Basic logic gates and their operations in ternary quantum domain are involved in the synthesis of ternary quantum circuits. Only a few works define ternary algebra for ternary quantum logic realization. In this paper, a ternary logic function is expressed in terms of projection operations including a new one. A method to realize new multi-qutrit ternary gates in terms of generalized ternary gat...

In 1963, the Dutch mathemetician F.J.M. Barning described an infinite, planar, ternary tree whose nodes are just the set of Primitive Pythagorean triples. Seven years later, A. Hall independently discovered the same tree. Both used the method of uni-modular matrices to transform one triple to another. A number of rediscoveries have occurred more recently. The purpose of this article is to annou...

In this paper we propose an efficient and regular ternary algorithm for scalar multiplication on elliptic curves over finite fields of characteristic three. This method is based on full signed ternary expansion of a scalar to be multiplied. The cost per bit of this algorithm is lower than that of all previous ones.

We propose a pipelined parallel multiplier in phase-mode logic. The multiplier can be composed of combinations of gates which are the basic devices ofthe phasemode logic. Experimental operations of the ICF gate and the Adder cell for the multiplier are reported. The proposed multiplier has a Wallace-tree structure comprising trees of carry save adders for the addition of partial products. This ...

Multiplier is one of the major arithmetic operations carried out in DSP applications. This paper presents a modified Booth multiplier based on adiabatic logic. It is composed of Booth encoder, multiplier containing partial product generators and 1-bit (half and full) adders and final adder. Booth multiplication allows for smaller, faster multiplication circuits through encoding the signed numbe...

This study examines the multiplier effects of the grain subsidy program in China, which is a large food self-sufficiency project that is implemented as a cash transfer program. Income multiplier effects have not been examined in the evaluation of the grain subsidy program although increasing the income of farmers is the original goal of this project. A large number of household-level observatio...

In this paper we propose a modified probabilistic estimation bias (PEB) formula for fixed-width radix-4 Booth multiplier. The modified PEB formula estimates the same compensation value as the existing PEB formula without rounding operation. A bias circuit based on modified PEB formula generates one less carry-bit and involves less logic resources than the existing PEB circuit. The partial produ...

We investigate the key management problem for broadcasting applications. Previous work showed that batch rekeying can be more cost-effective than individual rekeying. Under the assumption that every user has probability p of being replaced by a new user during a batch rekeying period, we study the structure of the optimal key trees. Constant bounds on both the branching degree and the subtree s...

In this paper, we propose novel representation of binary trees, named the balanced ternary-tree representation. We examine flexible division of binary trees in which we can divide a tree at any node rather than just at the root, and introduce the ternary-tree representation for the flexible division. Due to the flexibility of division, for any binary tree, balanced or ill-balanced, there is alw...