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We consider the problem of secure distributed matrix multiplication (SDMM). Coded computation has been shown to be an effective solution in distributed matrix multiplication, both providing privacy against workers and boosting the…
Many quantum computing platforms are based on a two-dimensional physical layout. Here we explore a concept called looped pipelines which permits one to obtain many of the advantages of a 3D lattice while operating a strictly 2D device. The…
Large-degree polynomial multiplication is an integral component of post-quantum secure lattice-based cryptographic algorithms like CRYSTALS-Kyber and Dilithium. The computational complexity of large-degree polynomial multiplication can be…
In this paper, we propose new classes of trapdoor functions to solve the closest vector problem in lattices. Specifically, we construct lattices based on properties of polynomials for which the closest vector problem is hard to solve unless…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
FALCON is a standardized quantum-resistant digital signature scheme that offers advantages over other schemes, but features more complex signature generation process. This paper presents Bi-Samplerz, a fully hardware-implemented,…
Since their introduction in 2004, Polynomial Modular Number Systems (PMNS) have become a very interesting tool for implementing cryptosystems relying on modular arithmetic in a secure and efficient way. However, while their implementation…
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…
In this thesis, a completely revisited data protection scheme based on selective encryption is presented. First, this new scheme is agnostic in term of data format, second it has a parallel architecture using GPGPU allowing performance to…
In this paper, we present an efficient algorithm to sample random sparse matrices to be used as check matrices for quantum Low-Density Parity-Check (LDPC) codes. To ease the treatment, we mainly describe our algorithm as a technique to…
Matrix computations are a fundamental building-block of edge computing systems, with a major recent uptick in demand due to their use in AI/ML training and inference procedures. Existing approaches for distributing matrix computations…
In this paper, we investigate the randomized algorithms for block matrix multiplication from random sampling perspective. Based on the A-optimal design criterion, the optimal sampling probabilities and sampling block sizes are obtained. To…
Interpolation is a fundamental technique in scientific computing and is at the heart of many scientific visualization techniques. There is usually a trade-off between the approximation capabilities of an interpolation scheme and its…
We propose a coding scheme that achieves the capacity of the compound MIMO channel with algebraic lattices. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned…
The number of Digital Signal Processor (DSP) resources available in Field Programmable Gate Arrays (FPGAs) is often quite limited. Therefore, full utilization of available DSP resources for the computationally intensive parts of an…
Recently, the construction of cryptographic schemes based on hard lattice problems has gained immense popularity. Apart from being quantum resistant, lattice-based cryptography allows a wide range of variations in the underlying hard…
A novel family of dynamical Monte Carlo algorithms for lattice polymers is proposed. Our central idea is to simulate an extended ensemble in which the self-avoiding condition is systematically weakened. The degree of the self-overlap is…
Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with…
Number theoretic transform (NTT) is the most efficient method for multiplying two polynomials of high degree with integer coefficients, due to its series of advantages in terms of algorithm and implementation, and is consequently…
Lattices are very important objects in the effort to construct cryptographic primitives that are secure against quantum attacks. A central problem in the study of lattices is that of finding the shortest non-zero vector in the lattice.…