques, achieving significantly improved efficiency. Second, we expand the prompt size up to thousands of tokens for contexts where only the final part of the input is sensitive and encrypted. Processing this requires handling standard plaintext-plaintext and ciphertext-ciphertext components, alongside a wide homomorphic computation for a novel plaintext-ciphertext component. To address this, we devise a dedicated homomorphic linear algebra algorithm, building a shallow homomorphic attention circuit that minimizes bootstrapping costs. Based on these ingredients, we present a CKKS-based end-to-end implementation of Llama-3-8B private inference. On 8 NVIDIA RTX PRO 6000 GPUs, 128 encrypted tokens take 20s for summarization and 18s/token for generation (vastly outperforming the SOTA 295s on costlier H100 GPUs). For a heterogeneous 4096-token input (last 128 encrypted), it takes 64s for summarization and 22s/token for generation.

cs.CR↗

arXiv2026

Integer points close to a transcendental curve: an algorithmic approach

In this article, we propose an algorithmic approach to determine the integer points located near a transcendental curve. This approach is closely related to a celebrated work by Bombieri and Pila and to the so-called Coppersmith's method. We establish the underlying theoretical foundations, prove the algorithms, study their complexity and present practical experiments; we also compare our approach with previously existing ones. From a practical point of view, we focus on an instance of our general problem, called the Table Maker's Dilemma, whose solving makes it possible to evaluate a given function with correct rounding. Our experiments show a significant speedup. In particular, our results show that the development of a correctly rounded mathematical library for the binary128 format is now possible at a much smaller cost than with previously existing approaches.

math.NT↗

arXiv2026

Fast Homomorphic Linear Algebra with BLAS

Homomorphic encryption is a cryptographic paradigm allowing to compute on encrypted data, opening a wide range of applications in privacy-preserving data manipulation, notably in AI. Many of those applications require significant linear algebra computations (matrix-vector products, and matrix-matrix products). This central role of linear algebra computations goes far beyond homomorphic algebra and applies to most areas of scientific computing. This high versatility led, over time, to the development of a set of highly optimized routines, specified in 1979 under the name BLAS (basic linear algebra subroutines). Motivated both by the applicative importance of homomorphic linear algebra and the access to highly efficient implementations of cleartext linear algebra able to draw the most out of available hardware, we explore the connections between CKKS-based homomorphic linear algebra and floating-point plaintext linear algebra. The CKKS homomorphic encryption system is the most natural choice in this setting, as it natively handles real numbers and offers a large SIMD parallelism. We provide reductions for matrix-vector products, vector-vector products for moderate-sized to large matrices to their plaintext equivalents. Combined with BLAS, we demonstrate that the efficiency loss between CKKS-based encrypted square matrix multiplication and double-precision floating-point square matrix multiplication is a mere 4-12 factor, depending on the precise situation.

cs.CR↗

arXiv2024

Fast and Accurate Homomorphic Softmax Evaluation

Homomorphic encryption is one of the main solutions for building secure and privacy-preserving solutions for Machine Learning as a Service. This motivates the development of homomorphic algorithms for the main building blocks of AI, typically for the components of the various types of neural networks architectures. Among those components, we focus on the Softmax function, defined by $\mathrm{SM}(\mathbf{x}) = \left(\exp(x_i) / \sum_{j=1}^n \exp(x_j) \right)_{1\le i\le n}$. This function is deemed to be one of the most difficult to evaluate homomorphically, because of its multivariate nature and of the very large range of values for $\exp(x_i)$. The available homomorphic algorithms remain restricted, especially in large dimensions, while important applications such as Large Language Models (LLM) require computing Softmax over large dimensional vectors. In terms of multiplicative depth of the computation (a suitable measure of cost for homomorphic algorithms), our algorithm achieves $O(\log n)$ complexity for a fixed range of inputs, where $n$ is the Softmax dimension. Our algorithm is especially adapted to the situation where we must compute many Softmax at the same time, for instance, in the LLM situation. In that case, assuming that all Softmax calls are packed into $m$ ciphtertexts, the asymptotic amortized multiplicative depth cost per ciphertext is, again over a fixed range, $O(1 + m/N)$ for $N$ the homomorphic ring degree. The main ingredient of our algorithms is a normalize-and-square strategy, which interlaces the exponential computation over a large range and normalization, decomposing both in stabler and cheaper smaller steps. Comparing ourselves to the state of the art, our experiments show, in practice, a good accuracy and a gain of a factor 2.5 to 8 compared to state of the art solutions.

cs.CR↗

arXiv2014

Markov Chain Monte Carlo Algorithms for Lattice Gaussian Sampling

Sampling from a lattice Gaussian distribution is emerging as an important problem in various areas such as coding and cryptography. The default sampling algorithm --- Klein's algorithm yields a distribution close to the lattice Gaussian only if the standard deviation is sufficiently large. In this paper, we propose the Markov chain Monte Carlo (MCMC) method for lattice Gaussian sampling when this condition is not satisfied. In particular, we present a sampling algorithm based on Gibbs sampling, which converges to the target lattice Gaussian distribution for any value of the standard deviation. To improve the convergence rate, a more efficient algorithm referred to as Gibbs-Klein sampling is proposed, which samples block by block using Klein's algorithm. We show that Gibbs-Klein sampling yields a distribution close to the target lattice Gaussian, under a less stringent condition than that of the original Klein algorithm.

cs.IT↗

arXiv2008

Worst-Case Hermite-Korkine-Zolotarev Reduced Lattice Bases

The Hermite-Korkine-Zolotarev reduction plays a central role in strong lattice reduction algorithms. By building upon a technique introduced by Ajtai, we show the existence of Hermite-Korkine-Zolotarev reduced bases that are arguably least reduced. We prove that for such bases, Kannan's algorithm solving the shortest lattice vector problem requires $d^{\frac{d}{2\e}(1+o(1))}$ bit operations in dimension $d$. This matches the best complexity upper bound known for this algorithm. These bases also provide lower bounds on Schnorr's constants $α_d$ and $β_d$ that are essentially equal to the best upper bounds. Finally, we also show the existence of particularly bad bases for Schnorr's hierarchy of reductions.

math.NT↗

arXiv2007

Improved Analysis of Kannan's Shortest Lattice Vector Algorithm

The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high dimensions. The best algorithms for these tasks are due to Kannan, and, though remarkably simple, their complexity estimates have not been improved since more than twenty years. Kannan's algorithm for solving the shortest vector problem is in particular crucial in Schnorr's celebrated block reduction algorithm, on which are based the best known attacks against the lattice-based encryption schemes mentioned above. Understanding precisely Kannan's algorithm is of prime importance for providing meaningful key-sizes. In this paper we improve the complexity analyses of Kannan's algorithms and discuss the possibility of improving the underlying enumeration strategy.

cs.CR↗

arXiv2007

Time- and Space-Efficient Evaluation of Some Hypergeometric Constants

The currently best known algorithms for the numerical evaluation of hypergeometric constants such as $ζ(3)$ to $d$ decimal digits have time complexity $O(M(d) \log^2 d)$ and space complexity of $O(d \log d)$ or $O(d)$. Following work from Cheng, Gergel, Kim and Zima, we present a new algorithm with the same asymptotic complexity, but more efficient in practice. Our implementation of this algorithm improves slightly over existing programs for the computation of $π$, and we announce a new record of 2 billion digits for $ζ(3)$.

cs.SC↗