Non-traditional Calculations of Elementary Mathematical Operations: Part 1. Multiplication and Division

Different computational systems are a set of functional units and processors that can work together and exchange data with each other if required. In most cases, data transmission is organized in such a way that enables for the possibility of connecting each node of the system to the other node of the system. Thus, a computer system consists of components for performing arithmetic operations, and an integrated data communication system, which allows for information interaction between the nodes, and combines them into a single unit. When designing a given type of computer systems, problems might occur if:– computing nodes of the system cannot simultaneously start and finish data processing over a certain time interval;– procedures for processing data in the nodes of the system do not start and do not end at a certain time;– the number of computational nodes of the inputs and outputs of the system is different.This article proposes an unconventional approach to constructing a mathematical model of adaptive-quantum computation of arithmetic operations of multiplication and division using the principle of predetermined random self-organization proposed by Ashby in 1966, as well as the method of the dynamics of averages and of the adaptive system of integration of the system of logical-differential equations for the dynamics of number-average states of particles S1, S2 of sets. This would make it easier to solve some of the problems listed above

NON-TRADITIONAL CALCULATIONS OF ELEMENTARY MATHEMATICAL OPERATIONS: Part 1. MULTIPLICATION AND DIVISION

Different computational systems are a set of functional units and processors that can work together and exchange data with each other if required. In most cases, data transmission is organized in such a way that enables for the possibility of connecting each node of the system to the other node of the system. Thus, a computer system consists of components for performing arithmetic operations, and an integrated data communication system, which allows for information interaction between the nodes, and combines them into a single unit. When designing a given type of computer systems, problems might occur if: – computing nodes of the system cannot simultaneously start and finish data processing over a certain time interval; – procedures for processing data in the nodes of the system do not start and do not end at a certain time; – the number of computational nodes of the inputs and outputs of the system is different. This article proposes an unconventional approach to constructing a mathematical model of adaptive-quantum computation of arithmetic operations of multiplication and division using the principle of predetermined random self-organization proposed by Ashby in 1966, as well as the method of the dynamics of averages and of the adaptive system of integration of the system of logical-differential equations for the dynamics of number-average states of particles S1, S2 of sets. This would make it easier to solve some of the problems listed above

A 3D Parallel Algorithm for QR Decomposition

Interprocessor communication often dominates the runtime of large matrix computations. We present a parallel algorithm for computing QR decompositions whose bandwidth cost (communication volume) can be decreased at the cost of increasing its latency cost (number of messages). By varying a parameter to navigate the bandwidth/latency tradeoff, we can tune this algorithm for machines with different communication costs

An Implementation of Digital Signature and Key Agreement on IEEE802.15.4 WSN Embedded Device

A wireless sensor network (WSN) now becomes popular in context awareness development to distribute critical information and provide knowledge services to everyone at anytime and anywhere. However, the data transfer in a WSN potentially encounters many threats and attacks. Hence, particular security schemes are required to prevent them. A WSN usually uses low power, low performance, and limited resources devices. One of the most promising alternatives to public key cryptosystems is Elliptic Curve Cryptography (ECC), due to it pledges smaller keys size. This implies the low cost consumption to calculate arithmetic operations in cryptographic schemes and protocols. Therefore, ECC would be strongly required to be implemented in WSN embedded devices with limited resources (i.e., processor speed, memory, and storage). In this paper, we present an implementation of security system on IEEE802.15.4 WSN device with the employment of Elliptic Curve Digital Signature Algorithm (ECDSA) and Elliptic Curve Diffie-Hellman (ECDH) key exchange protocol. Our experimental results on Intel Mote2 showed that the total time for signature generation is 110 ms, signature verification is 134 ms, and ECDH shared key generation is 69 ms on the setting of 160-bit security level