a biometric encryption system for the self-exclusion

8/4/2019 A Biometric Encryption System for the Self-Exclusion

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ABSTRACT

The processing speed of electronic digital computers is inherently

limited by the interconnection bottleneck. Even with the introduction of

parallel computer architectures, the processing speed is still restricted

by bus constraints and channel bandwidth. During the past two

decades, researchers in the optics community extensively studied

parallel digitalopticalcomputing systems to fully utilize the ultra-high

processing speed, massive parallelism and non-interfering

interconnection capability offered by optics. Opticalshadow-casting

(OSC) technique has shown excellent potential for opticallyimplementing two-operand parallel logic gates and array logic

operations. The 16 logic functions for two binary patterns (variables)

are optically realizable in parallel by properly configuring an array of

22 light emitting diodes. In this paper, we propose an enhanced OSC

technique for implementing four-operand parallel logic gates. The

proposed system is capable of performing 216

logic functions by simply

programming the switching mode of an array of 44 light emittingdiodes in the input plane. This leads to an efficient and compact

realization scheme when compared to the conventional two-operand

OSC system.

Keywords: Parallel optical computing; Shadow-casting; Four-operand;

Overlapping pattern


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INTRODUCTION

WHAT IS OPTICAL COMPUTING:

The procedure of calculating or determining something by

mathematical or logical methods is known as computing. In

other words the branch of engineering science that studies

(with the aid of computers) computable processes and

structures is called computing.

Optical computing refers to achieve the objective of

computing with the use of optical systems

WHY OPTICAL COMPUTING:

Due to the rapid progress towards an information-oriented

society in recent years, there are strong demands for massive

information processing in various fields, such as real-time

processing, image processing, database searching, and scientific

applications.

However, drastic improvement in the performance of

conventional electronic computing systems cannot be expected

owing to the problems caused by extreme integration, high wiring

density, signal delay, electromagnetic interference, and so on.

Optical technology is expected to provide significant advantages

in massive information processing. The effective use of lights

attractive physical properties, such as parallelism high speed, and

crosstalk-free interconnects, has the potential to solve the

problems currently experienced in massive data communication,

interconnects, and computing. For this reason, optical technology

is presently widely used in optical communication, and opticalinterconnects are actively being researched for future computer

systems.


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HOW TO IMPLEMENT:

Optical interconnects are fundamental building block of parallel

optical computers, and therefore, efficient optical interconnection

technologies must be developed before next-generation optical

computers can be realized.Several paradigms have been proposed for parallel digital optical

computing, such as Optical shadow casting

symbolic substitution

binary image algebra image logic algebra

optical array logic (OAL)

These paradigms are commonly based on discrete correlation

between a binary input image and a two-dimensional pattern

consisting of points.

Here only the optical shadow casting technique is discussed in

detail for implementing 2-operand and 4-operand parallel digital

optical computing. The OSC technique offers ultrafast parallel processing capability

with a simple lens less setup as well as programming capability via

the configuration of light sources.

In OSC system, by controlling the switching modes of the LEDs,

different logic operations of the input can be performed

simultaneously with a decoding mask.


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For each polygon in a scene, another polygon is created to

act as its shadow. The vertices of the shadow polygon will all

lie on the plane. The algorithm goes like this.

For each vertex:

Construct a vector from the light source to the vertex.

Lengthen that vector so that it touches the plane.

Add that vector to the position of the light source, and you

have the position for this vertex of the shadow polygon.

In the above picture, the polygon A,B,C is casting a shadow from

the light source L onto the plane to create polygon Sa,Sb,Sc. The

plane in this case is totally horizontal, i.e. parallel to the X and Z

axes. I'll start with vertex A and cast it's shadow Sa.

Construct a vector from the light source to the vertex.

V = A - L

Lengthen that vector so that it touches the plane.

V = V * ((y1+y2) / y1)

y1+y2 is the distance from the light source to the plane.

y2 is the distance from the point A to the plane.

Because this plane is horizontal, and passes through the origin,

the values ofy1 and y2 are easy to calculate.


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y2 is the Y coordinate of the vertex A, and (y1+y2) is the Y

coordinate of the point L.

Add that vector to the position of the light source, and you have

the position for this vertex of the shadow polygon.

Sa = L + V

The same procedure is applied for the other two vertices B and C to

create Sb and Sc. Then the polygon Sa, Sb, Sc can be drawn.

OPTICAL SHADOW CASTING FOR IMPLEMENTING 2-

OPERAND LOGIC SYSTEMS:

The principle of shadow casting technique for implementing two-operand optical parallel logic gates has been reported by Ichioka

and Tanida.

Fig. 1(a) shows the schematic diagram of an OSC system for

realizing two-operand logic gates. The two binary variables are

spatially encoded into two types of coded binary objects as shown

in Fig 1(b).

Fig 1. Lens less shadow-casting system for implementing parallel optical

logic gates(a) schematic diagram (b) coding for the binary variables.

This system is capable of performing the 16 logic Functions

associated with two binary variables as shown in Table 1.


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The two binary variables are spatially encoded into two types of

coded binary objects as shown in Fig 1(b). The spatially coded

input patterns are introduced input plane via spatial light

modulators (SLMs) or via transparencies and are intimately placed

with each other to generate a superimposed or overlapped

pattern.

The overlapped pattern in the input plane is illuminated by four

light-emitting diodes (LEDs), which are arranged in the form of a

square array in the source plane, to yield multiple shadow grams

of the coded input variables onto the output plane.

A decoding mask (DM) is then applied to the output detector

screen to yield the result for two-operand arithmetic and logical

operations. The 16 switching modes generated by the

combinations of the four LEDs are used to generate the 16 logic

Functions associated with twobinary variables as shown in table 1

Table 1. Two-operand conventional logical functions

The close relationship between the operation of an OSC system

used for implementing optical parallel logic operations and that of


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array logic used in digital computers has potential application in

parallel optical digital processing.

Arithmetic operations optical multiprocessor and all-optical

versions of parallel array logic systems have been implemented

using the OSC technique.

In the proposed OSC techniques, we only need to consider the

state of the central subcell i.e., whether it is opaque (false) or

transparent (true).To compensate for this limitation, in this paper,

the concept of OSC is used to implement parallel multi-operand

logic gates.

By increasing the size of the LED array from 22 to 44, the

number of realizable logic functions can be increased from 16 (24)

in two-operand functions to 65 536 (216

) four-operand functions.

Thus, employing a 44 LED array provides more flexibility for

realizing a wide range of arithmetic and logic functions compared

to that obtained from conventional OSC system incorporating 22

LED array.

4 OPERAND OSC SYSTEM:

Fig. 2 shows a schematic diagram of the proposed OSC systemcapable of performing four-operand parallel optical logic

functions. In Fig. 2, the source plane contains an array of 44LEDs

(or other inexpensive light source) arranged in the form of a

square array.

The four input binary variables A, B, C and D are spatially encoded

by using an orthogonal dual-rail encoding scheme. Each of the

spatially encoded input variables is then introduced into

corresponding SLMs in the input plane.

The four SLMs are set in parallel, physically close to one another,

in the input plane to form the superimposed overlapped input as

shown in Fig. 2. The light beam emanating from the LEDs


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illuminates the superimposed inputs and projectsmultiple

shadowgrams onto a output detector screen.

The output is obtained by decoding the interlaced shadowgrams

by using a decoding mask with square window in the output

plane. The 216 switching modes associated with the LEDs generate

216

logic functions.

Fig. 2. Schematic diagram of an optical shadow-casting system for implementing four-

operand arithmetic and logical functions.

Fig3.Four

operandOSCsystem(a)source map and (b) coding format.


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Fig. 3(a) shows the source-map which illustrates the location of

each LED in the source plane along with the minterm projected on

the screen when the LED is ON. The map contains four rows and

four columns. The rows correspond to the minterms , , ,

andAB, respectively. The columns correspond to minterms having

, , , and CD, respectively.

The decimal numbers shown in the 44 source map ofFig. 3(a)

are obtained by converting the binary numbers representing the

minterms for each subcell of the source map, and are used to

label the LEDs. For example, the LED in position (1,3) i.e., LED

number 2 of the source plane, yields the minterm when it is

ON and therefore it is represented by LED2.

To encode the four binary input variablesA, B, C, and D, a quad

rail coding scheme involving four horizontal or vertical opaque

(logic 0) and transparent (logic 1) strips are used as shown inFig.

3(b). The coding format ofFig. 3(b) is deduced from the source

map ofFig. 3(a).

For example, if the input variableA under observation is logic 1

(transparent), the locations of the transparent or white strips in

the encoded pattern correspond to the locations of the LEDshavingA in their minterms. If the input variableA under

observation is logic 0 (opaque), the locations of the opaque or

black strips in the encoded pattern correspond to the locations of

the LEDs having in their minterms. Coding format for the

remaining three inputs, B, C, and D can be obtained in a similar

manner as depicted inFig. 3(b).

Using the coding format ofFig. 3(b), a typical cell of the

overlapped or superimposed pattern corresponding to the fourinput variables may be obtained as shown inFig. 4. Fig. 4shows

that the each overlap pattern corresponding to each minterm of

the source map ofFig. 3(a) consists of 44 subcells involving 16

unique patterns where 15 subcells are opaque and only 1 subcell

is transparent.
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The location of the transparent subcell corresponds to the

location of the LED whose minterm is identical to that obtained by

an AND operation for the four input variables. For example, if we

consider minterm (i.e.,A=0, B=1, C=1, and D=0), the

superimposed encoded cell will have a transparent subcell at

location (2,3) as shown inFig. 4. Fig. 4shows the superimposed

patterns corresponding to 16 combinations of the input variables

A, B, C, and D.

Fig 4. Superimposed or overlapped patterns corresponding to different

combinations of the input variablesA, B, C, and D.
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4H-4CHHR27-2&_user=9124175&_coverDate=04%2F30%2F2005&_alid=1420576439&_rdoc=2&_fmt=high&_orig=search&_cdi=5759&_sort=r&_docanchor=&view=c&_ct=49240&_acct=C000110338&_version=1&_urlVersion=0&_userid=9124175&md5=eeeb33dac148f4d68b07a892e7f5acda#fig4http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4H-4CHHR27-2&_user=9124175&_coverDate=04%2F30%2F2005&_alid=1420576439&_rdoc=2&_fmt=high&_orig=search&_cdi=5759&_sort=r&_docanchor=&view=c&_ct=49240&_acct=C000110338&_version=1&_urlVersion=0&_userid=9124175&md5=eeeb33dac148f4d68b07a892e7f5acda#fig4http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4H-4CHHR27-2&_user=9124175&_coverDate=04%2F30%2F2005&_alid=1420576439&_rdoc=2&_fmt=high&_orig=search&_cdi=5759&_sort=r&_docanchor=&view=c&_ct=49240&_acct=C000110338&_version=1&_urlVersion=0&_userid=9124175&md5=eeeb33dac148f4d68b07a892e7f5acda#fig4http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4H-4CHHR27-2&_user=9124175&_coverDate=04%2F30%2F2005&_alid=1420576439&_rdoc=2&_fmt=high&_orig=search&_cdi=5759&_sort=r&_docanchor=&view=c&_ct=49240&_acct=C000110338&_version=1&_urlVersion=0&_userid=9124175&md5=eeeb33dac148f4d68b07a892e7f5acda#fig4http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4H-4CHHR27-2&_user=9124175&_coverDate=04%2F30%2F2005&_alid=1420576439&_rdoc=2&_fmt=high&_orig=search&_cdi=5759&_sort=r&_docanchor=&view=c&_ct=49240&_acct=C000110338&_version=1&_urlVersion=0&_userid=9124175&md5=eeeb33dac148f4d68b07a892e7f5acda#fig4http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4H-4CHHR27-2&_user=9124175&_coverDate=04%2F30%2F2005&_alid=1420576439&_rdoc=2&_fmt=high&_orig=search&_cdi=5759&_sort=r&_docanchor=&view=c&_ct=49240&_acct=C000110338&_version=1&_urlVersion=0&_userid=9124175&md5=eeeb33dac148f4d68b07a892e7f5acda#fig4http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V4H-4CHHR27-2&_user=9124175&_coverDate=04%2F30%2F2005&_alid=1420576439&_rdoc=2&_fmt=high&_orig=search&_cdi=5759&_sort=r&_docanchor=&view=c&_ct=49240&_acct=C000110338&_version=1&_urlVersion=0&_userid=9124175&md5=eeeb33dac148f4d68b07a892e7f5acda#fig4


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Fig. 5. Four-operand OSC system, (a) geometrical configuration, (b) shadowgram corresponding

to input variablesA, B, C, and D projected on the output detector screen, and (c) decoding

mask.

Fig. 5(a) illustrates the geometric configuration of the proposed

four operand OSC system, while 5(b) depicts the process of

overlapping the shadowgrams and the formation of the output

pattern.Fig. 5(c) shows the decoding mask used for retrieving the

output. The system operates satisfactory when the following

conditions are satisfied:

(1a)

(1b)
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where 4b and 4dare dimensions of the square cells used for

encoding the input variables and the projected patterns.L1 represents the distance from the source plane to the input

plane.

L2 represents the distance from the input plane to the output

detector screen.

s represents the spacing between individual LEDs in vertical and

horizontal directions in the source plane.

Under these conditions, the shadowgram generated from a

typical input cell when one of the LEDs is in the ON state,

generates a square cell of dimension 4d4don the output plane.

The shadowgrams of the input cell generated by turning the 16LEDs ON overlap on the output detector screen, shifted from one

another by a distance dalong the vertical and horizontal

directions as shown inFig. 5(b).

The 16 shadowgrams cover an area of dimension 7d7don the

output plane with the center subcell, located at position (4,4)

yielding the desired logic function output. The central subcell

becomes bright (logic 1) or dark (logic 0) according to the

combinations of switching states of the 16 LEDs. When the LEDshave equal brightness, the light intensity (P) of the central subcell

can be expressed as

(2)

where Sican take a value of 1 or 0 depending on the state of the ith

LED, Mi is the ith minterm, and . and + represents the AND and OR

operations, respectively
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4. CONCLUSION AND DISCUSSION:

The OSC technique can be extended to implement parallel logic

functions involving more than four operands. This can be achieved by

increasing the number of LEDs on the source plane. By employing anLED array consisting ofN=2

melements, arranged in Nrrows and

Nc=N/Nrcolumns, 2N

logic functions involving m operands can be

implemented the following results can be obtained. The operation of

such a generalized system is described below.

Each input object cell is spatially into (NrNc) subcells. The encoded

cell has either Nrhorizontal strips or Nc vertical strips. Half of the strips

are dark (opaque) and the other half is bright (transparent). The N shadowgrams of the superimposed cell projected on the screen

will interlace and cover (2Nr1)(2Nc1) subcells. The central subcell

i.e., the (Nr,Nc) subcell of the projection pattern or output detector

screen generates the output of the desired logic function.

In this paper, an OSC based system for optically implementing four-operand logic functions was presented. With this technique, 2

16or

65 536 logic functions can be optically implemented compared to the

16 in the two-operand system. The paper provides the designer a

flexible and programmable tool for realizing four-operand logic

functions in a compact and efficient manner.


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