# Reversible Karatsuba's Algorithm

@article{Kowada2006ReversibleKA, title={Reversible Karatsuba's Algorithm}, author={Luis Antonio Brasil Kowada and Renato Portugal and Celina M. H. de Figueiredo}, journal={J. Univers. Comput. Sci.}, year={2006}, volume={12}, pages={499-511} }

Karatsuba discovered the first algorithm that accomplishes multiprecision integer multiplication with complexity below that of the grade-school method. [...] Key Method These circuits can be used in reversible com- puters which have the advantage of being very efficient in terms of energy consumption. The algorithm can also be used in quantum computers and is an improvement of pre- vious circuits for the same purpose described in the literature. Expand

#### 22 Citations

Improved reversible and quantum circuits for Karatsuba-based integer multiplication

- Mathematics, Computer Science
- TQC
- 2017

A reversible circuit for integer multiplication that is inspired by Karatsuba's recursive method is presented, with the main improvement over circuits that have been previously reported in the literature is an asymptotic reduction of the amount of space required. Expand

Efficient hardware architecture of recursive Karatsuba-Ofman multiplier

- Computer Science
- 2008 3rd International Conference on Design and Technology of Integrated Systems in Nanoscale Era
- 2008

Two Sequential/Parallel architectures of Recursive Karatsuba-Ofman multiplier are presented, developed and implemented on the Spartan 3 FPGA platform and Mathematical Performances models for large number (n) are elaborated for the proposed architectures. Expand

Garbage-Free Reversible Integer Multiplication with Constants of the Form 2 k ±2 l ±1

- Mathematics, Computer Science
- RC
- 2012

Multiplication of integers is non-injective and, thus, requires garbage lines for any reversible logic implementation. However, multiplying with a fixed constant is injective, and should therefore be… Expand

The Compilation of Reversible Circuits and a New Optimization Game

- Computer Science
- 2016

The usefulness of the pebble games for circuit analysis is demonstrated by finding a new space bound for the Karatsuba algorithm and more generally for any similar algorithm based on recurrence relations. Expand

Self-Inverse Functions and Palindromic Circuits

- Physics, Computer Science
- ArXiv
- 2015

We investigate the subclass of reversible functions that are self-inverse and relate them to reversible circuits that are equal to their reverse circuit, which are called palindromic circuits. We… Expand

Quantum Circuit Design of Toom 3-Way Multiplication

- Computer Science
- 2021

In classical computation, Toom–Cook is one of the multiplication methods for large numbers which offers faster execution time compared to other algorithms such as schoolbook and Karatsuba… Expand

High Performance Quantum Modular Multipliers

- Physics, Computer Science
- ArXiv
- 2018

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,… Expand

Efficient Large Numbers Karatsuba-Ofman Multiplier Designs for Embedded Systems

- Computer Science
- 2009

A mixture of sequential and combinational system design techniques involving pipelining is applied to the proposed designs of implementing Karatsuba-Ofman multiplier and these designs are compared to other existing techniques. Expand

Synthesizing multiplier in reversible logic

- Computer Science
- 13th IEEE Symposium on Design and Diagnostics of Electronic Circuits and Systems
- 2010

Three methods are presented that address the drawbacks of previous approaches to synthesis of multiplier circuits in reversible logic, including the large number of circuit lines in the resulting realizations as well as the poor scalability. Expand

A reversible circuit synthesis algorithm with progressive increase of controls in generalized Toffoli gates

- 2021

We present a new algorithm for synthesis of reversible circuits for arbitrary n-bit bijective functions. This algorithm uses generalized Toffoli gates, which include positive and negative controls.… Expand

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