Computing Fibonacci Numbers Fast using the Chinese Remainder Theorem

نویسنده

  • Adam Murakami
چکیده

The purpose of this paper is to investigate the calculation of Fibonacci numbers using the Chinese Remainder Theorem (CRT). This paper begins by laying down some general conclusions that can be made about the Fibonacci sequence. It will then go into specific cases of the CRT and how to calculate Fibonacci numbers with reduced forms of the CRT equations. For each of the cases, algorithms and analysis will be presented to try and give some perspective of the outcomes.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Information technology Image encryption algorithm based on chaotic mapping and Chinese remainder theorem

When the image data are regularly changed, existing image encryption algorithm is easy to be decrypted. In order to improve the security of encryption algorithm, this paper proposes an image encryption algorithm based on chaotic mapping and Chinese remainder theorem. The encryption algorithm is divided into pixel scrambling and image diffusion. Firstly, the Chebyshev mapping is used to generate...

متن کامل

To Design and Implement Novel Method of Encryption using Modified RSA and Chinese Remainder Theorem

Security can only be as strong as the weakest link. In this world of cryptography, it is now well established, that the weakest link lies in the implementation of cryptographic algorithms. This paper deals with RSA algorithm with and without Chinese Remainder Theorem. In practice, RSA public exponents are chosen to be small which makes encryption and signature verification reasonably fast. Priv...

متن کامل

Fast Parallel Garner Algorithm for Chinese Remainder Theorem

This paper presents a fast parallel garner algorithm for Chinese remainder theorem. The variables in garner algorithm are divided into public parameters that are constants for fixed module and private parameters that represent random input integers. We design the parallel garner algorithm by analyzing the data dependencies of these arithmetic operations for computing public variables and privat...

متن کامل

A fast algorithm for computing large Fibonacci numbers

We present a fast algorithm for computing large Fibonacci numbers. It is known that the product of Lucas numbers algorithm uses the fewest bit operations to compute the Fibonacci number Fn. We show that the number of bit operations in the conventional product of Lucas numbers algorithm can be reduced by replacing multiplication with the square operation.  2000 Elsevier Science B.V. All rights ...

متن کامل

The Matrices of Fibonacci Numbers

In a recent paper, Kalman [3] derives many interesting properties of generalized Fibonacci numbers. In this paper, we take a different approach and derive some other interesting properties of matrices of generalized Fibonacci numbers. As an application of such properties, we construct an efficient algorithm for computing matrices of generalized Fibonacci numbers. The topic of generalized Fibona...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003