Linear Algorithm for Imbricate Cryptography Using Pseudo Random Number Generator

Transcription

1 Linear Algorithm for Imbricate Cryptography Using Pseudo Random Number Generator Rohit Rastogi Sr. Asst Professor, CSE-Dept, ABES Engg. College Ghaziabad (U.P.), INDIA Id: Shashank Mittal CSE-Dept ABES Engg. College Ghaziabad (U.P.), INDIA Shashank Shekhar CSE-Dept, ABES Engg. College Ghaziabad (U.P.), INDIA Abstract In this paper we are going to establish the relationship between Randomness and Cryptography. We are going to generate an algorithm by combining the result of the Linear Congruential Pseudo Random Number Generator with Imbricate Cryptography. The following algorithm is Symmetric type Cryptography. It uses a layered approach. The first layer involves implanting a randomly generated number in the text and then transforming the text to form the cipher text at the very first layer. Second layer involves implanting the key to the cipher text obtained in the first layer thus making the security a two way approach. Therefore, the message can only be recovered by using the correct key and the correct Random number generated. The Random number generated is transmitted to the user with the key. Here the message and the key are inwardly plaited. It is not possible to find the key by permutation and combination since the user can choose key of variable length. Multiple Layers of encryption and decryption provide security. The advantage of the process is that it prevents cipher text only attack and known plain text attack. It is also easily computable and efficient. [6] Keywords Bitmap File, Encryption, Imbricate Cryptography, Linear Congruential Generator, Network security. I. INTRODUCTION The electronic communication is increasing by leaps and bounds and its usage in E-Business has increased phenomenally. To transact in E-Business, it is imperative that electronic communication has high degree of security and privacy. Data protection is required during transmission and thereby there is increasing utility of network security measures. Parties exchanging sensitive business information in secured manner find usage of Cryptography as highly reliable. Cryptography involves converting a simple decipherable message into an unintelligible and then converting that message to its original form. [5, 6] When the sender and receiver use the same key, it is known as Symmetric Key Cryptography or Conventional Encryption. When the sender and receiver use different keys, it is known as Asymmetric Key Cryptography or Public Encryption. Perfect secrecy can be achieved only if the key of encipherment is truly a random number. True random generator approach involves a natural random process, e.g., tossing of coin. Random Generator processes have some limitations. All the natural random generator processes are slow. It also suffers from the fact that if needed, random stream cannot be repeated. Alternatively, Pseudo Random Number Generator process is used. It involves usage of a deterministic process to generate a short random stream. This random stream of bits is used as the input. There are two broad categories of Pseudo Random Number Generators which are Congruential Generators and Generators using Cryptographic ciphers. [2] II. OUR AIM IN THIS PAPER This paper is going to establish the relationship between the Randomness and Cryptography. Higher the Randomness of predicting the next bit in cipher, higher will be the secrecy and thereby increasing the efficiency. Here an algorithm is generated by combining the Pseudo Random Number Generator with Imbricate Cryptography. A new algorithm is being formed by using Linear Congruential Pseudo Random Number Generator s result to circularly shift the characters in the input. [5] Linear Congruential method is the most common technique for generating the pseudo random numbers. When adequate criteria is followed for selecting the coefficient of the congruence equation and the value of the modules, then the sequence generated by a linear congruential equation delivers reasonable randomness.[2] In the algorithm the key is used in second layer, which is implanted in the message. To recover the message correct key is used. Here the message and key are inwardly plaited. It is not possible to find the key by permutation and combination since the user can choose key of variable lengths. Layers of Encryption and Decryption provide security. [3] /15/$31.00 c 2015 IEEE 89

2 it gets repeatedly used. The number of times depending upon the length of the message. Formulated as Character New = (Character Old) XOR (~Character of K). [1] C. Layer 3: Bitmap Conversion Layer This layer is responsible for converting ASCII characters into their binary equivalents and this result is stored as a Bitmap file. Here each character is taken individually, and then its binary equivalent is obtained. The binary equivalent is then written in a file that is of type bitmap. Due to its bitmap nature, this layer is commonly referred as Bitmap Conversion Layer. [1] Fig. 1. Our Approach using Pseudo Random III. NOTION OF LAYER The new algorithm being formed comprises of three layers of Encryption, each having its own contribution and thereby increasing the security of the new formed algorithm. The three layers are Pseudo Shifting Layer, Core Encoding Layer and Bitmap Conversion Layer. The three layers are described below. A. Layer 1: Pseudo Shifting Layer It is called Pseudo Shifting Layer. Each character in the input is shifted by number of places that is generated by the Pseudo Random Number Generator. Replacing character is present at the position which is at a place which is away from the current character by the number of places that is generated by Pseudo Random Number Generator. Here the difference between the repeated (these are the characters whose occurrence is high e.g. a, e, h, r) and non-repeated characters is omitted and thus completing the first level of encipherment. The XOR operation of input string with random generated value is canceled out. It also eases out the task as there is no need to remember the probability of each alphabet. Thus each character in the input set is mapped according to the value obtained by the generator. [1, 4] B. Layer 2: Core Encoding Layer This layer uses the technique of the bitwise logics (0, 1) and ASCII format to encode the characters obtained after first level of encipherment. The characters obtained from the first layer can be a number, alphabet or symbol as entered in the input seed, hence naming the layer as Core Encoding Layer. [1] The first character of encipherment obtained by Layer1 is XORed with negated ASCII character of first character of the password. The same process is repeated for the rest of the enciphered text. The length of password is small due to which IV. ENCRYPTION ALGORITHM 1. Getting input Message say M from the user. 2. Generating pseudo random number say N by Pseudo Random Number Generator. 3. Layer 1: Left shift the characters in M by N to generate cipher text say M2 i.e. M2 = M<<N 4. Layer 2: Encoding the above generated cipher M2 using the key say K which is transferred to the receiver secretly by other means. The formula used to generate new cipher say M3:-- Character New of M3 = (Character Old of M2) XOR (~Character of K) 5. Layer 3: The above generated cipher M3 is then converted into its binary equivalent and then placing the binary values in the bitmap file. [1] 6. The bitmap file generated at the end of Layer 3 is transferred to the receiver which is then decrypted using the decryption algorithm to produce the original message M. Fig. 2. Encryption Algorithm Block Diagram nd International Conference on Computing for Sustainable Global Development (INDIACom)

3 V. DECRYPTION ALGORITHM The Bitmap Image is transmitted to the receiver by the sender. 1. The random number generated by the Pseudo Random Number Generator i.e. N and the key K is transferred to the receiver by other means secretly. 2. Take 8 bits at a time from the input bitmap image and XNOR it with the key K i.e. M2 [i] = (8 bits of bitmap) XNOR (K[i]) 3. The above step produces the ciphered text M2 that was produced at Level 2 of Encryption. 4. Right shift the characters of M2 with pseudo random number generated value N to obtain the original message M at this step. 5. The original text is obtained here. M3[2] = h ^ ~i = ^ = = 254 = Character of ASCII code 254 mod 127 M3[3] = e ^ ~h = ^ = = 242 = Character of ASCII code 242 mod 127 M3[4] = l ^ ~a = ^ = = 242 = Character of ASCII code 242 mod Layer 3: M3 = [][][][][] where [] = character at ASCII code at that position. M3 = { } This M3 is now converted into Bitmap Image BI i.e. BI = The Bitmap file BI generated at the end of Layer 3 is transferred to the receiver which is then decrypted using the Decryption algorithm to produce the original message M. 7. Perfect secrecy will be maintained when transmitting the Bitmap Image BI and the reader will be baffled after seeing the Bitmap Image BI in place of original text. Fig. 3. Decryption Algorithm Block Diagram VI. AN EXAMPLE OF SPECIFIC CASE A. Encryption Let us illustrate our technique of Encryption by the following example: 1. Input Message from Sender i.e. M = hello 2. Generated pseudo random number i.e. N = 3 3. Layer 1: M2 = M<<N M2 = hello <<3 M2 = lohel 4. Layer2: M3[i] = M2[i] XOR ~K[j] Where, i goes from 0 to length of input Message M. j goes to 0 to length of key K and repeats if length K less than length of M. M3[0] = l ^ ~h = ^ = = 251 = Character of ASCII code 251 mod 127 M3[1] = o ^ ~a = ^ = = 241 = Character of ASCII code 241 mod 127 Fig. 4. Encryption Algorithm Flow Chart nd International Conference on Computing for Sustainable Global Development (INDIACom) 91

4 B. Decryption Let us illustrate the Decryption Algorithm by following example: 1. The Bitmap Image is BI, Key K, Random Number N are given as input. BI = Key K = hai Random Number N = 3 2. Layer 3 M2 [i] = (8 bits of bitmap) XNOR (K[j]) M2 [0] = XNOR h = XNOR = = l M2 [1] = XNOR a = XNOR = = o M2 [2] = XNOR i = XNOR = = h M2 [3] = XNOR h = XNOR = = e M2 [4] = XNOR a = XNOR = = l 4. Layer 2 The above step produces the ciphered text M2 that was produced at Level 2 of encryption i.e. M2 = lohel 5. Layer 3 Right shifting the characters of M2 with pseudo random number generated value N to obtain the original message M at this step i.e. M = N >> M2 M = 3 >> lohel = hello 6. The original text is obtained here in form of M = hello = M In this example, ^ represents XOR operation. ~ represents one s complement operation There is one to many mapping as we can see in case of hello first l is replaced by h and second l is replaced by e (but the mapping can be one to one if all the characters in the message are different and one to many if there are some same characters in it). From this it can be concluded that the resultant code will be highly unpredictable. As much as the code is unpredictable, as much is the security for transmitting it over any network which can ensure more and more security. Also there will be huge randomness in the prediction of the calculation of (i+1) th bit from i th bit. [1] Fig. 5. Decryption Algorithm Flow Chart VII. COMPLEXITY ANALYSIS Input message M and random number N generated by the Pseudo Random Number generator are provided to the algorithm as inputs. Let L be the length of input message M and P be the length of the key K. A. For Shifting Cost of each Shift = Unit Time = 1 For an input message M to be shifted by N places, Total time taken= Cost of each shift * Number of shifts. => 1 * N =>O (N) B. For XOR Operations Cost of each XOR operation = Unit Time = nd International Conference on Computing for Sustainable Global Development (INDIACom)

5 Total time taken =Cost of each XOR Operation * Number of Operation Performed. => 1 * L =>O (L) C. For XNOR Operations Cost of each XNOR operation = Unit Time = 1 Total time taken = Cost of each XNOR Operation * Number of Operation Performed. => 1 * L => O (L) D. For all Binary to Decimal and Decimal to Binary Conversions Cost of each Conversion = Unit time = 1 Number of conversions = 2 * L Total time taken = Cost of each Conversion * Number of Conversions. => 1 * 2 * L =>O (L) E. For all ASCII Code to Character conversions Cost of each conversion = Unit Time = 1 Number of conversions = 2 * L Total time taken = Cost of each Conversion * Number of Conversions => 1 * 2 * L => O (L) Thus for both Encryption and Decryption algorithms, So over all steps involved in both the algorithms = O (L) + O (N) Since L is greater than N i.e. L > N Overall Complexity of the algorithms = O (L) Thus for both Encryption and Decryption algorithms, The Running time complexity = O (L) where L is the Length of the Input Message M. VIII. NOVELTY IN OUR PAPER THROUGH THIS APPROACH Imbricate Cryptography follows layered approach providing security and confidentiality at various levels. It s a type of a Symmetric Key Cryptography, thereby using only single key which can t be guessed using permutation and combination as the size of the key is unknown. Output can baffle anyone as it comes in the combinations of 0 s and 1 s. Thus its key provides confidentiality. It is simple and can easily be computed. It provides layers of security. The incorporated key at layer two provides protection. Using random generator at the first layer makes it very fast and simple. It uses minimal amount of memory. [1] The advantage of this new process is that it saves the input text from the cipher text only Attack and known plain text attack. Thereby improving the performance of the generator. The first step of the algorithm doesn t require the key. Apart from this, we have an advantage that mapping is done unpredictably as the key length being smaller than the message length. It is also easily computable and efficient. [5] IX. LIMITATIONS The Linear Congruential Generator can only be used when the Encryption is taking places in layers else it would be like affine cipher and prone to frequency analysis. Moreover, Imbricate Cryptography is designed in layers make it long and slow. Computer simulations are everywhere, from the corporate office to the local video game parlor. The message to be transferred should be space insensitive to ensure more security With the increased role being played by these simulations, it is important for students to be completely aware of the limitations of Pseudo Random Number Generators. The fact that random number generators in use today are not truly random is no secret (The New York Times, C1-C8). Since most simulations produce reasonable results it might be difficult to convince students that there are any problems involved in trusting these Random Number Generators. A simple simulation which can be used as a programming exercise in any language can dramatically reveal these dangers. The exercise used requires a statistical evaluation of π which yields horrible results. The results are not difficult to explain and the exercise can be extended by allowing students to experiment with modifications to the Pseudo Random Number Generator used in attempts to "fix" the problem. This can be useful, as the attempts to fix the Pseudo Random Number Generator usually aggravate rather than alleviate the problem. X. CONCLUSION AND FUTURE SCOPE Cryptography plays an important role in providing security and confidential to data. Imbricate Cryptography is used to provide security to the data sent to the other user through an insecure network. This is done in an efficient manner so as to obtain maximum benefit by utilizing minimum cost and resources. This paper establishes that the security of imbricate Cryptography is enhanced by using pseudo random generator which increases the randomness of determining the cipher text. This method provides protection and confidentiality. Moreover it can be easily computed. Thus Through this paper, it has been the endeavor to enhance the security of Imbricate Cryptography Encryption and Decryption algorithms for ensuring better security results in data transmission. In the second layer of Imbricate Cryptography key can be replaced by some other method so as to increase the security of the system. Also storing key also involves security issues nd International Conference on Computing for Sustainable Global Development (INDIACom) 93

6 The Algorithm can baffle anyone by seeing the cipher text but even then it s less secure in terms of white space consisting text as when there is are white spaces in the small length words can be easily detected. Thus some new method can be added to it so as to make it more secure to white space consisting text. Here we have to transfer the key K and the random number generated N to the receiver through other means to ensure security which increase the steps and cost of transferring. A new algorithm can be developed in which both key K and random number N can be embedded in the message Bitmap Image with same security which can reduce the cost of transferring. XI. RECOMMENDATIONS This algorithm will be useful to all those who study Cryptography. To the organizations who are willing to improve their security systems. Also to the users who want to transfer data over an insecure channel. Moreover today many of the important text messages are transferred over various messaging services through mobile phones. We can use this technology in both sender s and receiver s mobile phone so that if both of them have the same key then they can read the messages and if anyone somehow get excess to the message send by the sender then he will be baffled by seeing the bitmap image generated by the Encryption Algorithm. Imbricate Cryptography Algorithm can be used by those who wants to make CAPTCHA generation a secure but not a completely random process as it provides security with very little randomness and thus makes CAPTCHA generation a more secure but controlled process by the user. [5] Behrouz. A Forouzan and Debdeep Mukhopadhyay Cryptography and Network Security second edition, TMH. Chapter and concept pg607 [6] SongY.Yan.Cryptanalytic attacks on RSA, Springer [7] William Stallings Network Security Essentials (Applications and Standards), Pearson Education, ACKNOWLEDGEMENT With due regards, we would like to thank the actual people behind this paper. We would like to thank our head of department, Dr. Prof. R.RadhaKrishnan, HOD-CSE of ABES Engineering College, Ghaziabad for his guidance at every step. We would like to thank our friends, family members for their extreme support and blessings and to the ALMIGHTY for HIS blessings. REFERENCES [1] Murali Kumar R Imbricate Cryptography for network security electronics for you, MAY [2] Johan Hastad, Russell Impagliazzoy, Leonid A. Levinz, Michael Luby A Pseudo random generator from any one way function, SIAM Journal on computing. [3] Blaze, Matt, Diffle Whitefield, Rivest, Ronald L. Schneier, Bruce; Shimomura, Tsutomu, Thompson, Eric; Wiener, Miachel (January 1996). Minimal key lengths for symmetric ciphers to provide adequate commercial security. [4] Robert B Davies, Exclusive OR (XOR) and hardware random number generators, feburary28, nd International Conference on Computing for Sustainable Global Development (INDIACom)