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In this paper, the execution of Berlekamp-Massey algorithm to happen the additive complexness for any given sequences is introduced. A new two methods for assailing watercourse cypher are proposed. The first 1 is assailing with known uniting portion utilizing hypothesis trial to happen the information important degree compromising the appropriate one, while the 2nd method for assailing unknown uniting portion by happening the behaviour ( truth tabular array ) of the uniting portion through two algorithms. Once the truth tabular array of the uniting portion is found, the initial values of the registries can be found in the impulsive portion or pulling the uniting portion maps utilizing Carnough map or Mcloski algorithm for contrary technology and retrace the uniting portion.

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Keywords: LFSR, Cryptography, Stream Cipher, Cryptanalysis

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1. Introduction

Many modern communications and unafraid systems such as ( mobile phone, Bluetooth, SSL, Computer

web, etc. ) require high velocity algorithms to code binary coded plaintext messages which may be

several million spots long and show noteworthy construction. The most normally used cypher in this instance is a

watercourse cypher. A watercourse cypher denotes the procedure of encoding where binary plaintext is encrypted one spot

at a clip. The simplest and most frequently used watercourse cypher for coding binary plaintext is where the spot at a

clip interval T of a pseudo random sequence zt, is combined utilizing faculty two add-on with the plaintext spot

meitnerium, at clip interval T to bring forth the cypher text spot at clip interval T, denoted by Nutmeg State. The sequence zt is called

the cardinal watercourse for the watercourse. The encoding procedure can be expressed as:

Nutmeg State =mtaS•Z ( 1.1 )

Where aS• denotes module two add-ons ( xor ) . The decoding procedure can be expressed as:

meitnerium =ctaS•Zt ( 1.2 )

It should be noted, as indicated by equations ( 1 ) and ( 2 ) ; that both the encryptor and decryptor need to

able to bring forth the same cardinal watercourse sequence zt. The cardinal K for the cypher is the initial seed to get down the

generator. Both the encryptor and decryptor need to treat this key. A common method for organizing the key

watercourse ; zt is to use a nonlinear Boolean map degree Fahrenheit to the end product binary sequences formed by several additive

feedback displacement registries ( LFSR ‘s ) whose characteristic multinomials are crude.

In this paper, we study some techniques and attacks for watercourse cyphers analysis and their

demands. The proposed methods of onslaughts in this paper are provides three different stairss, they are:

aˆ? Determining the additive complexness of the cardinal watercourse sequences generated by the proposal key

generators in this paper.

aˆ? Determining the initial provinces of driving portion LFSRs or identify where the uniting portion is known utilizing

+ .E-mail reference: musbahaqel @ yahoo.com

++ E-mail reference: natalia_maw @ yahoo.com

+++ E-mail reference: doctor_ebrahim @ yahoo.com

Published by World Academic Press, World Academic Union

Journal of Information and Computing Science, 2 ( 2007 ) 1, pp 288-298 289

cypher text merely attack.

aˆ? Determining the initial provinces of driving portion LFSRs ( cardinal ) every bit good as to find the combine

map of the uniting portion utilizing cipher text merely attack.

2. Cryptanalysis

Cryptography ( or cryptanalysis ) is a subject of mathematics and computing machine scientific discipline concerned with

information security and related issues, peculiarly encoding and hallmark and such applications as

entree control. Cryptography, as an interdisciplinary topic, draws on several Fieldss. Prior to the early twentieth

century, cryptanalysis was chiefly concerned with lingual forms. Since so, the accent has shifted,

and cryptanalysis now makes extended usage of mathematics, including subjects from information theory,

computational complexness, statistics, combinatory, and particularly figure theory. Cryptography is besides a

subdivision of technology, but an unusual one as it deals with active, intelligent and malevolent resistance.

Cryptanalysis is the chief tool used in computing machine and web security for such things as entree control

and information confidentiality.

Cryptography finds many applications that touch mundane life: the security of ATM cards, computing machine

watchwords, and electronic commercialism all depend on cryptanalysis.

2.1. Stream Ciphers

In cryptanalysis, a watercourse cypher is a symmetric cypher in which the plaintext figures are encrypted one at

a clip, and in which the transmutation of consecutive figures varies during the encoding [ 1 ] . An alternate

name is a province cypher, as the encoding of each figure is dependent on the current province. In pattern, the figures

are typically individual spots or bytes.

Stream cyphers represent a different attack to symmetric encoding from block cyphers. Block cyphers

operate on big blocks of figures with a fixed, unvarying transmutation. This differentiation is non ever clearcut:

some manners of operation use a block cypher primitive in such a manner that it so acts efficaciously as a

watercourse cypher. Stream cyphers typically execute at a higher velocity than block cyphers and have lower

hardware complexness.

Systems where the alteration of province does non depend on the input ( plaintext ) to the system are called

synchronal ( in contrast to asynchronous systems ) . These systems have the belongings that every plaintext spot

is enciphered independently of the others and an mistake in one spot does non propagate to other parts of the

cypher text.

As described in [ 2 ] this has two drawbacks: First, it limits the possibility to observe mistakes when

decoding. Second, an aggressor can infix controlled alterations to parts of the cypher text and may accomplish a

wanted alteration of the plaintext.

Fig.1 An linear synchronal watercourse cypher

Therefore in the most synchronal watercourse cypher common signifier, binary figures are used ( spots ) , and the key

watercourse is combined with the plaintext utilizing the sole or operation ( XOR ) .This is termed a double star

linear watercourse cypher, but other maps can besides be used. Stream cyphers which use add-on as the

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290 M. J. Aqel, et Al: Analysis of Stream Cipher Security Algorithm

uniting map as shown in Fig. ( 1 ) . will be referred to as linear. The sequence produced by the

map applied to the internal province is called the key watercourse. Hereafter merely additive synchronal watercourse

cyphers will be discussed.

If we assume that an aggressor knows the combine map and is capable of deducing the cardinal watercourse,

the security of a watercourse cypher depends on whether or non the following character of the cardinal watercourse can be

predicted. There does non look to be any incorporate manner to find if a cardinal watercourse generator green goodss

sequences that are difficult to foretell. Alternatively there are legion trials defined [ 3 ] and if a sequence fails any of

these trials it is non suited for usage as a cardinal watercourse. However, a sequence that passes all these trials might yet

be vulnerable to some other onslaught. One of import belongings of a sequence is its period. If used as a key

watercourse it is of import that it does non reiterate itself during encoding of a plaintext. Thus the period must be

longer than the plaintext.

Another trial is to utilize Berlekamp-Massey ‘s algorithm [ 5 ] on the sequence to happen the shortest linear

feedback displacement registry ( LFSR ) that can bring forth the same sequence. The length of this shortest LFSR is

called the additive complexness of the sequence.

2.2. Cryptanalysis

Cryptanalysis ( from the Greek kryptos, “ hidden ” , and analyein, “ to loosen ” or “ to unbrace ” ) is the survey of

methods for obtaining the significance of encrypted information, without entree to the secret information which

is usually required to make so. Typically, this involves happening the secret key. In non-technical linguistic communication, this

is the pattern of codification breakage or checking the codification, although these phrases besides have a specialised proficient

significance. Cryptanalysis is besides used to mention to any effort to besiege the security of other types of

cryptanalytic algorithms and protocols in general, and non merely encoding. However, cryptanalytics normally

excludes onslaughts that do non chiefly aim failings in the existent cryptanalysis ; methods such as graft,

physical coercion, burglary, cardinal logging, and so away, although these latter types of onslaught are an of import

concern in computing machine security, and are progressively going more effectual than traditional cryptanalytics.

Even though the end has been the same, the methods and techniques of cryptanalytics have changed

drastically through the history of cryptanalysis, accommodating to increasing cryptanalytic complexness, runing

from the pen-and-paper methods of the yesteryear, through machines like Enigma in World War II, to the

computer-based strategies of the present.

The consequences of cryptanalytics have besides changed it is no longer possible to hold limitless success in codification

breakage, and there is a hierarchal categorization of what constitutes a rare practical onslaught. In the mid-1970s,

a new category of cryptanalysis was introduced: asymmetric cryptanalysis. Methods for interrupting these

cryptosystems are typically radically different from before, and normally affect work outing carefully-constructed

jobs in pure mathematics, the best-known being integer factorisation.

The basic construct of cryptanalytics were developed as a subdivision of applied mathematics, the cryptanalytics

uses the undermentioned tools [ 2 ] :

aˆ? Probability theory and statistics

aˆ? Linear algebra

aˆ? Abstract algebra ( group theory )

aˆ? Computer linguistic communications

aˆ? Complexity theory

One of the most of import cryptanalytics tools is a additive complexness of any given sequences, to

find the additive complexness the following subdivision discuss one of the greatest algorithm to cipher the linear

complexness.

2.2.1 The Berlekamp Massey Algorithm

The additive complexness of a binary sequence is the length of the shortest LFSR on which the sequence can

be generated. For a sequence to be suited for usage as an coding sequence in a watercourse cypher system it is

of import that it has a sufficiently big additive complexness. There are two signifiers of additive complexness ; planetary

additive complexness, which applies to infinite period binary sequence, and local additive complexness, which

applies to binary sequences of finite length.

See an n-bit sequence s0 s1 aˆ¦ sn-1.The local additive complexness LC ( n ) of s0 s1 aˆ¦ sn-1 can be

computed utilizing the undermentioned Berlekamp-Massey algorithm:

1. F ( x ) a†? 1 B ( x ) a†? 1 D a†? 1

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Journal of Information and Computing Science, 2 ( 2007 ) 1, pp 288-298 291

L a†? 0 ba†? 1 Na†? 0

2. If N=n, Stop.

Otherwise compute vitamin D = SN + I?a?’

a?’

Liter

I

one N I C S

1

1. If d=0, so D a†? D+1 and goto ( 6 )

2. if d a‰ 0 and 2L & gt ; N, so F ( x ) a†? F ( x ) -db-1xDB ( x )

Da†?D+1 and goto ( 6 )

3. if d a‰ 0 and 2La‰¤N, so

T ( x ) a†? F ( x ) { impermanent storage of F ( x ) }

F ( x ) a†?F ( x ) – db-1xDB ( x )

La†?N+1-L

B ( x ) a†?T ( x )

B a†? vitamin D

D a†? 1

4. N a†? N+1 and return to ( 2 )

Measure K requires O ( K ) operations. Hence the algorithm needs, operations to analyse a

sequence of complexness L.

( ) ( 2 )

0

O K O L

Liter

K

= I?=

3. Stream Ciphers Analysis

In this subdivision we introduce the execution of Berlekamp-Massey algorithm to happen the additive

complexness for any given sequences, in add-on to two new methods for assailing watercourse cypher the first is

assailing with known uniting portion utilizing hypothesis trial to happen the information important degree compromising

the appropriate one, the 2nd method for assailing unknown uniting portion by happening the behaviour ( truth

tabular array ) of the uniting portion through two algorithms. Once we find the truth tabular array of the uniting portion, we

can happen the initial values of the registries in the impulsive portion or pulling the uniting portion maps utilizing

Carnough map or Mcloski algorithm for contrary technology and retrace the uniting portion.

3.1. Cipher text merely onslaught for watercourse cypher utilizing Statistic Methods

This method assumes that the cypher text is afforded, so it is a cypher text merely attack. The cypher text is

converted into binary signifier. The Binary sequence of the cypher text is divided into N samples ( N & gt ; =2 ) each of

which consist of K ( K & gt ; =2 ) blocks, for each sample we compute one consecutive 0 ‘s preceded and followed by a

1 are called a 0-run of length i. i consecutive 1 ‘s preceded and followed by a 0 are called a 1-run of length I.

n0i = # 0-run of length I

n1i = # 1-run of length I

The expected chance of each tally:

It is non hard to do these distributions and look into the hypothesis.

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292 M. J. Aqel, et Al: Analysis of Stream Cipher Security Algorithm

For proving zero hypothesis H0 refering entropy of binary watercourse ( cipher text watercourse ) , it is non

sufficient to analyze distribution of spreads and blocks in one sample merely. It is utile to hold information

from batch of samples, and utilize them for doing determination. ( Sample consists of K blocks incorporating 2048 spots

each. It is recommended K a‰? 2. Recommended Numberss of samples is N a‰? 2.

System of proposed algorithm consists of the undermentioned stairss:

aˆ? In the created spot watercourse, distributions of frequences of blocks and spreads are determined.

aˆ? For given figure of the blocks and the spreads expected distribution of frequences of the blocks and

the spread is determined. Since I‡2 standards are applied, none of expected frequences should non be less

than 10. Because of that, grouping of expected and absolute frequences is performed. I‡2 distribution

with n grades of freedom is calculated from map [ 8 ] :

Where: ?“ is a gamma map which is extends the factorial to complex and non-integer Numberss ( it is

already defined on the naturals, and has simple poles at the negative whole number ) . Denoted as [ 7 ] :

When the statement omega is an whole number, the gamma map is merely the familiar factorial map, but offset

by one,

n! = I“ ( n + 1 )

The gamma map satisfies the return relation

I“ ( z + 1 ) = zI“ ( omega )

and consequence of ( equation * ) checked whether the chance of deliberate I‡2 is above the threshold of

significance I? . In the same manner both distributions ( blocks and spreads ) are evaluated.

Every I‡2 have I‡2 distribution means that if it is tested N samples, this random value should hold I‡2

distribution.

Fig.2 Divide watercourse cypher text into samples

Algorithm 1.

1. Low-level formatting

N=number of samples ; C=-1

M=50 ; O©=0.001 significance threshold for samples

­=0.00001 significance threshold for all informations

Pass0=0 ; pass1=0

2. Increment C by 1

3. Calculate 2

1

0 1

2

) ( I?=

+

=

m

I

I i i n Ns

R

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Journal of Information and Computing Science, 2 ( 2007 ) 1, pp 288-298 293

4. Calculate the vector I

Y I R

2

( ) =

5. Compute until za‰?10 I?=

=

1

( )

T m

omega Y T

6. d=t-1 ( Degree of Freedom )

7. Calculate the vector component Y ( T ) =z

8. Compute and I?

+ =

=

m

I vitamin D

I sn N

1

0 0 I?

+ =

=

m

I vitamin D

I sn N

1

1 1

9. Calculate the vector component 0 and vector S

( 1 )

0 S vitamin D = Sn +

0

( T ) = n0i, i=1, aˆ¦d

10. Calculate the vector component S1

( d+1 ) =sn1 and vector S1

( T ) =n1i, i=1. , aˆ¦d

11. Compute X2: I?+

=

a?’

=

1

1

( )

( ) ( ) 2

0

0

vitamin D ( )

I

T

T T

Y

Ten S Y and I?+

=

a?’

=

1

1

( )

( ) ( ) 2

1

1

vitamin D ( )

I

T

T T

Y

Ten S Y

12. utilizing equation ( * ) to calculate X0

-1 and X1

-1 utilizing X0 and X1 with vitamin D

13. D.O.F as input parametric quantities.

14. if X0

-1 & lt ; O© increment base on balls 0 by 1

if X1

-1 & lt ; O© increment pass1 by 1

15. Calculate the vector and the vector, j=1,2, aˆ¦m I?=

=

m

I

J

n J N

1

0

( )

0 I?=

=

m

I

J

n J N

1

1

( )

1

16. spells to step ( 2 ) .

17. Compute and I?=

=

m

I

in I

1

( )

0 0 I„ I?=

=

m

I

in I

1

( )

1 1 I„

18. Calculate 2

0 1

2

I„ I„

+

=

19. Calculate the vector I

I

2

( ) I»

I? = , i=1,2, aˆ¦ , m

20. Compute until I® a‰? 10 I?a?’

=

1

( )

degree Fahrenheits m

I· I? degree Fahrenheit

21. I¦ = degree Fahrenheit -1 ( D.O.F )

22. Calculate the vector component I? ( degree Fahrenheit ) =I·

23. Calculate the I? and

a?’I?+

=

m

I

Ns T

1

( )

0 0 I? I?

a?’I?+

=

m

I

Ns T

1

( )

1 1

I?

24. Calculate the vector component 0 and the vector

( 1 )

0 S = O I?+ ( )

0

( )

0

S T = O T

25. Calculate the vector component 1 and the vector

( 1 )

1 S = O I?+ ( )

1

( )

1

S T = O T

26. Compute I?+

I?

=

a?’

=

1

1

( )

( ) ( ) 2

0

0

2 ( )

:

I

I

S I i X Ten

I?

I?

and I?+

I?

=

a?’

=

1

1

( )

( ) ( ) 2

1

1

( )

I

I

S I i X

I?

I?

27. utilizing equation ( * ) to calculate X0

-1 and X1

-1 utilizing X0 and X1 with D.O.F= as I¦ input parametric quantities.

28. if initial generate the belongingss [ ( max-pass0 and max-pass1 ) and ( X0

-1 & lt ; ?­ ) or ( X1

-1 & lt ; ?­ ) ) ] so it is

the right initial and it is solution

29. Stop

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294 M. J. Aqel, et Al: Analysis of Stream Cipher Security Algorithm

As a instance survey for the execution of this method a Geffe system is used as a cardinal generator with

LFSR ‘s of length ( 17, 11, and 13 ) severally with tapping as shown in Fig.3.

Fig.3 Geffe Stream Cipher System

Table ( 1 ) shows the algorithm execution for each cypher text.

3.1.1 Attack construction

The onslaught construction flow chart is explained in Figure ( 4 ) . The construction can be explained by the

following stairss:

aˆ? Using beast force to happen the initial values of the first LFSR, each cardinal sequence generated from

distinguishable initial is assorted ( xor ) with ciplhertext sequences and the resulted sequence evaluate utilizing

algorithm ( 1 ) .

aˆ? Using beast force to happen the initial values of the first LFSR, each cardinal sequence generated from

distinguishable initial is assorted ( xor ) with cypher text sequences and the resulted sequence evaluate utilizing

algorithm ( 1 ) .

aˆ? Using beast force to happen the initial of the 2nd LFSR ( control ) , utilizing the initial values of the first

and 3rd LFSR from above to bring forth the alternate cardinal sequence the resulted cardinal sequence mixed

( xor ) with cypher text to calculate the 0 ‘s per centum of the resulted sequence, the right plaintext will

find the right initial.

As we can carry through the construction of the onslaught, the divide and conquer method with cypher text merely

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Journal of Information and Computing Science, 2 ( 2007 ) 1, pp 288-298 295

onslaught are used to cut down the complexness from hunt infinite ( 2^ ( 17+11+13 ) =2^41=219902325552 initial

system possible to less than or equal hunt infinite ( 2^17+2^11+2^13=141312 ) initial system possible.

Fig.4 Attack Structure

3.2. Attacking with unknown uniting maps

In this subdivision we use this ways stream cyphers for utilizing a proposed techniques. We exploit the

relative concretion to change over any combination of maps to truth table. Besides, we can change over any

truth tabular array to non-linear map by utilizing Carnough map or Mcloski algorithm [ 9 ] .

3.2.1 Proposed Algorithms for Attacking Stream Cipher

In this subdivision we produce a method for assailing watercourse cyphers algorithms with unknown uniting

portion. To execute this method we have to hold the undermentioned demands:

1. The driving portion of the watercourse cypher algorithm. For case, if we assume that we have an LFSRbased

watercourse cypher, so we have to unknown the figure, the length, and the tapping of the LFSR ‘s.

The uniting portion is assumed to be unknown.

2. A cypher text spots of length L. Determining the value of L depending on the figure of the end product spots

of the impulsive portion at each measure, such that:

L=P*2^n

where N is the figure of LFSR ‘s in the impulsive portion, and

3 a‰? P a‰¤ 5

For illustration, if we have 4 LFSR ‘s we need about ( 48-80 ) cypher text spots.

In this onslaught we use brute-force method to bring forth all possible end product of the driving portion as an illustration

to demo that we can use this onslaught on watercourse cypher, whatsoever is the type of the constituent of its drive

portion, besides to analyze all possible instances that pass the checking of the onslaught. In this research, we use an

LFSR-based watercourse cypher with three LFSR ‘s of length 5, 6, 7 with tapping explained in Fig.5.

This method of assailing is supposed to assail a cardinal generator with unknown uniting portion degree Fahrenheit, so we

can presume that the uniting portion degree Fahrenheit is a black box of unknown input and end product. For this ground we may

stand for the uniting portion as a tabular array of 2^n entries. Where N is the figure of the driving portion registries.

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296 M. J. Aqel, et Al: Analysis of Stream Cipher Security Algorithm

Each input may see as an reference for an empty entry, and the consequence of the onslaught is the values that will

make full the empty entries. This means that we have to build the truth tabular array of the uniting portion, in other

words, the onslaught will give the behaviour of the uniting portion. One can infer the construction of the

uniting portion by utilizing K-map or McLoski method.

Fig.5 Geffe Stream Cipher System

This method of assailing is supposed to assail a cardinal generator with unknown uniting portion degree Fahrenheit, so we

can presume that the uniting portion degree Fahrenheit is a black box of unknown input and end product. For this ground we may

stand for the uniting portion as a tabular array of 2^n entries. Where N is the figure of the driving portion registries.

Each input may see as an reference for an empty entry, and the consequence of the onslaught is the values that will

make full the empty entries. This means that we have to build the truth tabular array of the uniting portion, in other

words, the onslaught will give the behaviour of the uniting portion. One can infer the construction of the

uniting portion by utilizing K-map or McLoski method.

The onslaught method can be divided into two chief stairss, they are:

1. Determining the right initial province of the impulsive portion.

2. Constructing the truth tabular array of the uniting portion.

The first measure may be done by bring forthing all possible input and look intoing the end product. In our illustration we

are utilizing brute-force onslaught which produces all possible initial phases for the registries of the driving portion, we

make so to prove all possible generated provinces to measure the assailing method therefore we selected a comparatively

short registries but for long registries one can utilize random hunt or familial algorithm techniques.

Table ( 2 ) Algorithm execution parametric quantities

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Journal of Information and Computing Science, 2 ( 2007 ) 1, pp 288-298 297

Determining the right initial province can execute by calculating the frequences of nothing ‘s and one ‘s of

cypher text at certain stairss for each input, and calculating the highest frequence of the generated references.

The plaintext must hold the belongings that the frequence of nothing ‘s is greater than the frequence of one ‘s

this premise is derived from proving a big sum of different length plaintext tabular array ( 2 ) shows a consequence

sample of proving 10 sample with different length.

So if the frequences are equal or likely equal so the initial province of the impulsive portion is dropped. The

initial province will be right if there is a well difference between frequences. In this instance if the

frequence of nothing ‘s is greater than the frequence of one ‘s so the cardinal spot equal to zero otherwise it is equal

to one. This fact is derived from the fact that a indiscriminately selected sample will has the characteristic of the

population. The cardinal spot will be the value of the table entry at certain reference. This can be done utilizing the

following algorithm:

Algorithm ( 2 )

Count=0, find=false, m=p*2n

1. Generate an initial province for the LFSR ‘s

2. Determine the largest frequence reference ( FL ) and the figure of its stairss

3. For these stairss that mentioned in point 4, compute the frequence of nothing ‘s ( f0 ) and frequence of

one ‘s ( f1 ) of the cypher text spots.

4. if |f0-f1|/f1? 0.40 so find=true and travel 9

5. increment count by 1

6. if count a‰¤ m so travel to step2

7. halt

Measure 6 brand usage of the fact that the per centum of being the plaintext spot equal to zero Pr ( p=0 ) =0.60 for a

suited length of plaintext.

The procedure of bring forthing the initial province of the impulsive portion is really of import to measure the correct

plaintext. There are two types of beast force onslaught message exhaustion and cardinal exhaustion. In message

exhaustion we obtain the plaintext message which the chief mark of any onslaught while in cardinal exhaustion we

obtained the secret key which is efficient if the complete ciphering algorithm is known we might utilize the key

to obtain the plaintext message. In the above algorithm we use a cardinal exhaustion brute-force that produces the

initial key which is no sufficient because we do n’t cognize the uniting portion of the watercourse cypher algorithm,

so we need to build the uniting portion in order to measure the plaintext message ( the mark text ) .

Once we obtained the right initial values of the registries which construct the deducing portion Constructing the

truth tabular array of the uniting portion may be done by the undermentioned algorithm:

Algorithm ( 3 )

1. a dr=0

2. Calculate the frequence of adr among M stairss

3. For these stairss that mentioned in step2, compute f0 and f1

4. If f0 & gt ; f1 so table [ adr ] =0

5. If f1 & gt ; f0 so table [ adr ] =1

6. increment adr by 1

7. If adr & lt ; 2n goto 2

8. Stop

This algorithm did n’t vouch that the tabular array will be completed, but there will be an empty entries for

that instances where f0=f1 ( if exist ) , and this will be filled by decoding the cypher text and corrected the incorrect

plaintext spots.

4. Decisions

It could be concluded the undermentioned, as a consequence of using the methods discussed in this paper:

aˆ? Stream cypher is non recommended to be used for confidentiality because there are many onslaughts in

literatures besides the onslaughts discussed in this paper, which means that watercourse cypher is vulnerable.

aˆ? To avoid the proposed onslaughts we recommended that the figure of LFSR ‘s in the deriving portion must

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298 M. J. Aqel, et Al: Analysis of Stream Cipher Security Algorithm

transcend the ability to execute the algorithms, which means the figure of LFSR must be above 20

with nowadays computational capableness.

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