Related papers: An Efficient Elliptic Curve Cryptography Arithmeti…
This paper presents a new probabilistic approach to embedding message text on an elliptic curve, by using the concept of the RSA Algorithm and its security, and such approach allows us discovering the message from the point, only according…
Code-based cryptography is one of the main propositions for the post-quantum cryptographic context, and several protocols of this kind have been submitted on the NIST platform. Among them, BIKE and HQC are part of the five alternate…
High-performance techniques to simulate quantum programs on classical hardware rely on exponentially large vectors to represent quantum states. When simulating quantum algorithms, the quantum states that occur are often sparse due to…
Elliptic partial differential equations must be solved numerically for many problems in numerical relativity, such as initial data for every simulation of merging black holes and neutron stars. Existing elliptic solvers can take multiple…
Decimal multiplication is the task of multiplying two numbers in base $10^N.$ Specifically, we focus on the number-theoretic transform (NTT) family of algorithms. Using only portable techniques, we achieve a 3x-5x speedup over the mpdecimal…
When building a cylindrical algebraic decomposition (CAD) savings can be made in the presence of an equational constraint (EC): an equation logically implied by a formula. The present paper is concerned with how to use multiple ECs,…
The modular inverse is an essential piece of computation required for elliptic curve operations used for digital signatures in Bitcoin and other applications. A novel approach to the extended Euclidean algorithm has been developed by…
We provide a framework for using elliptic curves with complex multiplication to determine the primality or compositeness of integers that lie in special sequences, in deterministic quasi-quadratic time. We use this to find large primes,…
Securing communication channels is especially needed in wireless environments. But applying cipher mechanisms in software is limited by the calculation and energy resources of the mobile devices. If hardware is applied to realize…
Historically, Elliptic Curve Cryptography (ECC) is an active field of applied cryptography where recent focus is on high speed, constant time, and formally verified implementations. While there are a handful of outliers where all these…
Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of…
This whitepaper seeks to elucidate implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and mitigation strategies. First, we provide new resource estimates for breaking the 256-bit…
Matrix multiplication is integral to various scientific and engineering disciplines, including machine learning, image processing, and gaming. With the increasing data volumes in areas like machine learning, the demand for efficient…
The rapid development of computer technology will be the whole world as a whole, the widespread application of instant messaging technology to bring great convenience to people's lives, while privacy protection has become a more significant…
In this study, we propose a two-party computation protocol for approximate matrix multiplication of fixed-point numbers. The proposed protocol is provably secure under standard lattice-based cryptographic assumptions and enables matrix…
The interpolation step in the Guruswami-Sudan algorithm is a bivariate interpolation problem with multiplicities commonly solved in the literature using either structured linear algebra or basis reduction of polynomial lattices. This…
We look for elliptic curves featuring rational points whose coordinates form two arithmetic progressions, one for each coordinate. A constructive method for creating such curves is shown, for lengths up to 5.
The widespread use of wireless sensor networks (WSNs) that are consisted of resource-constrained sensor nodes in communication with gateways in open-space environments and industries has highlighted the need for a secure yet fast…
Matrix multiplication is fundamental in the backpropagation algorithm used to train deep neural network models. Libraries like Intel's MKL or NVIDIA's cuBLAS implemented new and optimized matrix multiplication techniques that increase…
Let {\alpha} be the maximal value such that the product of an n x n^{\alpha} matrix by an n^{\alpha} x n matrix can be computed with n^{2+o(1)} arithmetic operations. In this paper we show that \alpha>0.30298, which improves the previous…