Related papers: Efficient long division via Montgomery multiply
The factorization of a large digit integer in polynomial time is a challenging computational task to decipher. The exponential growth of computation can be alleviated if the factorization problem is changed to an optimization problem with…
This article is concerned with the efficient computation of modular matrix multiplication C=AB mod p, a key kernel in computer algebra. We focus on floating-point arithmetic, which allows for using efficient matrix multiplication libraries.…
We give an $O(N\cdot \log N\cdot 2^{O(\log^*N)})$ algorithm for multiplying two $N$-bit integers that improves the $O(N\cdot \log N\cdot \log\log N)$ algorithm by Sch\"{o}nhage-Strassen. Both these algorithms use modular arithmetic.…
In this work a rationalized algorithm for calculating the quotient of two complex numbers is presented which reduces the number of underlying real multiplications. The performing of a complex number division using the naive method takes 4…
This paper presents a new refutation procedure for multimodular systems of integer constraints that commonly arise when verifying cryptographic protocols. These systems, involving polynomial equalities and disequalities modulo different…
We study reinforcement learning in infinite-horizon average-reward settings with linear MDPs. Previous work addresses this problem by approximating the average-reward setting by discounted setting and employing a value iteration-based…
We present recent developments on the topic of the integrand reduction of scattering amplitudes. Integrand-level methods allow to express an amplitude as a linear combination of Master Integrals, by performing operations on the…
Compiling a given quantum algorithm into a target hardware architecture is a challenging optimization problem. The compiler must take into consideration the coupling graph of physical qubits and the gate operation dependencies. The existing…
This paper describes several new improvements of modular arithmetic and how to exploit them in order to gain more efficient implementations of commonly used algorithms, especially in cryptographic applications. We further present a new…
Multiplication is indispensable and is one of the core operations in many modern applications including signal processing and neural networks. Conventional right-to-left (RL) multiplier extensively contributes to the power consumption, area…
We consider the problem of mapping a logical quantum circuit onto a given hardware with limited two-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
This paper presents arithmetic operations like addition, subtraction and multiplications in Modulo-4 arithmetic, and also addition, multiplication in Galois field, using multi-valued logic (MVL). Quaternary to binary and binary to…
CPUs and operating systems are moving from 32 to 64 bits, and hence it is important to have good pseudorandom number generators designed to fully exploit these word lengths. However, existing 64-bit very long period generators based on…
We consider the problem of computing the monic gcd of two polynomials over a number field L = Q(alpha_1,...,alpha_n). Langemyr and McCallum have already shown how Brown's modular GCD algorithm for polynomials over Q can be modified to work…
We introduce a framework for quasi-Newton forward--backward splitting algorithms (proximal quasi-Newton methods) with a metric induced by diagonal $\pm$ rank-$r$ symmetric positive definite matrices. This special type of metric allows for a…
Recent innovations in generative large language models (LLMs) have made their applications and use-cases ubiquitous. This has led to large-scale deployments of these models, using complex, expensive, and power-hungry AI accelerators, most…
Granlund and Montgomery proposed an optimization method for unsigned integer division by constants [3]. Their method (called the GM method in this paper) was further improved in part by works such as [1] and [7], and is now adopted by major…
In previous research, quantum resources were concretely estimated for solving Elliptic Curve Discrete Logarithm Problem(ECDLP). In [1], the quantum algorithm was optimized for the binary elliptic curves and the main optimization target was…
This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…