相关论文: Gr\"obner Basis Cryptanalysis of Ciminion and Hydr…

High-speed long polynomial multiplication is important for applications in homomorphic encryption (HE) and lattice-based cryptosystems. This paper addresses low-latency hardware architectures for long polynomial modular multiplication using…

Homomorphic encryption (HE) is a promising technique used for privacy-preserving computation. Since HE schemes only support primitive polynomial operations, homomorphic evaluation of polynomial approximations for non-polynomial functions…

The security of multivariate cryptosystems and digital signature schemes relies on the hardness of solving a system of polynomial equations over a finite field. Polynomial system solving is also currently a bottleneck of index-calculus…

We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…

Wiener's attack is a well-known polynomial-time attack on a RSA cryptosystem with small secret decryption exponent d, which works if d<n^{0.25}, where n=pq is the modulus of the cryptosystem. Namely, in that case, d is the denominator of…

Dimer models (also known as brane tilings) are special bipartite graphs on a torus $\mathbb{T}^2$. They encode the structure of the 4d $\mathcal{N} = 1$ worldvolume theories of D3 branes probing toric affine Calabi-Yau singularities.…

We consider the problem of computing a grevlex Gr\"obner basis for the set $F_r(M)$ of minors of size $r$ of an $n\times n$ matrix $M$ of generic linear forms over a field of characteristic zero or large enough. Such sets are not regular…

We consider the problem of secure distributed matrix multiplication (SDMM), where a user has two matrices and wishes to compute their product with the help of $N$ honest but curious servers under the security constraint that any information…

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…

The world needs diverse and unbiased data to train deep learning models. Currently data comes from a variety of sources that are unmoderated to a large extent. The outcomes of training neural networks with unverified data yields biased…

Visual document understanding typically requires separate retrieval and generation models, doubling memory and system complexity. We present Hydra, a dual-head approach that provides both ColBERT-style late-interaction retrieval and…

The LPN (Learning Parity with Noise) problem has recently proved to be of great importance in cryptology. A special and very useful case is the RING-LPN problem, which typically provides improved efficiency in the constructed cryptographic…

Scaling up model depth and size is now a common approach to raise accuracy in many deep learning (DL) applications, as evidenced by the widespread success of multi-billion or even trillion parameter models in natural language processing…

We discuss the advantages and limitations of cyclotomic fields to have fast polynomial arithmetic within homomorphic encryption, and show how these limitations can be overcome by replacing cyclotomic fields by a family that we refer to as…

The recently proposed excitonic renormalization framework presents an alternative ansatz to elec- tronic structure theory of weakly interacting fragments. It makes use of absolutely localized orbitals and correlated states evaluated on…

Homomorphic encryption (HE) allows computations to be directly carried out on ciphertexts and is essential to privacy-preserving computing, such as neural network inference, medical diagnosis, and financial data analysis. Only addition and…

Contemporary models of high dimensional physical systems are constrained by the curse of dimensionality and a reliance on dense data. We introduce KHRONOS (Kernel Expansion Hierarchy for Reduced Order, Neural Optimized Surrogates), an AI…

In the numerical analysis of strongly correlated quantum lattice models one of the leading algorithms developed to balance the size of the effective Hilbert space and the accuracy of the simulation is the density matrix renormalization…

For associative algebras in many different categories, it is possible to develop the machinery of Gr\"obner bases. A Gr\"obner basis of defining relations for an algebra of such a category provides a "monomial replacement" of this algebra.…

Let R=F[D;sigma,delta] be the ring of Ore polynomials over a field (or skew field) F, where sigma is a automorphism of F and delta is a sigma-derivation. Given a an m by n matrix A over R, we show how to compute the Hermite form H of A and…