Related papers: Modulo-$(2^{2n}+1)$ Arithmetic via Two Parallel n-…
-Residue Number System (RNS) is a valuable tool for fast and parallel arithmetic. It has a wide application in digital signal processing, fault tolerant systems, etc. In this work, we introduce the 3-moduli set {2^n, 2^{2n}-1, 2^{2n}+1} and…
Modulo-$(2^q + 2^{q-1} \pm 1)$ adders have recently been implemented using the regular parallel prefix (RPP) architecture, matching the speed of the widely used modulo-$(2^q \pm 1)$ RPP adders. Consequently, we introduce a new moduli set…
Quantum modular adders are one of the most fundamental yet versatile quantum computation operations. They help implement functions of higher complexity, such as subtraction and multiplication, which are used in applications such as quantum…
We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…
The moduli of the form 2n + 1 belong to a class of low-cost odd moduli, which have been frequently selected to form the basis of various residue number systems (RNS). The most efficient computations modulo (mod) 2n + 1 are performed using…
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…
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…
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…
Conventional analog-to-digital converters (ADCs) clip when signals exceed their input range. Modulo (unlimited) sampling overcomes this limitation by folding the signal before digitization, but existing recovery methods are either…
We study the fundamental problem of \emph{moduli selection} in the Robust Chinese Remainder Theorem (RCRT), where each residue may be perturbed by a bounded error. Consider $L$ moduli of the form $m_i = \Gamma_i m$ ($1 \le i \le L$), where…
A generalized Chinese remainder theorem (CRT) for multiple integers from residue sets has been studied recently, where the correspondence between the remainders and the integers in each residue set modulo several moduli is not known. A…
We study the problem of multiplying two bit matrices with entries either over the Boolean algebra $(0,1,\vee,\wedge)$ or over the binary field $(0,1,+,\cdot)$. We engineer high-performance open-source algorithm implementations for…
We present a method to increase the dynamical range of a Residue Number System (RNS) by adding virtual RNS layers on top of the original RNS, where the required modular arithmetic for a modulus on any non-bottom layer is implemented by…
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…
We show how one can use non-prime-power, composite moduli for computing representations of the product of two $n\times n$ matrices using only $n^{2+o(1)}$ multiplications.
Modulo sampling is a promising technology to preserve amplitude information that exceeds the observable range of analog-to-digital converters during the digitization of analog signals. Since conventional methods typically reconstruct the…
Electronic devices primarily aim to offer low power consumption, high speed, and a compact area. The performance of very large-scale integration (VLSI) devices is influenced by arithmetic operations, where multiplication is a crucial…
Residue number systems based on pairwise relatively prime moduli are a powerful tool for accelerating integer computations via the Chinese Remainder Theorem. We study a structured family of moduli of the form $2^n - 2^k + 1$, originally…
The root raised-cosine pulse commonly used in linear digital modulations yields exactly two intersymbol interference components from the preceding and the subsequent data symbols, provided that the roll-off factor is $100\%$ and the…
Multiplication of quantum states is a frequently used function or subroutine in quantum algorithms and applications, making quantum multipliers an essential component of quantum arithmetic. However, quantum multiplier circuits suffer from…