Cryptic Mining: Apriori Analysis of Parameterized Automatic Variable Key based Symmetric Cryptosystem

International Journal of Computer Science and Information Security (IJCSIS), Vol. 14, No. 2, February 2016

 

Cryptic Mining: Apriori Analysis of Parameterized Automatic Variable Key based Symmetric Cryptosystem Shaligram Prajapat 1(corresponding author ) and Ramjeevan Singh Thakur2 1 Research Scholar, 2 Associate Professor Maulana Azad National Institute of Technology(MANIT) , Bhopal, INDIA Abstract- This paper presents enhanced model of security of symmetric key based cryptosystem[1]. The enhancement of model by variable keys and key exchange using parameters only approach is also presented. The issue of fixing up the minimum length of key for AVK is also a big challenge in AVK model. Selection of shorter key length leads to vulnerability/compromise of system, on the other side, larger then optimum key size would involve unnecessary overheads and wastage of resources[2]. Further, ensuring high protection against malicious attack, is achieved through IDS software tools, that attempts to detect and prevent the system from malicious network users. Apart from these tools, various network security applications using pattern mining to extract the threat from cipher log. Faster and more efficient pattern matching algorithm to overcome the performance issue is demonstrated in[3], parameterized model of automatic variable key. Presented parameters only exchanged instead of key, has been analyzed using association rule discovery from hacker’s perspective. This paper applies apriori method to investigate association rule among parameters used for generation of key and prediction of future key in the cryptosystem based on parameter only communication for AVK model[11]. In other words, the paper attempts to answer, How much the method is secure against association rule for future parameter prediction? Index term: AVK, Symmetric Key, cryptosystem, IDS, Parameterized model I.

INTRODUCTION

In recent era exchange of all the information including financial and e-commerce transaction takes place among parties or entities that might not known to each other but participates in communication. During this transmission of information public network is used hence ensuring the security of these information and confidentialities of involved parties is mandatory. The information stored in computers or during information, to avoid unauthorized access or damage of information technique known as Encryption and Decryption mechanism is used. Before transmission of information Encryption and after receiving of information Decryption process is used[1]. Securing information based on used key is classified into symmetric, asymmetric or hash. If both sender and receiver use the same key then it is symmetric cryptosystem. And if encryption and  

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decryption key are different then it is known as asymmetric cryptosystem. In any of the situation, the used key decides the level of security of cryptosystem. There are various alternatives to control the security of a cryptosystem like Hind the Encryption, Decryption algorithms. But by doing reverse engineering if the behavior of algorithm is known then whole cryptosystem will fame. Or by increasing the key size [6] (Increasing the key size will result in increase in key guess time or by increasing brute force attack time/trials that ultimately will increase the system security. But increasing the key size will increase the time in encryption or decryption process .By increasing computing resources or energy required to process will definitely be affected once the key length has been increased beyond a threshold[5]. Hacker or cryptanalyst may use parallel processing; multiword computing and advanced algorithms usage may lead to compromise the system security. Another alternative in this direction we fixed up the key with a specific length and try to vary it from session to session. This approach forms the basis of self variable key based AVK-Model, In this AVK model as we fixed up the length of key to a minimum threshold then the number of resources are freed. Up. Since the key varies from session to session so if hacker or cryptanalysis gains the access of key of a particular session even though it is invalid for next session. So the level of security of cryptosystem is enhanced. In AVK model. since the key changes from session to session, so the issue of new key exchange arises .To handle this issue we apply parameters AVK model that exchanges only parameters for key generation. Since on the public network only parameters are exchanged, so both sender and receiver will computer key at their own end and construct the key. The AVK approach with parameterized model is to be investigated from the perspective of hackers or cryptanalyst. The detailed analysis will decide the success of the AVK model of symmetric cryptosystem. This analysis is termed as Cryptic Mining[8,12]. Cryptic mining as a set of cryptic algorithm [2,3,4]that analyses the captured plaintext-cipher text, plaintext-key logs, parameters-key logs and captured cipher logs and provides useful knowledge, process and developing the knowledge based or AI based framework[8 ]. In future cryptic mining algorithm group will be useful for auditing and classification of cryptic algorithms. Theoretically cryptic algorithms provides random ciphers, but in practice it is not so, these algorithm uses pseudo random numbers that are generated by some computer or mathematical formula. So these ciphers have some sort of patterns, by extracting these patterns cryptic mining algorithms may find possible sequence or hints about key or association among key and plaintext or cipher. Depending upon the degree of patterns in the output the class of cryptic algorithms can be decided[2]. In this way, in future AVK algorithm may contribute in the extension of symmetric algorithm design. Certainly this provide strength to mechanism of maintenance and exchange of information. According to Moore’s law the power of personal computers has historically doubled approximately every 18 months what is the effect of this growth on key prediction and key computation? Obviously for high security, cryptography domain recommends that length of key must be kept sufficiently large to prevent form systematic attack the length of key is also increasing with passage of time. Moreover, cryptanalyst or hacker is well equipped with latest  

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techniques, devices and powerful algorithms to exploit threats or efficacy of key search attacks[ 5,8]. Therefore, estimates of the time required for successful key search attacks must be revised downward as the computing power and resources available to attacker’s increases. AVK approach of cryptography can be a better alternative in this direction. For immixing the threats of key leakage, instead of key exchanged some parameters can be exchanged that would be sufficient for construction of key for both Alice and Bob. As parameters only are exchanged so the security of the system would not be compromised. In the next sections, some related work has been presented for symmetric cryptosystem ,Then parameterized model of AVK process has been discussed. The success of this model has been investigated with association rule discovery of cryptic mining technique. This cryptanalysis perspective for extraction of key parameters using one of the popular techniques of cryptic mining as association rule discovery does auditing of cryptosystem. The same has been checked from WEKA tool.At the end other technique of crytic mining has been pointed out. II.

BACKGROUND

Encryption: Database of important and Sensitive information such as: Credit card information, passwords, financial data etc. are made difficult to understand by man in middle this essential process is used .It uses a secret key is used to transfer text; audio or video is converted in to non understandable form. Input file that is to be secured is popularly known as plain text. And transformed file that has been enciphered is known as cipher text or cryptogram. Decryption: The received encrypted file is transformed back to understandable form using key is known as decryption. Apart from privacy preservation domain [1], data mining techniques are being explored for applicability in cryptographic domain. In [2, 8, and 9] classification method of encrypted text is attempted, in [3] machine learning domain also has been related with data mining algorithm tasks. Various symmetric key cryptographic algorithms have been compared for different key length and available in literature. Data Mining Techniques [4, 5, 6, and 7] for cryptographic domain has been discussed and needs to be explored in greater depth further. Recently, in [11, 12, 13] AVK approach has been discussed with Fibonacci –Q matrix, sparse based schemes. In [14] automatic variable key under various approaches in cryptographic system has been analyzed. In this research community P. Chakrabarti has proposed approaches of key computation using parameters using fuzzy concepts [10]. This AVK approach can be further improved for enhancing security level. This can be achieved by parameter -only exchange of information. The scheme is reviewed from the perception of cryptanalyst for association rule inference. The subsequent sections 3, 4, 5 respectively presents the model with illustration of simply mean based method and later on it is analyzed in the light of association rule mining. III.

PARAMETER BASED COMMUNICATION SCHEME

 

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This section presents Scheme of Parameters exchange only for secure communication for automatic variable key. Consider sample algorithm-1 and 2, to demonstrate working of information exchange based on parameters only scheme in fig. - 1. Algorithm-1 parameters4Key-Alice (parameters x1, x2, …, xm,) { 1. 2. 3. 4.

Read parameters x1, x2, …, xm2; Compute the key for information exchange by: keyi =( x1* x2* …,* xm)1/2 ; Sense the information to exchange=Di ; If (mode==transmit) Generate Cipher text C i =Encrypt( Di, keyi); Transmit Ci;

5. else Receive Plain text P i = Decrypt( Di, keyi); Use P i ; } Algorithm-2 Parameters4Key-Bob (parameters x1, x2, …, xm) { 1. 2. 3. 4. 5.

Receive parameters x1, x2, …, xm; Compute the Arithmetic Mean A.M.= (x1+ x2+ …,+xm )/2; Compute the Harmonic Mean H.M.-2* x1* x2* …,* xm /( x1+ x2+ …,+xm ) Compute the Key i =(A.M*H.M)1/2 If (mode==transmit) { Generate Cipher text C i =Encrypt( Di, key i); Transmit Ci;}

6. else Receive Plain text P i = Decrypt ( Di, key i); Use P i ; } These algorithms have following advantages over traditional key exchange algorithm. (1)Without exchanging entire key Alice and Bob will securely communicate with each other. Without exchanging entire key Alice and Bob will securely communicate with each other. (2)In

 

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this model keys are computed using different functions, which also enhance level of security. At Node A: 1. Compute k1=A.M. of Parameters { p1,p2,....pk} 2. Compute k2= Harmonic Mean of Parameters { p1,p2,....pk} 3. Compute product p=1*pp2.......*.pk 4. Compute Key=sqrt(p) 5. Use key for sending and receiving information. And at node-B: 1. 2. 3.

Compute product of parameters = p i.e. { p1,p2,....pk} Compute Key=sqrt(p) where p={ p1,p2,....pk} Use key for sending and receiving information

Fig 1: Secure communication scheme using Parameter exchange IV.

ASSOCIATION RULES FOR PARAMETER EXCHANGE SCHEME

Conventionally association rule Key→ Parameter sets indicates that if Key (antecedent) appears then Parameter set (consequent) pi, pj,…,pk also tends (with highly probable) to appear, where X and Y may be single parameters or set of parameters (in which the same parameter does not appear in both sets) in other words X and Y would be found together frequently in the given training set and they does not show a causal relationship. Notations: The number of parameters in session table is n. Key of a particular session is constituted from parameter terms from key { pi, pj,…,pk } and it is denoted by f(pi, pj,…,pk )where pi, pj,…,pk are variables specific to a particular session. Further, assume that there are nsessions information is available (n=10, for session-parameter table). Each session of this table is  

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denoted by S={ Si, Sj,…,Sk }with a unique session-Id, specifying a set of parameter constituting the key (possibly a small subset).Each session key of m parameters be with key Ki={ pi, pj,…,pk }. Typically session key is varied due to differences in the number of parameters. The goal of cryptanalyst here is to find association relationships from a given large number of session keys, such that parameters that tend to occur together are identified. As Cryptanalyst has record of what each session key parameters used for generally session keys. In table 1.1 each row of the table gives the set of parameters that may be used in sessions.

Table 1: Session wise parameters of key Session No.

Key

Key Parameters

S1

SK1=f(p1, p2, p8)

p1, p2, p8

S2

SK2=f(p1, p2, p4)

p1, p2, p4

S3

SK3=f(p1, p5)

p1, p5

S4

SK4=f(p2,p3,p4,,p5)

p2,p3,p4,,p5

S5

SK5=f(p3,p6,p7,p8,p9)

p3,p6,p7,p8,p9

S6

SK6=f(p3,p4,p5,p7,p8,p9 p3,p4,p5,p7,p8,p9 )

S7

SK7=f(p1,p2)

p1,p2

S8

SK8=f(p1,p2,p3,p4)

p1,p2,p3,p4

S9

SK9=f(p1,p5)

p1, p5

S10

SK10=f(p1,p3,p4,p5,p6,p p1, p3, p4, p5, p6, p8, p9 8,p9)

Cryptanalyst would be interested to find which parameters set are used frequently in a session table. Say, p9, p6 are the two parameters that are used together frequently then the hacker may start predicting by having one parameter information, in the hope that the second parameter information can be found by obtained association rule. Given a large set of transactions, we seek a procedure to discover all association rules which has at least p% support with at least q% confidence such that all rules satisfying these constraints are found m efficient manner. Out of these rules we are also interested to find rules that are practical or actionable. V.

APRIORI APPROACH FOR PARAMETER PREDICTION

Consider a Transaction log with information about 25 session i.e. S={ S1, S2,…..S25}with  

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exchanging the key using parameters only method from parameter space of 16 possibilities i.e. P={p1,p2,…..,P16}.A key of a particular session will be random selection of some parameters from P and then applying secret algorithm to compute key of that particular session. In the automatic variable key environment, We assume that cryptanalyst or hacker somehow recorded traces of parameters used in few sessions say 25, without the information of function he may be interested to know the frequent parameters or guessing future parameters based on association rules , applied on these parameter to recomputed the future key session. Table 2.

Transaction log containing parameter traces S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25

p1, p2, p4, p6, p16 p1, p3, p4, p6 p4, p5, p7, p9,p10 p2, p4, p6, p3, p9 p2, p3, p5, p7, p9 p10, p15 p1, p2, p4, p6, p10 p8, p10, p15 p2, p3, p4, p5 ,p6 p2, p3, p5, p7, p9 p2, p4, p9 p2, p4, p6, p7, p9 p1, p2, p3 p3, p4, p5, p7, p9 p5, p6 p7 p7, p8, p9 p1, p2, p4 p6 p2, p3, p5, p7, p9 p4, p5, p7,p9 p10, p15, p16 p2, p3, p4, p6 p5, p7, p9, p10, p11 p11, p12, p13 p13, p14, p15

The frequency of each parameter in the session logs is given in following set , where set element={parameter, frequency of parameter} is listed below: {{p1 :4}, {p2:13}, {p3:10}, {p4:11}, {p5:9}, {p6:9}, {p7:10}, {p8:2}, {p9:11}, {p10:6}, {p11:2}, {p12:1}, {p13:2}, {p14:1},  

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{p15:4}, {p16:2} } Phase-1: Computation of frequent set .Assuming support of parameters (25% supports in 25 sessions) to occur in at least 7 sessions for computing first frequent parameter sets L1: Table 3. L1: First frequent parameter set Paramete P2 p3 p4 p5 p6 p7 p9 r Frequenc 13 10 1 9 9 10 11 y 1 Computation of C2: There are 21 candidates for, 2-parameter set of C2 {(p2, p3), (p2, p4), (p2, p5), (p2, p6), (p2, p7), (p2, p9),(p3, p4), (p3, p5), (p3, p6), (p3, p7), (p3, p9),(p4, p5), (p4, p6), (p4, p7), (p4, p9),(p5, p6), (p5, p7), (p5, p9),(p6, p7), (p6, p9),(p7, p9)} Table 4: C 2 parameter set (p2,p3)

Frequency 9

(p2,p4)

8

(p2,p5)

4

(p2,p6)

8

(p2,p7)

4

(p2,p9)

6

(p3,p4)

5

(p3,p5)

4

(p3,p6)

5

(p3,p7)

4

(p3,p9)

6

(p4,p5)

4

(p4,p6)

9

(p4,p7)

3

(p4,p9)

4

(p5,p6)

1

(p5,p7)

7

 

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(p5,p9)

7

(p6,p7)

1

(p6,p9)

2

(p6,p9)

9

Table 5. L2: The frequent 2-parameter set (p2,p3) 9 (p2,p4)

8

(p2,p6)

8

(p4,p6)

9

(p5,p7)

7

(p5,p9)

7

(p7,p9)

9

Table 6. C3: candidate Sets of 3- parameter set and frequency Candidate set 3-parameter set

Frequenc y

p2, p3, p4 p2, p3, p6 p2, p4, p6 p5, p7, p9

4 4 8 7

Table 7. L3: 3-frequent-parameter set 3-frequent - Frequency parameter set p2, p4, p6 8 p5, p7, p9 7 Phase-2 Computation of association rule We compute 3-frequent-parameter set i.e. L2, Taking one parameter in antecedence from {p2, p4,  

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p6} we get: { p2 → p4, p6 : p4 → p2, p6:

p6 → p2, p4 }

Rules with 2-parameter set in antecedence position {p4, p6 → p2: p2, p6 → p4 :p2, p4 → p6 } Taking support =8 computation of Confidence of association rules for parameters p2, p4, p6.are given in following table7. Table 8. Association rules for p2, p4, p6 Rule

Supp Frequen Confid of ence ort of cy (p2, Anteced p4, ence p6) p2, p4, p6 8 13 0.61 p4, p2, p6 8 11 0.72 p6, p2, p4 8 9 0.89 p4, p6 àp2 8 9 0.89 p2, p6àp4 8 8 1 p2, p4à p6 8 8 1 With support =7, computation of confidence for p5, p7, p9 is shown in following table: Table 9. Association rules for p5, p7, p9 Rule

Su ppo rt

p5, p7, p9 p7, p5, p9 p9, p5, p7 p7, p9, p5 p5, p9,p7 p5, p7, p9

7.0 7.0 7.0 7.0 7.0 7.0

Frequenc y of Antecede nt 9 10 11 9 7 7

Confidence

0.78 0.7 0.64 0.78 1 1

Results: With confidence=0.7 cryptanalyst or hacker may infer all-7 rules (without rule number 3). So 5 of them also satisfy after checking L2 also we get p2→ p3 and p3-->p2 and they both have confidence. p4→p2, p4→p6, p6→p2, p6→ p4, p4, p6→ p2, p2, p6→ p4, p2, p4→p6, p5→p7,  

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p5→p9, p7→ p5, p7→p9, p7, p9→ p5 , p5, p9→p7, p5, p7→p9, p2 →p3, p3→p2.; ( rules have been decomposed like p4→ p2, p6 by two rules p4→p2, and p4→ p6 ). VI.

EXPERIMENTAL SETUP

In order to verify association rule using WEKA-64 bit tool kit, we compare association rule obtained from analytical method with corresponding rules generated from WEKA. The same can be generalized and verified for more number of parameters and session logs. The Run information is elucidated below: For hypothetical input session in Table 10 results are in Table 11. The same is computed from WEKA tool elucidate in table 12. Obviously, output of association process has been presented in the format X => Y. The count associated with the antecedent = absolute coverage in the dataset. The number next to the Y = absolute number of instances that match the X and the Y. The number in brackets on the end is the support for the rule (no. of X divided by the number of matching consequents). Table 9. Session wise parameters for AVK Session ID

Parameters for Key

s1

p1, p2

s2

p1, p2, p4

s3

p1, p5

s4 p2, p4, p5 Table 9. Association rules with confidence Possible Rule p1 Æp2 p2Æp1 p2Æp4 p5Æp2

Confidence 2/3 2/3 2/3 3/3

Desirable confidence < 0.75 p2=t 2 conf:(1) 2. p1=t p4=t 1 ==> p2=t 1 conf:(1) 3. p4=t p5=t 1 ==> p2=t 1 conf:(1) 4. p2=t p5=t 1 ==> p4=t 1 conf:(1)

So one can say that a cutoff of 50% was used in selecting rules, of “Association rule generation” window and indicated in that no rule has coverage less than 0.50This aligns with analytical result. So the association rules can be extracted for large number of parameter set and cryptanalyst may generate rule based for key computation. VII.

FUTURE ENHANCEMENT

Apart form association rule the model is to be tested for following crytic mining techniques.(1)Statistical-Cryptic Pattern :Using statistical inferences, accurate notification of malicious activities that are appearing over several time periods acts as indicators of inferring denial-of-service attacks. Challenging task is to determine thresholds to balance the errors and probability of false positive/negative results. It is desirable to have accurate statistical distributions; further challenge is to model all behavior purely using statistical methods. The statistical cryptic pattern identification attempts with features only without consider the relations between features.(2).Cryptic Clustering: IDS-cryptic clustering is to learn from and detect intrusions without requiring the explicit descriptions of various attack classes. The common methods are hierarchical clustering and partition clustering.(3)Fuzzy approach: Using Boolean boundary the intrusion data are partitioned into the interval, with sharp boundary problem for cipher classification. The concept of fuzzy logic uses partial membership among items of set to integrate with the association rules and frequent patterns may provide different insights of cipher logs (abstraction and generalization). (4) Artificial Neural Networks (ANN):Concept of Artificial Neural Network (ANN) supports to design useful nonlinear classifiers of cryptosystems (m- inputs and n-outputs), based on instances of input-output relationship (such as plain text –cipher text pairs).with minimum priory knowledge, and sufficient layers and neurons.(5)Structural Pattern Recognition: using the patterns and structure of plain text –cipher text information, Structural pattern recognition (Syntax and structure) finds some simple sub-patterns that composes longer pattern. The basis of syntax analysis is theory of formal language (handles with symbol information) and of structure analysis is some special technique of mathematics based on sub-patterns (static classification or artificial neural networks). (6).Support Vector Machine (SVM): Support Vector Machine is an effective tool for cryptic pattern recognition. (7)Approximate reasoning approach: Combined fuzzy and compositional rule of inference approach may be used to  

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generate rule based pattern identification.

VIII.

CONCLUSION

This paper examines novel scheme of secure information exchange over the network that may be useful for effective systems. AVK approach is to be tested on real implementation using secured parameter based communication adding extra security feature in the system. Association rule for predicting probable parameters from parameter space using association rule may provide hints for future parameters to predict key. But since both number of parameters as well as key of session is variable and changing from session to session, so the security of the system would not be compromised with the automatic variable scheme. Cryptic pattern identification influenced by a lot of methods from numerous domains. Apart from association rule discovery, other techniques of cryptic mining needs to be examined and implemented. REFERENCES [1]. Shaligram Prajapat, R.S. Thakur, (2014).Time variant approach towards symmetric key. SAI-Conference London. Cosponsored by IEEE. [2]. Shaligram Prajapat ,R. S. Thakur(2015).Optimal Key Size of the AVK for Symmetric Key Encryption.CJICT,2015. [3]. Rivets (1993).Cryptography and machine learning. In Advances in Cryptology— ASIACRYPT'91. [4]. Dunham H (2008).Data Mining: Introductory and Advanced Topics. Pearson education: p.p.-4. [5]. Shaligram Prajapat, G. Parmar, R. S. Thakur (2015).Investigation For Efficient Cryptosystem Using SGcrypter.IJAER.pp.853-858 [6]. Saxena G., Karnik H., Agawam M. (2008). Classification of Ciphers using Machine learning [7]. Rao B. M.(2003). Classification of RSA and IDEA Ciphers. [8]. Shaligram Prajapat. Thakur. Maheshwari,R. S. Thakur(2015).Cryptic Mining in Light of Artificial Intelligence. DOI: 10.14569/IJACSA.2015.060808. [9]. Shaligram Prajapat, R.S. Thakur. (2015). Various Approaches towards Cryptanalysis. International Journal of Computer Applications. 127(14):15-24, October 2015. Published by: Foundation of Computer Science (FCS), NY, and USA.doi: 10.5120/ijca2015906518. [10]. P. Chakrabarti (2008).Key Generation in the Light of Mining and Fuzzy Rule. IJCSNS. [11]. Shaligram Prajapat, Amber Jain, R. S. Thakur,(2012) A Novel Approach For Information Security With Automatic Variable Key Using Fibonacci Q-Matrix. www.interscience.in, IJCCT, Vol.3, Issue 3.

 

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[12]. Shaligram Prajapat, Ramjeevan Singh Thakur (2015). Cryptic-Mining: Association Rules Extractions Using Session Log. Computational Science and Its Applications. proceeding of ICCSA 2015.Volume 9158 of the series Lecture Notes in Computer Science pp 699-711 [13]. Shaligram Prajapat, R.S. Thakur et al. (2014).Sparse approach for realizing AVK for Symmetric Key Encryption. IJRDET and in proceeding of International Research Conference on Engineering, Science and Management (IRCESM) Dubai, UAE. [14]. Goswami R., Chakrabarti S., Bhunia A., Bhunia C.( 2014.). Generation of automatic variable key under various approaches in cryptographic system. J. Institute of Engineers India. [15]. Shaligram Prajapat,R.S.Thakur.(2016).Cryptic Mining for Automatic Variable Key based Cryptosystem. Procedia Computer Science.Elesevier.

 

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