相关论文: Long Polynomial Modular Multiplication using Low-C…

The Number Theoretic Transform (NTT) can be regarded as a variant of the Discrete Fourier Transform. NTT has been quite a powerful mathematical tool in developing Post-Quantum Cryptography and Homomorphic Encryption. The Fourier Transform…

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…

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…

Polynomial multiplication is one of the fundamental operations in many applications, such as fully homomorphic encryption (FHE). However, the computational inefficiency stemming from polynomials with many large-bit coefficients poses a…

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…

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…

Designing privacy-preserving deep learning models is a major challenge within the deep learning community. Homomorphic Encryption (HE) has emerged as one of the most promising approaches in this realm, enabling the decoupling of knowledge…

Number Theoretic Transform (NTT) is an essential mathematical tool for computing polynomial multiplication in promising lattice-based cryptography. However, costly division operations and complex data dependencies make efficient and…

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…

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…

In this paper, we propose a novel joint coding-modulation technique based on serial concatenation of orthogonal linear transform, such as discrete Fourier transform (DFT) or Walsh-Hadamard transform (WHT), with memoryless nonlinearity. We…

Homomorphic encryption (HE) allows computations to be directly carried out on ciphertexts and enables privacy-preserving cloud computing. The computations on the coefficients of the polynomials involved in HE are always followed by modular…

We explore a new form of DFT, which we call the Polynomial Transform. It functions over finite fields, and a size $n$ transform takes $O(n)$ operations. In the multitape Turing machine model, it allows us to multiply two $n$ bit numbers in…

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…

In the paper it is shown that there exist infinite classes of fast DFT algorithms having multiplicative complexity lower than O(NlogN), i.e. smaller than their arithmetical complexity. The derivation starts with nesting of Discrete Fourier…

In this paper, we propose an encrypted dynamic controller that executes an unlimited number of recursive homomorphic multiplications on a Ring Learning With Errors (Ring-LWE) based cryptosystem without bootstrapping. The proposed controller…

The Learning with Errors (LWE) problem is the fundamental backbone of modern lattice based cryptography, allowing one to establish cryptography on the hardness of well-studied computational problems. However, schemes based on LWE are often…

Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…

Training large-scale CNNs that during inference can be run under Homomorphic Encryption (HE) is challenging due to the need to use only polynomial operations. This limits HE-based solutions adoption. We address this challenge and pioneer in…

Discrete transforms such as the discrete Fourier transform (DFT) or the discrete Hartley transform (DHT) furnish an indispensable tool in signal processing. The successful application of transform techniques relies on the existence of the…