相关论文: Efficient Parallel Verification of Galois Field Mu…
We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
Programmable Logic Devices (PLDs) continue to grow in size and currently contain several millions of gates. At the same time, research effort is going into higher-level hardware synthesis methodologies for reconfigurable computing that can…
We present a matrix-free multigrid method for high-order discontinuous Galerkin (DG) finite element methods with GPU acceleration. A performance analysis is conducted, comparing various data and compute layouts. Smoother implementations are…
Computing discrete logarithms in finite fields is a main concern in cryptography. The best algorithms in large and medium characteristic fields (e.g., {GF}$(p^2)$, {GF}$(p^{12})$) are the Number Field Sieve and its variants (special,…
A method is presented for accelerating inference in transformer language models by exploiting the low effective rank of the token activation manifold at each layer. The method decomposes each activation vector into a subspace component and…
Resource-efficient and robust validation of systems designed to measure a multi-dimensional parameter space is an unsolved problem as it would require millions of test permutations for comprehensive validation coverage. In the paper, an…
Nonlinearities in the gravitational evolution, galaxy bias, and redshift-space distortion drive the observed galaxy density fields away from the initial near-Gaussian states. Exploiting such a non-Gaussian galaxy density field requires…
Cloud computing platforms have created the possibility for computationally limited users to delegate demanding tasks to strong but untrusted servers. Verifiable computing algorithms help build trust in such interactions by enabling the…
In this work faster unsigned multiplication has been achieved by using a combination of High Performance Multiplication [HPM] column reduction technique and implementing a N-bit multiplier using 4 N/2-bit multipliers (recursive…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
This paper presents pragmatic solutions for verifying complex mathematical algorithms implemented in hardware in an efficient and effective manner. Maximizing leverage of a known-answer-test strategy, based on predefined data scenarios…
A representation of finite fields that has proved useful when implementing finite field arithmetic in hardware is based on an isomorphism between subrings and fields. In this paper, we present an unified formulation for multiplication in…
Additive Fourier Transform is sdudied. A fast multiplication algorithm for polynomials over the binary field is given. The bit complexity of the algorithm is $O(n(log n)(\log\log n)^2)$.
We propose an effective parallel program debugging approach based on the timing annotation technique. With prevalent multi-core platforms, parallel programming is required to fully utilize the computing power. However, the non-determinism…
Various post-quantum cryptography algorithms have been recently proposed. Supersingluar isogeny Diffie-Hellman key exchange (SIKE) is one of the most promising candidates due to its small key size. However, the SIKE scheme requires numerous…
Finite field transforms are offered as a new tool of spreading sequence design. This approach exploits orthogonality properties of synchronous non-binary sequences defined over a complex finite field. It is promising for channels supporting…
For a graph $G$, let $\nu_s(G)$ be the induced matching number of $G$. We prove that $\nu_s(G) \geq \frac{n(G)}{(\lceil\frac{\Delta}{2}\rceil+1) (\lfloor\frac{\Delta}{2}\rfloor+1)}$ for every graph of sufficiently large maximum degree…
The Number Theoretic Transform (NTT) is an indispensable tool for computing efficient polynomial multiplications in post-quantum lattice-based cryptography. It has strong resemblance with the Fast Fourier Transform (FFT), which is the most…
Automatic software verification is a valuable means for software quality assurance. However, automatic verification and in particular software model checking can be time-consuming, which hinders their practical applicability e.g., the use…