Implementation of Karatsuba Algorithm Using Polynomial Multiplication

نویسندگان

  • SUDHANSHU MISHRA
  • MANORANJAN PRADHAN
چکیده

Abstract Efficiency in multiplication is very important in applications like signal processing, cryptosystems and coding theory. This paper presents the design of a fast multiplier using the Karatsuba algorithm to multiply two numbers using the technique of polynomial multiplication. The Karatsuba algorithm saves coefficient multiplications at the cost of extra additions as compared to the ordinary multiplication method. The Karatsuba algorithm is more efficient for multiplication of large numbers.

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

Alternative to the karatsuba algorithm for software implementations of GF(2n) multiplications

In [11], a new approach to subquadratic space complexity multiplication for extended finite fields has recently been proposed for hardware implementation. In this article, we develop the corresponding algorithm for software implementation. Compared to the Karatsuba algorithm, the proposed algorithm has a lower theoretical time complexity when the size of the input is greater than a fixed intege...

متن کامل

Scalable Systolic Multiplier over Binary Extension Fields Based on Two-Level Karatsuba Decomposition

Shifted polynomial basis (SPB) is a variation of polynomial basis representation. SPB has potential for efficient bit level and digi -level implementations of multiplication over binary extension fields with subquadratic space complexity. For efficient implementation of pairing computation with large finite fields, this paper presents a new SPB multiplication algorithm based on Karatsuba scheme...

متن کامل

Overlap-free Karatsuba-Ofman Polynomial Multiplication Algorithms for Hardware Implementations

We describe how a simple way to split input operands allows for fast VLSI implementations of subquadratic GF (2)[x] Karatsuba-Ofman multipliers. The theoretical XOR gate delay of the resulting multipliers is reduced significantly. For example, it is reduced by about 33% and 25% for n = 2 and n = 3 (t > 1), respectively. To the best of our knowledge, this parameter has never been improved since ...

متن کامل

ACTA UNIVERSITATIS APULENSIS Special Issue KARATSUBA AND TOOM-COOK METHODS FOR MULTIVARIATE POLYNOMIALS

Karatsuba and Toom-Cook are well-known methods used to efficiently multiply univariate polynomials and long integers. For multivariate polynomials, asymptotically good approaches like Kronecker’s trick combined with FFT become truly effective only when the degree is above some threshold. In this paper we analyze Karatsuba and some of Toom-Cook methods for multivariate polynomials, considering d...

متن کامل

Synthesis Comparison of Karatsuba Multiplierusing Polynomial Multiplication, Vedic Multiplier and Classical Multiplier

In this paper, the authors have compared the efficiency of the Karatsuba multiplier using polynomial multiplication with the multiplier implementing Vedic mathematics formulae (sutras), specifically the Nikhilam sutra. The multipliers have been implemented using Spartan 2 xc2s200 pq208 FPGA device having speed grade of -6. The proposed Karatsuba multiplier has been found to have better efficien...

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 2012