Related papers: An Open-source Library of Large Integer Polynomial…
With the surge of the powerful quantum computer, lattice-based cryptography proliferated the latest cryptography hardware implementation due to its resistance against quantum computers. Among the computational blocks of lattice-based…
Polynomial multiplication is a key algorithm underlying computer algebra systems (CAS) and its efficient implementation is crucial for the performance of CAS. In this paper we design and implement algorithms for polynomial multiplication…
This paper presents a low-latency hardware accelerator for modular polynomial multiplication for lattice-based post-quantum cryptography and homomorphic encryption applications. The proposed novel modular polynomial multiplier exploits the…
We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this…
This paper presents digital hardware for computing polynomial multiplication using Number Theoretic Transform (NTT), specifically designed for implementation on Field Programmable Gate Arrays (FPGAs). Multiplying two large polynomials…
We present a quantum algorithm for multiplying two $n$-bit integers with overall circuit depth and $T$-depth both bounded by $O(\log^{2} n)$, while using $O(n^{2})$ gates and ancillary qubits. Our construction generates partial products via…
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 era of diverse and heterogeneous computer architectures, the programmability issues, such as productivity and portable efficiency, are crucial to software development and algorithm design. One way to approach the problem is to step…
We present the design and implementation of PolyBlocks, a modular and reusable MLIR-based compiler infrastructure for AI programming frameworks and AI chips. PolyBlocks is based on pass pipelines that compose transformations on loop nests…
We consider a large-scale matrix multiplication problem where the computation is carried out using a distributed system with a master node and multiple worker nodes, where each worker can store parts of the input matrices. We propose a…
In cryptographic algorithms, the constants to be multiplied by a variable can be very large due to security requirements. Thus, the hardware complexity of such algorithms heavily depends on the design architecture handling large constants.…
Homomorphic encryption (HE) enables arithmetic operations to be performed directly on encrypted data. It is essential for privacy-preserving applications such as machine learning, medical diagnosis, and financial data analysis. In popular…
Fast combinational multipliers with large bit widths can occupy significant silicon area, which also drives up power consumption. Area can be reduced through resource sharing (i.e., folding) at the expense of lower throughput, which is…
Code-based cryptography is one of the main propositions for the post-quantum cryptographic context, and several protocols of this kind have been submitted on the NIST platform. Among them, BIKE and HQC are part of the five alternate…
In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…
Homomorphic Encryption (HE) enables users to securely outsource both the storage and computation of sensitive data to untrusted servers. Not only does HE offer an attractive solution for security in cloud systems, but lattice-based HE…
Existing GPU libraries often struggle to fully exploit the parallel resources and on-chip memory (SRAM) of GPUs when chaining multiple GPU functions as individual kernels. While Kernel Fusion (KF) techniques like Horizontal Fusion (HF) and…
One of the biggest concerns in IoT is privacy and security. Encryption and authentication need big power budgets, which battery-operated IoT end-nodes do not have. Hardware accelerators designed for specific cryptographic operations provide…
Cryptographic schemes like Fully Homomorphic Encryption (FHE) and Zero-Knowledge Proofs (ZKPs), while offering powerful privacy-preserving capabilities, are often hindered by their computational complexity. Polynomial multiplication, a core…
Elliptic curve cryptography (ECC) has emerged as the dominant public-key protocol, with NIST standardizing parameters for binary field GF(2^m) ECC systems. This work presents a hardware implementation of a Hybrid Multiplication technique…