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This PDF contains :

Abstract,

Keywords,

1. Introduction,

2. Vedic Mathematics Sutra,

2.1 Nikhilam navata charanam Dashatah,

2.2 Urdhva-tiryakbyham,

3. Uses of Vedic Sutras,

3.1 VLSI Implementation of RSA encryption,

3.2 Multiplier and square architecture,

3.3 Discrete Fourier Transform,

3.4 Digital Signal Processing,

3.5 Block Convolution,

3.6 ALU Design,

3.7 Elliptic Curve Encryption,

4. Performance Analyses of Vedic Algorithms,

Conclusion

Abstract,

Keywords,

1. Introduction,

2. Vedic Mathematics Sutra,

2.1 Nikhilam navata charanam Dashatah,

2.2 Urdhva-tiryakbyham,

3. Uses of Vedic Sutras,

3.1 VLSI Implementation of RSA encryption,

3.2 Multiplier and square architecture,

3.3 Discrete Fourier Transform,

3.4 Digital Signal Processing,

3.5 Block Convolution,

3.6 ALU Design,

3.7 Elliptic Curve Encryption,

4. Performance Analyses of Vedic Algorithms,

Conclusion

1.
“VEDIC MATHEMATICS-THE COSMIC SOFTWARE FOR IMPLEMENTATION OF FAST

ALGORITHMS”

Dr.S.M.Khairnar Ms. Sheetal Kapade Mr.Naresh Ghorpade

Professor and Head Assistant Professor Assistant Professor

Maharashtra Academy of Sinhgad Academy of Engineering, Sinhgad College of Science,Pune

Engineerimg,Alandi,Pune Pune [email protected]

[email protected] [email protected]

Abstract principles. These principles are general in nature

Veda, by definition, is ‘store house of and can be applied in many ways. In practice

knowledge’. Hence Vedic Mathematics has a many applications of the sutras may be learned

much ancient origin though attributed to the and combined to solve actual problems. The

techniques rediscovered between 1911, 1918. beauty of Vedic mathematics lies in the fact that

Mathematicians from across the spectrum from it reduces otherwise cumbersome looking

Hindu, Buddha and Jaina subcultures have calculations in conventional mathematics to a

contributed immensely to this body of very simple ones [2]. This is so because the

knowledge. Now a day’s interest in Vedic Vedic formulae are claimed to be based on the

Mathematics is growing in the field of computer natural principles on which the human mind

science where researchers are looking for a new works. This is a very interesting field and

and better approach to the subject. Even foreign presents some effective algorithms which can be

researchers are said to be using this ancient applied to various branches of engineering such

technique for implementation of fast algorithms. as computing , VLSI implementation and

In this survey paper, we will provide the readers digital signal processing.

an overview of the Vedic mathematics, as well as This paper is organized as follow: Section 2

several extended work in the area. In addition, provides overview of the vedic sutras like

we also review several state-of-art applications “Nikhilam navata charanam Dashatah”,

that take full advantage of such simple ancient “Urdhva-tiryakbyham”, Uses of these sutras are

Vedic Mathematical technique. elaborated in section 3, performance of Vedic

algorithms analyzed in section 4, and last section

Key words: Vedic mathematics, Nikhilam sutra, concludes the paper.

Urdhva-tiryakbyham, RSA algorithm 2. Vedic Mathematics Sutra

1. Introduction Vedic Mathematics essentially rests on the 16

The ancient system of Vedic Mathematics was Sutras or mathematical formulas as referred to in

rediscovered from the Indian Sanskrit texts the Vedas. Sri Sathya Sai Veda Pratishtan has

known as the Vedas, between 1911 and 1918 by compiled these 16 Sutras and 13 sub-Sutras [1].

Sri Bharati Krishna Tirthaji (1884-1960) [1]. The In the field of engineering most of the researcher

word ‘Vedic’ is derived from the word ‘Veda’ are using following sutras

which means the store-house of all knowledge. i) Nikhilam navata charanam Dashatah,

Vedic Mathematics is based on sixteen sutras or ii) Urdhva-tiryakbyham

ALGORITHMS”

Dr.S.M.Khairnar Ms. Sheetal Kapade Mr.Naresh Ghorpade

Professor and Head Assistant Professor Assistant Professor

Maharashtra Academy of Sinhgad Academy of Engineering, Sinhgad College of Science,Pune

Engineerimg,Alandi,Pune Pune [email protected]

[email protected] [email protected]

Abstract principles. These principles are general in nature

Veda, by definition, is ‘store house of and can be applied in many ways. In practice

knowledge’. Hence Vedic Mathematics has a many applications of the sutras may be learned

much ancient origin though attributed to the and combined to solve actual problems. The

techniques rediscovered between 1911, 1918. beauty of Vedic mathematics lies in the fact that

Mathematicians from across the spectrum from it reduces otherwise cumbersome looking

Hindu, Buddha and Jaina subcultures have calculations in conventional mathematics to a

contributed immensely to this body of very simple ones [2]. This is so because the

knowledge. Now a day’s interest in Vedic Vedic formulae are claimed to be based on the

Mathematics is growing in the field of computer natural principles on which the human mind

science where researchers are looking for a new works. This is a very interesting field and

and better approach to the subject. Even foreign presents some effective algorithms which can be

researchers are said to be using this ancient applied to various branches of engineering such

technique for implementation of fast algorithms. as computing , VLSI implementation and

In this survey paper, we will provide the readers digital signal processing.

an overview of the Vedic mathematics, as well as This paper is organized as follow: Section 2

several extended work in the area. In addition, provides overview of the vedic sutras like

we also review several state-of-art applications “Nikhilam navata charanam Dashatah”,

that take full advantage of such simple ancient “Urdhva-tiryakbyham”, Uses of these sutras are

Vedic Mathematical technique. elaborated in section 3, performance of Vedic

algorithms analyzed in section 4, and last section

Key words: Vedic mathematics, Nikhilam sutra, concludes the paper.

Urdhva-tiryakbyham, RSA algorithm 2. Vedic Mathematics Sutra

1. Introduction Vedic Mathematics essentially rests on the 16

The ancient system of Vedic Mathematics was Sutras or mathematical formulas as referred to in

rediscovered from the Indian Sanskrit texts the Vedas. Sri Sathya Sai Veda Pratishtan has

known as the Vedas, between 1911 and 1918 by compiled these 16 Sutras and 13 sub-Sutras [1].

Sri Bharati Krishna Tirthaji (1884-1960) [1]. The In the field of engineering most of the researcher

word ‘Vedic’ is derived from the word ‘Veda’ are using following sutras

which means the store-house of all knowledge. i) Nikhilam navata charanam Dashatah,

Vedic Mathematics is based on sixteen sutras or ii) Urdhva-tiryakbyham

2.
2.1 Nikhilam navata charanam Dashatah From the above equation we can derive the left

The formula simply means: “all from 9 and the hand side of the product as {x – y1} or {y– x1}

last from 10”. The algorithm has its best case in and the right hand side as (x1.y1)

multiplication of numbers, which are nearer to The basic operations involved in the algorithm

bases of 10, 100, 1000 i.e. increased powers of for a given set of numbers are given below.

10. The procedure of multiplication using the Consider 98 x 97

Nikhilam involves minimum mental manual Here the Nearest Base = 100

calculations, which in turn will lead to reduced

number of steps in computation, reducing the

space, saving more time for computation. The

numbers taken can be either less or more than the

base considered. The mathematical derivation of

the algorithm is given below.

Consider two n-bit numbers x and y to be

multiplied. Then their complements can be

represented as x1 = 10n - x and y1 = 10n – y. The

product of the two numbers can be given as p =

(x, y). Now a factor 102n +10n (x + y) is added

and subtracted on the right hand side of the

Result = 98 x 97 = 9506

product equation, which is mathematically

The Nikhilam Sutra can also be modified for

expressed as shown below.

binary arithmetic.

p = xy + 102n +10n (x + y) - 102n - 10n ( x + y)

2.2 Urdhva-tiryakbyham

On simplifying we get,

This is the general formula which is applicable to

p = {10n (x + y) - 102n} + {102n -10n (x + y) + xy}

all cases of multiplication. Urdhva Triyagbhyam

= 10n {(x + y) - 10n} + {(10n – x) ( 10n – y)} =

means “Vertically and Crosswise”, which is the

10n {x – y1} + {x1 y1}

method of multiplication followed.

= 10n {y – x1} + {x1 y1}

Illustration: Consider the product (325 X 738)

The formula simply means: “all from 9 and the hand side of the product as {x – y1} or {y– x1}

last from 10”. The algorithm has its best case in and the right hand side as (x1.y1)

multiplication of numbers, which are nearer to The basic operations involved in the algorithm

bases of 10, 100, 1000 i.e. increased powers of for a given set of numbers are given below.

10. The procedure of multiplication using the Consider 98 x 97

Nikhilam involves minimum mental manual Here the Nearest Base = 100

calculations, which in turn will lead to reduced

number of steps in computation, reducing the

space, saving more time for computation. The

numbers taken can be either less or more than the

base considered. The mathematical derivation of

the algorithm is given below.

Consider two n-bit numbers x and y to be

multiplied. Then their complements can be

represented as x1 = 10n - x and y1 = 10n – y. The

product of the two numbers can be given as p =

(x, y). Now a factor 102n +10n (x + y) is added

and subtracted on the right hand side of the

Result = 98 x 97 = 9506

product equation, which is mathematically

The Nikhilam Sutra can also be modified for

expressed as shown below.

binary arithmetic.

p = xy + 102n +10n (x + y) - 102n - 10n ( x + y)

2.2 Urdhva-tiryakbyham

On simplifying we get,

This is the general formula which is applicable to

p = {10n (x + y) - 102n} + {102n -10n (x + y) + xy}

all cases of multiplication. Urdhva Triyagbhyam

= 10n {(x + y) - 10n} + {(10n – x) ( 10n – y)} =

means “Vertically and Crosswise”, which is the

10n {x – y1} + {x1 y1}

method of multiplication followed.

= 10n {y – x1} + {x1 y1}

Illustration: Consider the product (325 X 738)

3.
Figure 1: Steps for multiplication by Urdhva tiryakbhyam Sutra

has a small box common to a digit of the

Let us consider the multiplication of (5498 × multiplicand. These small boxes are partitioned

2314). The conventional method which is into two halves by the crosswise lines. Each digit

already known to us will require 16 of the multiplier is then independently multiplied

multiplications and 15 additions. with every digit of the multiplicand and the two

An alternative method of multiplication using digit product is written in the common box. All

Urdhva tiryakbhyam Sutra is shown in figure 2. the digits lying on a crosswise dotted line are

The numbers to be multiplied are written on two added to the previous carry. The least significant

consecutive sides of the square as shown in the digit of the obtained number acts as the result

figure 1. The square is divided into rows and digit and the rest as the carry for the next step.

columns where each row/column corresponds to Carry for the first step (i.e., the dotted line on the

one of the digit of either a multiplier or a extreme right side) is taken to be zero.

multiplicand. Thus, each digit of the multiplier

has a small box common to a digit of the

Let us consider the multiplication of (5498 × multiplicand. These small boxes are partitioned

2314). The conventional method which is into two halves by the crosswise lines. Each digit

already known to us will require 16 of the multiplier is then independently multiplied

multiplications and 15 additions. with every digit of the multiplicand and the two

An alternative method of multiplication using digit product is written in the common box. All

Urdhva tiryakbhyam Sutra is shown in figure 2. the digits lying on a crosswise dotted line are

The numbers to be multiplied are written on two added to the previous carry. The least significant

consecutive sides of the square as shown in the digit of the obtained number acts as the result

figure 1. The square is divided into rows and digit and the rest as the carry for the next step.

columns where each row/column corresponds to Carry for the first step (i.e., the dotted line on the

one of the digit of either a multiplier or a extreme right side) is taken to be zero.

multiplicand. Thus, each digit of the multiplier

4.
Figure 2: Alternative way of multiplication by Urdhva tiryakbhyam Sutra

• Algorithm for 3 by 3 multiplication

Step 1 Step 2 Step 3 Step 4 Step 5

• Algorithm for 4 by 4 multiplication

Step 1 Step 2 Step 3 Step 4

Step 5 Step 6 Step 7

3. Uses of Vedic Sutras designing, Discrete Fourier Transform , High

Vedic mathematics is used by several researchers speed low power VLSI arithmetic and algorithm,

in the field of Digital signal processing, Chip RSA encryption system . Most of the researchers

• Algorithm for 3 by 3 multiplication

Step 1 Step 2 Step 3 Step 4 Step 5

• Algorithm for 4 by 4 multiplication

Step 1 Step 2 Step 3 Step 4

Step 5 Step 6 Step 7

3. Uses of Vedic Sutras designing, Discrete Fourier Transform , High

Vedic mathematics is used by several researchers speed low power VLSI arithmetic and algorithm,

in the field of Digital signal processing, Chip RSA encryption system . Most of the researchers

5.
have used the vedic mathematics method such as There are many algorithms for finding DFT. But

multiplication, division, squares and cubes in now a day’s only VAN-NEUMAN architectural

above mention fields. implementation of classical method is found to

3.1 VLSI Implementation of RSA encryption be used in digital computers.

H. Thapliyal [3] implementated RSA encryption Mr.S.Kulkarni [5] analyzes and compares the

or decryption algorithm using the algorithm of implementation of Discrete Fourier Transform

ancient Indian vedic mathematics which is being algorithm by existing and by vedic mathematics

modified to improve the performance .The most techniques. It is suggested that architectural level

significant aspect is the development of divisor changes in the entire computation system to

architecture based on straight division algorithm accommodate the Vedic Mathematics method

of Vedic mathematics and embedding it in RSA increases the overall efficiency of DFT

encryption or decryption circuitry for improved procedure.

efficiency .They proved that RSA circuitry 3.4 Digital Signal Processing

implemented using vedic division and Digital Signal processing is a technology that is

multiplication is efficient in terms of area and present in almost every engineering discipline. It

speed compared to its implementation using is also the fastest growing technology of the

conventional multiplication and division century and hence it posses tremendous

architecture. challenges to the engineering community. Faster

3.2 Multiplier and square architecture addition and multiplication are of extreme

Time, area and power efficient multiplier and importance in DSP for Convolution, DFT and

square architecture based on ancient Indian vedic Digital filters .The core computing process is

mathematics is developed by H. Thapliyal [4]. always a multiplication routine and hence DSP

Developed algorithm was for low power and engineers are constantly looking for new

high speed applications. It is based on generating algorithms and hardware to implement them. The

partial product and their sums in one step. The methods in Vedic Mathematics are

design implemented is described at both gate and complementary directly and easy. Mr. Mangesh

high level using verilog Hardware Description Karad and Mr. Chidgupkar [6] highlight the use

Language. The design code is tested using of multiplication process based on vedic

“Veriwelsimulator. Their work relates to the algorithms and implemented on 8085 and 8086

field of mathematical coprocessor in computers microprocessors. Use of Vedic algorithms shows

and more specifically to improve speed and appreciable saving of processing time.

power over the conventional co-processor. 3.5 Block Convolution

The Vedic multiplier and square architecture In DSP applications convolution with very long

developed by them were faster than array sequence is often required. To compute

multiplier and booth multiplier in FPGA convolution of long sequence overlap add

implementation. method (OLA) and overlap solve method (OLS)

3.3 Discrete Fourier Transform can be considered which are well known

multiplication, division, squares and cubes in now a day’s only VAN-NEUMAN architectural

above mention fields. implementation of classical method is found to

3.1 VLSI Implementation of RSA encryption be used in digital computers.

H. Thapliyal [3] implementated RSA encryption Mr.S.Kulkarni [5] analyzes and compares the

or decryption algorithm using the algorithm of implementation of Discrete Fourier Transform

ancient Indian vedic mathematics which is being algorithm by existing and by vedic mathematics

modified to improve the performance .The most techniques. It is suggested that architectural level

significant aspect is the development of divisor changes in the entire computation system to

architecture based on straight division algorithm accommodate the Vedic Mathematics method

of Vedic mathematics and embedding it in RSA increases the overall efficiency of DFT

encryption or decryption circuitry for improved procedure.

efficiency .They proved that RSA circuitry 3.4 Digital Signal Processing

implemented using vedic division and Digital Signal processing is a technology that is

multiplication is efficient in terms of area and present in almost every engineering discipline. It

speed compared to its implementation using is also the fastest growing technology of the

conventional multiplication and division century and hence it posses tremendous

architecture. challenges to the engineering community. Faster

3.2 Multiplier and square architecture addition and multiplication are of extreme

Time, area and power efficient multiplier and importance in DSP for Convolution, DFT and

square architecture based on ancient Indian vedic Digital filters .The core computing process is

mathematics is developed by H. Thapliyal [4]. always a multiplication routine and hence DSP

Developed algorithm was for low power and engineers are constantly looking for new

high speed applications. It is based on generating algorithms and hardware to implement them. The

partial product and their sums in one step. The methods in Vedic Mathematics are

design implemented is described at both gate and complementary directly and easy. Mr. Mangesh

high level using verilog Hardware Description Karad and Mr. Chidgupkar [6] highlight the use

Language. The design code is tested using of multiplication process based on vedic

“Veriwelsimulator. Their work relates to the algorithms and implemented on 8085 and 8086

field of mathematical coprocessor in computers microprocessors. Use of Vedic algorithms shows

and more specifically to improve speed and appreciable saving of processing time.

power over the conventional co-processor. 3.5 Block Convolution

The Vedic multiplier and square architecture In DSP applications convolution with very long

developed by them were faster than array sequence is often required. To compute

multiplier and booth multiplier in FPGA convolution of long sequence overlap add

implementation. method (OLA) and overlap solve method (OLS)

3.3 Discrete Fourier Transform can be considered which are well known

6.
efficient schemes for high order filtering. a high speed power efficient multiplier in the co-

Hanumantharaju M. C., Jayalakshami H.[7] processor. Using Vedic techniques various

proposed a high performance and area efficient arithmetic modules can be designed and

architecture for FPGA implementation of block integrated into a Vedic ALU, which is

convolution. By using vertically and crosswise compatible for co-processor. The advantages of

structure of vedic mathematics new multiplier Vedic multipliers are increase in speed, decrease

architecture is developed and embedded it into in delay, decrease in power consumption and

OLA and OLS methods for improved efficiency. decrease in area occupancy. This Vedic co-

The result shows that the proposed vedic processor is more efficient than the conventional

multiplier architecture achieves a significant one.

improvement in performance over the traditional 3.7 Elliptic Curve Encryption

multiplier architectures. If the bits in the number H. Thapliyal and M.B. Srinivas [9] developed an

are continuously increased to N by N ( N is any algorithm for point doubling using square

number) bits then Vedic Mathematics algorithm of ancient Indian Vedic mathematics.

architecture shows greatest advantage as In order to calculate efficient hardware circuit,

compare to other architectures of the multipliers square of a number and duplex D property of

over gate delays and regularity of structure. binary numbers. Also the techniques for

3.6 ALU Design computation of fourth power of number are

The ever increasing demands in enhancing the proposed. A considerable input in the point

ability of processors to handle the complex and addition and doubling has been observed when

challenging processes has resulted in the implemented using proposed techniques for

integration of number of processor cores into one exponentiation.

chip still the load on processor is not less. This 4. Performance Analyses of Vedic Algorithms

load is reduced by supplementing the main co- Various parameters are recommended by

processor which is designed to work on specific researchers to evaluate the performance of Vedic

types of functions like numeric computations, Maths algorithm. Researchers suggested many

signal processing, graphics etc. The speed of parameters few of them are: Time, Delay, Power

ALU depends on the multipliers. In algorithm and Number of slices.

and structure levels, numerous multiplication The following table shows the comparison of

techniques have been developed to enhance the Delay (ns) factor for multiplication implemented

efficiency of multiplier which concentrates on in different algorithms between Conventional

reducing the partial product and their additions. and Vedic way.

But in this case principle behind the Conclusion

multiplication remains same. Use of Vedic Vedic mathematics can be used in

mathematics for multiplication strikes difference implementation of fast algorithms in various

in actual process. M. Ramalatha [8] used Urdhva fields of engineering. The performance analysis

tiryakbhyam Sutra of Vedic mathematics to build of Vedic algorithms is done on the basis of delay.

Hanumantharaju M. C., Jayalakshami H.[7] processor. Using Vedic techniques various

proposed a high performance and area efficient arithmetic modules can be designed and

architecture for FPGA implementation of block integrated into a Vedic ALU, which is

convolution. By using vertically and crosswise compatible for co-processor. The advantages of

structure of vedic mathematics new multiplier Vedic multipliers are increase in speed, decrease

architecture is developed and embedded it into in delay, decrease in power consumption and

OLA and OLS methods for improved efficiency. decrease in area occupancy. This Vedic co-

The result shows that the proposed vedic processor is more efficient than the conventional

multiplier architecture achieves a significant one.

improvement in performance over the traditional 3.7 Elliptic Curve Encryption

multiplier architectures. If the bits in the number H. Thapliyal and M.B. Srinivas [9] developed an

are continuously increased to N by N ( N is any algorithm for point doubling using square

number) bits then Vedic Mathematics algorithm of ancient Indian Vedic mathematics.

architecture shows greatest advantage as In order to calculate efficient hardware circuit,

compare to other architectures of the multipliers square of a number and duplex D property of

over gate delays and regularity of structure. binary numbers. Also the techniques for

3.6 ALU Design computation of fourth power of number are

The ever increasing demands in enhancing the proposed. A considerable input in the point

ability of processors to handle the complex and addition and doubling has been observed when

challenging processes has resulted in the implemented using proposed techniques for

integration of number of processor cores into one exponentiation.

chip still the load on processor is not less. This 4. Performance Analyses of Vedic Algorithms

load is reduced by supplementing the main co- Various parameters are recommended by

processor which is designed to work on specific researchers to evaluate the performance of Vedic

types of functions like numeric computations, Maths algorithm. Researchers suggested many

signal processing, graphics etc. The speed of parameters few of them are: Time, Delay, Power

ALU depends on the multipliers. In algorithm and Number of slices.

and structure levels, numerous multiplication The following table shows the comparison of

techniques have been developed to enhance the Delay (ns) factor for multiplication implemented

efficiency of multiplier which concentrates on in different algorithms between Conventional

reducing the partial product and their additions. and Vedic way.

But in this case principle behind the Conclusion

multiplication remains same. Use of Vedic Vedic mathematics can be used in

mathematics for multiplication strikes difference implementation of fast algorithms in various

in actual process. M. Ramalatha [8] used Urdhva fields of engineering. The performance analysis

tiryakbhyam Sutra of Vedic mathematics to build of Vedic algorithms is done on the basis of delay.

7.
This shows efficiency of Vedic multiplier in

terms of high speed and less complexity

Sr. No. Implemented in Conventional Vedic

8 bit 16 bit 8 bit 16 bit

01 VLSI Implementation of High 31.241 57.973 26.081 54.973

Performance RSA Algorithm

02 High Speed Energy Efficient 31.029 46.811 15.418 22.604

ALU Design

03 An Efficient Method of Elliptic 30.370 60.646 15.193 23.600

Curve Encryption ( for square)

04 An Efficient Method of Elliptic 604.861 1327.809 542.325 1207.677

Curve

Encryption ( for point

doubling)

Table No. 1

. References: Vedic Mathematics”, Proceedings of

[1] Swami Bharati Krishna Tirthaji , Vedic International Conference on Computational

Mathematics. Delhi: Motilal Banarsidass Intelligence and Multimedia Applications,

Publishers, 1965. 2007.

[2] Vedic Mathematics [Online]. Available: [8] M. Ramalatha, K. Deena Dayalan, P. Dharani,

http://www.hinduism.co.za/vedic.htm. “ High Speed Energy Efficient ALU Design

Accessed November 2010. using Vedic Multiplication Techniques”

[3] H. Thapliyal and M. B. Srinivas “VLSI ACTEA, IEEE pp 600-603

implementation of RSA Encryption system [9] H. Thapliyal and M. B. Srinivas, “An

using Vedic Mathematics”, Proceedings of Efficient Method of Elliptic Curve

International Conferenceon Security Encryption Using Ancient Indian Vedic

Management, 2005. Mathematics”, Proc. IEEE MIDWEST

[4] H. Thapliyal and M. B. Srinivas, “High symp.Circuits and systems, pp. 826{829,

Speed Efficient N by N Bit Parallel Cincinnati, Aug. 2005.

Hierarchical Overlay Multiplier Architecture

Based", pp. 225-228, Dec. 2004.

[5] Mr.Shripad Kulkarni “ Discrete Fourier

Transform by Vedic Mathematics”

[6] P. D. Chidgupkar and M. T. Karad, “The

Implementation of Vedic Algorithms in

Digital Signal Processing”, Global J. of

Engg. Edu., Vol.8, No. 2, pp. 153-158, 2004.

[7] Hanumantharaju M. C., Jayalakshami H.,

Renuka R, Ravishankar M., “High Speed

Block Convolution using Ancient Indian

terms of high speed and less complexity

Sr. No. Implemented in Conventional Vedic

8 bit 16 bit 8 bit 16 bit

01 VLSI Implementation of High 31.241 57.973 26.081 54.973

Performance RSA Algorithm

02 High Speed Energy Efficient 31.029 46.811 15.418 22.604

ALU Design

03 An Efficient Method of Elliptic 30.370 60.646 15.193 23.600

Curve Encryption ( for square)

04 An Efficient Method of Elliptic 604.861 1327.809 542.325 1207.677

Curve

Encryption ( for point

doubling)

Table No. 1

. References: Vedic Mathematics”, Proceedings of

[1] Swami Bharati Krishna Tirthaji , Vedic International Conference on Computational

Mathematics. Delhi: Motilal Banarsidass Intelligence and Multimedia Applications,

Publishers, 1965. 2007.

[2] Vedic Mathematics [Online]. Available: [8] M. Ramalatha, K. Deena Dayalan, P. Dharani,

http://www.hinduism.co.za/vedic.htm. “ High Speed Energy Efficient ALU Design

Accessed November 2010. using Vedic Multiplication Techniques”

[3] H. Thapliyal and M. B. Srinivas “VLSI ACTEA, IEEE pp 600-603

implementation of RSA Encryption system [9] H. Thapliyal and M. B. Srinivas, “An

using Vedic Mathematics”, Proceedings of Efficient Method of Elliptic Curve

International Conferenceon Security Encryption Using Ancient Indian Vedic

Management, 2005. Mathematics”, Proc. IEEE MIDWEST

[4] H. Thapliyal and M. B. Srinivas, “High symp.Circuits and systems, pp. 826{829,

Speed Efficient N by N Bit Parallel Cincinnati, Aug. 2005.

Hierarchical Overlay Multiplier Architecture

Based", pp. 225-228, Dec. 2004.

[5] Mr.Shripad Kulkarni “ Discrete Fourier

Transform by Vedic Mathematics”

[6] P. D. Chidgupkar and M. T. Karad, “The

Implementation of Vedic Algorithms in

Digital Signal Processing”, Global J. of

Engg. Edu., Vol.8, No. 2, pp. 153-158, 2004.

[7] Hanumantharaju M. C., Jayalakshami H.,

Renuka R, Ravishankar M., “High Speed

Block Convolution using Ancient Indian