Related papers: PaReNTT: Low-Latency Parallel Residue Number Syste…
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…
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…
This tutorial aims to establish connections between polynomial modular multiplication over a ring to circular convolution and discrete Fourier transform (DFT). The main goal is to extend the well-known theory of DFT in signal processing…
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…
Lattice-based cryptography (LBC) exploiting Learning with Errors (LWE) problems is a promising candidate for post-quantum cryptography. Number theoretic transform (NTT) is the latency- and energy- dominant process in the computation of LWE…
BCH (Bose-Chaudhuri-Hocquenghen) error correcting codes ([1]-[2]) are now widely used in communication systems and digital technology. Direct LFSR(linear feedback shifted register)-based encoding of a long BCH code suffers from serial-in…
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…
The Number Theoretic Transform (NTT) is a fundamental operation in privacy-preserving technologies, particularly within fully homomorphic encryption (FHE). The efficiency of NTT computation directly impacts the overall performance of FHE,…
Fully Homomorphic Encryption (FHE) relies heavily on the Number Theoretic Transform (NTT), making NTT a major performance bottleneck due to its intensive polynomial computations. Hybrid Homomorphic Encryption (HHE), which integrates…
Chinese Remainder Theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to…
In this work, we propose an open-source, first-of-its-kind, arithmetic hardware library with a focus on accelerating the arithmetic operations involved in Ring Learning with Error (RLWE)-based somewhat homomorphic encryption (SHE). 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…
This paper investigates polynomial remainder codes with non-pairwise coprime moduli. We first consider a robust reconstruction problem for polynomials from erroneous residues when the degrees of all residue errors are assumed small, namely…
Recently Homomorphic Encryption (HE) is used to implement Privacy-Preserving Neural Networks (PPNNs) that perform inferences directly on encrypted data without decryption. Prior PPNNs adopt mobile network architectures such as SqueezeNet…
The Chinese remainder theorem (CRT) provides an efficient way to reconstruct an integer from its remainders modulo several integer moduli, and has been widely applied in signal processing and information theory. Its multidimensional…
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…
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…
Homomorphic encryption (HE) is a core building block in privacy-preserving machine learning (PPML), but HE is also widely known as its efficiency bottleneck. Therefore, many GPU-accelerated cryptographic schemes have been proposed to…
CRYSTAL-Kyber (Kyber) is one of the post-quantum cryptography (PQC) key-encapsulation mechanism (KEM) schemes selected during the standardization process. This paper addresses optimization for Kyber architecture with respect to latency and…