Related papers: PaReNTT: Low-Latency Parallel Residue Number Syste…

As a fundamental theorem in number theory, the Chinese Reminder Theorem (CRT) is widely used to construct cryptographic primitives. This paper investigates the security of a class of image encryption schemes based on CRT, referred to as…

To address the privacy protection problem in cloud computing, privacy enhancement techniques such as the Paillier additive homomorphism algorithm are receiving widespread attention. Paillier algorithm allows addition and scalar…

Fast time-domain algorithms have been developed in signal processing applications to reduce the multiplication complexity. For example, fast convolution structures using Cook-Toom and Winograd algorithms are well understood. Short length…

Homomorphic encryption (HE) draws huge attention as it provides a way of privacy-preserving computations on encrypted messages. Number Theoretic Transform (NTT), a specialized form of Discrete Fourier Transform (DFT) in the finite field of…

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…

Large Language Models (LLMs) are powerful but often too slow and costly for real-world use during inference. Looped transformers save on parameters by reusing the same weights for multiple computational steps, or "loops." However, this…

Based on unique decoding of the polynomial residue code with non-pairwise coprime moduli, a polynomial with degree less than that of the least common multiple (lcm) of all the moduli can be accurately reconstructed when the number of…

The Number Theoretic Transform (NTT) is a critical computational bottleneck in many lattice-based postquantum cryptographic (PQC) algorithms. By leveraging the Fast Fourier Transform (FFT) algorithm, the NTT of a polynomial of degree N - 1…

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…

Efficient large-scale inference of transformer-based large language models (LLMs) remains a fundamental systems challenge, frequently requiring multi-GPU parallelism to meet stringent latency and throughput targets. Conventional tensor…

Residue Number System (RNS), which originates from the Chinese Remainder Theorem, offers a promising future in VLSI because of its carry-free operations in addition, subtraction and multiplication. This property of RNS is very helpful to…

Privacy-preserving neural network (NN) inference can be achieved by utilizing homomorphic encryption (HE), which allows computations to be directly carried out over ciphertexts. Popular HE schemes are built over large polynomial rings. To…

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…

The problem of robustly reconstructing a large number from its erroneous remainders with respect to several moduli, namely the robust remaindering problem, may occur in many applications including phase unwrapping, frequency detection from…

Modern implementations of homomorphic encryption (HE) rely heavily on polynomial arithmetic over a finite field. This is particularly true of the CKKS, BFV, and BGV HE schemes. Two of the biggest performance bottlenecks in HE primitives and…

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…

This research explores the use of superconductor electronics (SCE) for accelerating fully homomorphic encryption (FHE), focusing on the Number-Theoretic Transform (NTT), a key computational bottleneck in FHE schemes. We present SCE-NTT, a…

Ternary quantization has emerged as a powerful technique for reducing both computational and memory footprint of large language models (LLM), enabling efficient real-time inference deployment without significantly compromising model…

A numerical irreducible decomposition for a polynomial system provides representations for the irreducible factors of all positive dimensional solution sets of the system, separated from its isolated solutions. Homotopy continuation methods…

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…