Cryptography And Network Security Behrouz A. Forouzan PDF

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Scilab Textbook Companion for Cryptography And Network Security by Behrouz A. Forouzan1 Created by Subbulakshmi T Cyber Security Computer Engineering VIT Chennai College Teacher None Cross-Checked by None July 31, 2019

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Funded by a grant from the National Mission on Education through ICT, http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab codes written in it can be downloaded from the ”Textbook Companion Project” section at the website http://scilab.in

Book Description Title: Cryptography And Network Security Author: Behrouz A. Forouzan Publisher: Tata Mcgraw-Hill, New Delhi India Edition: 1 Year: 2007 ISBN: 978-0-07-066046-5

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Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular Example of the above book) For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 means a scilab code whose theory is explained in Section 2.3 of the book.

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Contents List of Scilab Codes

4

2 Mathematics of Cryptography

5

3 Traditional Symmetric key Ciphers

61

6 Data Encryption Standard

116

9 Mathematics of Cryptography

133

10 Asymmetric key Cryptography

160

12 Cryptographic Hash function

178

15 Key Management

187

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List of Scilab Codes Exa Exa Exa Exa Exa Exa Exa Exa

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

Exa 2.9 Exa 2.10 Exa 2.11 Exa 2.12 Exa 2.14 Exa 2.16 Exa 2.17 Exa Exa Exa Exa Exa Exa Exa Exa Exa

2.18 2.19 2.21 2.22 2.23 2.24 2.25 2.26 2.27

Binary operations on two integers . . . . . . Division Algorithm . . . . . . . . . . . . . . Convert negative to postive . . . . . . . . . integer divison . . . . . . . . . . . . . . . . Division properties . . . . . . . . . . . . . . Positive integer division . . . . . . . . . . . Find the greatest common divisor . . . . . . Find the greatest common divisor of 25 and 60 . . . . . . . . . . . . . . . . . . . . . . . Find the GCD . . . . . . . . . . . . . . . . find gcd of a and b and also the values of s and t . . . . . . . . . . . . . . . . . . . . . . Find the GCD . . . . . . . . . . . . . . . . Find the particular and general solution of the equation . . . . . . . . . . . . . . . . . . Finding Results of various mod operations . Performing arithmetic operations in Zn . . . Performing arithmetic operations From Z or Zn . . . . . . . . . . . . . . . . . . . . . . . Applications of mod operation . . . . . . . . Finding remainder of Powers . . . . . . . . . Find all additive inverse pairs in Z10 . . . . Find the Multiplicative Inverse of 8 in Z10 . Find all multiplicative inverses in Z10 . . . . Find all multiplicative inverse pair in Z11 . Find all multiplicative inverse of 11 in Z26 . Find the Multiplicative Inverse of 23 in Z100 Find the inverse of 12 in Z26 . . . . . . . . 4

5 6 8 9 10 12 14 15 17 18 20 22 23 25 28 30 32 34 35 36 38 39 41 43

Exa 2.28 Exa 2.29 Exa 2.30 Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa

2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 3.1 3.2 3.3

Exa 3.4 Exa 3.5 Exa 3.6 Exa 3.7 Exa Exa Exa Exa Exa Exa Exa Exa

3.8 3.9 3.10 3.11 3.12 3.15 3.17 3.18

Exa 3.20 Exa 3.21 Exa 3.22 Exa 3.23

shows an Example of addition and substraction . . . . . . . . . . . . . . . . . . . . . . Product of row matrix by column matrix . . Shows the product of 2x3 matrix by a 3x4 matrix and result is 2x4 matrix . . . . . . . Scalar multiplication . . . . . . . . . . . . . Calculating determinant of a 2x2 matrix . . Calculating determinant of a 3x3 matrix . . A residue matrix and its multiplicative inverse Solve the equation 10x is 2 mod of 5 . . . . Solve the equation 14x is 2 mod of 18 . . . . Solve the equation 3x and 4 is 6 mod of 13 . Solve the set of three equations . . . . . . . Plait text to cipher text . . . . . . . . . . . Cipher is not monoalphabetic . . . . . . . . Use the additive cipher with key 15 to encrypt message hello . . . . . . . . . . . . . . . . . Use the additive cipher with key 15 to decrypt the message WTAAD . . . . . . . . . . . . . Brute force attack to break the ciphers . . . Find plain text using statistical attack . . . What is the key domain for any multiplicative Cipher . . . . . . . . . . . . . . . . . . . . . Multiplicative cipher to encrypt the message The Affine cipher . . . . . . . . . . . . . . . use of affine cipher to encrypt the message . use of affine cipher to deecrypt the message The Additive Cipher is Special case of an affine Playfair cipher . . . . . . . . . . . . . . . . Vigenerc Cipher . . . . . . . . . . . . . . . . additive cipher is a special case of vigenere cipher . . . . . . . . . . . . . . . . . . . . . the key matrix in the hill cipher needs to have a multiplicative inverse . . . . . . . . . . . . Cryptanalysis of Hill Ciphers . . . . . . . . A transposition cipher reorders symbols . . A transposition cipher reorders symbols . .

5

45 46 48 49 50 51 52 54 55 57 59 61 64 65 67 70 73 75 76 78 79 81 83 84 91 92 93 97 98 100

Exa 3.24 Exa 3.27 Exa Exa Exa Exa Exa Exa Exa Exa

3.30 3.31 3.32 3.33 3.34 3.35 3.36 6.1

Exa 6.2 Exa 6.3 Exa 6.4 Exa 6.5

Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa Exa

9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 9.10 9.11 9.12 9.13 9.14

Exa 9.15

Permutation of Each character in plaintext into the ciphertext based on the position . . Use matrices to show the encryption decryption processes for transposition cipher . . . Additive ciphers categorized as stream ciphers Mono alphabetic substitution ciphers . . . . Vigenere Ciphers are also stream ciphers . . divide stream ciphers base on key streams . Playfair ciphers are block ciphers . . . . . . Hill ciphers are block ciphers . . . . . . . . Every Block cipher is a polyalphabetic cipher Find the output of the initial permutation box when the input is given in hexadecimal Prove that the initial and final permutation are inverse of each other . . . . . . . . . . . The input to the S box is 100011 and what is the output . . . . . . . . . . . . . . . . . . . The input to the S box 8 is 100011 and what is the output . . . . . . . . . . . . . . . . . Choose random plaintext block and a random key and determine what the cipher text block would be . . . . . . . . . . . . . . . . . . . . List the Primes smaller than 10 . . . . . . . Three primes greater than 17 . . . . . . . . Find the number of primes less than 1000000 is 97 a prime . . . . . . . . . . . . . . . . . is 301 a prime . . . . . . . . . . . . . . . . . Find the Eulers phi function value for 13 . . Find the Eulers phi function value for 10 . . Find the Eulers phi function for 240 . . . . Check the given derivation . . . . . . . . . . Find the number of elements in Z of 14 . . . Find the result of 6 Pow 10 and mod 11 . . Find the result of 3 Pow 12 and mod 11 . . Multiplicative inverse modulo a prime number can be found without using the extended Euclidean algorithm . . . . . . . . . . . . . Find the result of 6 pow 24 mod 35 . . . . . 6

104 107 108 109 110 111 112 113 114 116 118 120 121

123 133 134 135 136 138 139 141 142 144 146 148 149

151 152

Exa 9.16 Exa 9.17 Exa 10.3 Exa Exa Exa Exa Exa

10.5 10.7 10.8 10.9 10.10

Exa 10.11 Exa 10.12 Exa 10.13 Exa 10.14 Exa 12.1 Exa 12.2 Exa 12.3 Exa 12.4 Exa 12.5 Exa Exa Exa Exa Exa

12.6 12.7 12.8 15.1 15.2

Exa 15.3 Exa 15.4 Exa 15.5

Find the result of 20 pow 62 Mod 77 . . . . 154 Multiplicative inverses . . . . . . . . . . . . 156 how the tuple x is found using inverse knapsacksum routine . . . . . . . . . . . . . . . 160 Proof of RSA . . . . . . . . . . . . . . . . . 162 Proof of RSA . . . . . . . . . . . . . . . . . 164 RSA encryption and decryption . . . . . . . 165 Rabin Cryptosystem . . . . . . . . . . . . . 167 Elgamal Algorithm to develop ciphertext and plaintext . . . . . . . . . . . . . . . . . . . . 169 Elgamal Algorithm to develop ciphertext and plaintext . . . . . . . . . . . . . . . . . . . . 171 Elgamal Algorithm to develop ciphertext and plaintex . . . . . . . . . . . . . . . . . . . . 172 Elliptic curve cryptosystem . . . . . . . . . 174 Finding points on curve using the given elliptic curve equation . . . . . . . . . . . . . . . 175 example to show message length limitation in SHA 512 . . . . . . . . . . . . . . . . . . . . 178 pages occupied by message 2 pow 128 bits in SHA 512 . . . . . . . . . . . . . . . . . . . . 179 Padding bit generation in SHA 512 for a given message . . . . . . . . . . . . . . . . . . . . 180 Need of padding if original message length multiple of 1024 bits . . . . . . . . . . . . . 181 Minimum and maximum number of padding bits . . . . . . . . . . . . . . . . . . . . . . 182 how to develop W60 . . . . . . . . . . . . . 183 conditional function . . . . . . . . . . . . . 184 conditional function . . . . . . . . . . . . . 185 SYMMETRIC KEY AGREEMENT . . . . 187 SYMMETRIC KEY AGREEMENT PROGRAM TO CREATE RANDOM INTEGER . . . . 188 how user 1 obtains verified copy of User 3 public key . . . . . . . . . . . . . . . . . . . 190 finding list of roots n the internet explorer . 191 How Alice obatains Bobs verified public key 192

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Chapter 2 Mathematics of Cryptography

Scilab code Exa 2.1 Binary operations on two integers 1

2 3 4 5 6 7

8 9 10 11

// C h a pt er No : 2 E x e r c i s e Number : 2 . 1 o f t h e Book Name : C r y p t o g r a p h y and N etwo rk S e c u r i t y by B eh r ou z Fo ro uz an , S p e c i a l I n d i a n E d i t i o n , 2 00 7 // T h i s f i l e must be us ed u nd er t h e t er m s o f t h e CeCILL . // T h i s s o u r c e f i l e i s l i c e n s e d a s d e s c r i b e d i n t h e f i l e COPYING, w h ic h // you s h o u l d h av e r e c e i v e d a s p a r t o f t h i s d i s t r i b u t i o n . The te r m s // a r e a l s o a v a i l a b l e a t // h t t p : / /www . c e c i l l . i n f o / l i c e n c e s / L ic en c e C eC I L L V 2 −en . t x t // T hi s S o u r c e f i l e i s W r i t te n by S t u d e n t S h r e ya R a j i v Somkuwar ( 1 5 BCE1225 ) , S t u d en t J Ro bin Raj ( 1 5 BCE1325 ) G uided by Dr . T . S u bb u l ak s hm i , P r o f e s s o r // S c h o o l o f Computing S c i e n c e and E n g i n e e r i n g , VIT U n i v e r s i t y C h enn a i // The O p e r a t i n g Sy stem u s ed f o r w r i t i n g t h e c o d e f o u n d i n t h i s f i l e i s Windows 8 // SCILAB v e r s i o n 5 . 5 . 2 // 8

|−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− 12

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

// | T hi s wo rked o u t e xa m pl e f o u n d i n Page No : 16 o f t h e book w i l l do t h e f o l l o w i n g B i n a r y o p e r a t i o n s | // | 1 . A d d i t i o n // | 2 . S u b s t r a c t i o n // | 3 . M u l t i p l i c a t i o n clear ; clc ; a =5; b =9; printf ( ”−−−−−−−−−B i na r y O p e r a t i o n s −−−−−−−\n” ) ; printf ( ” \nADD\ n ” ) printf ( ”%d + %d = %d\n ” ,a ,b , a + b ) ; printf ( ”(−%d) + %d = %d\n ” ,a , b ,( - a ) + b ) ; printf ( ”%d + (−%d) = %d\n ” ,a ,b , a + ( - b) ); printf ( ”(−%d) + (−%d) = %d\n ” ,a ,b ,( - a) + ( -b )) ; printf ( ” \nSUBTRACT\ n ” ) printf ( ”%d − %d = %d\n ” ,a ,b , a - b ); printf ( ”(−%d) − %d = %d\n ” ,a ,b ,( - a) - b ); printf ( ”%d − (−%d) = %d\n ” ,a ,b , a - ( - b) ); printf ( ”(−%d) − (−%d) = %d\n ” ,a ,b ,( - a) - ( -b )) ; printf ( ” \nMULTIPLY\ n ” ) printf ( ”%d x %d = %d\n ” ,a ,b , a * b ) ; printf ( ”(−%d) x %d = %d\n ” ,a , b ,( - a ) * b ) ; printf ( ”%d x (−%d) = %d\n ” ,a ,b , a * (- b )) ; printf ( ”(−%d) x (−%d) = %d\n ” ,a ,b ,( - a ) * ( -b )) ;

Scilab code Exa 2.2 Division Algorithm // C h a pt er No : 2 E x e r c i s e Number : 2 . 2 o f t h e Book Name : C r y p t o g r a p h y and N etwo rk S e c u r i t y by B eh r ou z Fo ro uz an , S p e c i a l I n d i a n E d i t i o n , 2 00 7 2 // T h i s f i l e must be us ed u nd er t h e t er m s o f t h e

1

9

3 4 5 6 7

8 9 10 11

12

13 14 15 16 17 18 19 20 21 22 23 24 25 26

CeCILL . // T h i s s o u r c e f i l e i s l i c e n s e d a s d e s c r i b e d i n t h e f i l e COPYING, w h ic h // you s h o u l d h av e r e c e i v e d a s p a r t o f t h i s d i s t r i b u t i o n . The te r m s // a r e a l s o a v a i l a b l e a t // h t t p : / /www . c e c i l l . i n f o / l i c e n c e s / L ic en c e C eC I L L V 2 −en . t x t // T hi s S o u r c e f i l e i s W r i t te n by S t u d e n t S h r e ya R a j i v Somkuwar ( 1 5 BCE1225 ) , S t u d en t J Ro bin Raj ( 1 5 BCE1325 ) G uided by Dr . T . S u bb u l ak s hm i , P r o f e s s o r // S c h o o l o f Computing S c i e n c e and E n g i n e e r i n g , VIT U n i v e r s i t y C h enn a i // The O p e r a t i n g Sy stem u s ed f o r w r i t i n g t h e c o d e f o u n d i n t h i s f i l e i s Windows 8 // SCILAB v e r s i o n 5 . 5 . 2 // |−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− // | T hi s wo rked o u t e xa m pl e f o u n d i n Page No : 17 o f t h e book w i l l do t h e f o l l o w i n g o p e r a t i o n s | // | 1 . D i v i s i o n A l g o r i t h m f o r a = 25 5 and n=11 // | 2 . P r i n t t h e r e s u l t i n t h e p r o p e r o r d e r w it h t h e r e s u l t f o r q and r i n t h e s c i l a b command l i n e clc ; clear ; a =25 5; n =11; q = int ( a / n ) ; r =a -( q *n ); printf ( ” %d\n ” ,q) ; printf ( ” −−−−−−−−−−\n” ) ; printf ( ”%d | %d\n ” ,n , a) ; printf ( ” | %d\n ” ,n* q ) ; printf ( ” −−−−\n ” ) ; printf ( ” %d” , r) ;

10

Scilab code Exa 2.3 Convert negative to postive 1

2 3 4 5 6 7

8 9 10 11

12

13 14 15 16

// C h a pt er No : 2 E x e r c i s e Number : 2 . 3 o f t h e Book Name : C r y p t o g r a p h y and N etwo rk S e c u r i t y by B eh r ou z Fo ro uz an , S p e c i a l I n d i a n E d i t i o n , 2 00 7 // T h i s f i l e must be us ed u nd er t h e t er m s o f t h e CeCILL . // T h i s s o u r c e f i l e i s l i c e n s e d a s d e s c r i b e d i n t h e f i l e COPYING, w h ic h // you s h o u l d h av e r e c e i v e d a s p a r t o f t h i s d i s t r i b u t i o n . The te r m s // a r e a l s o a v a i l a b l e a t // h t t p : / /www . c e c i l l . i n f o / l i c e n c e s / L ic en c e C eC I L L V 2 −en . t x t // T hi s S o u r c e f i l e i s W r i t te n by S t u d e n t S h r e ya R a j i v Somkuwar ( 1 5 BCE1225 ) , S t u d en t J Ro bin Raj ( 1 5 BCE1325 ) G uided by Dr . T . S u bb u l ak s hm i , P r o f e s s o r // S c h o o l o f Computing S c i e n c e and E n g i n e e r i n g , VIT U n i v e r s i t y C h enn a i // The O p e r a t i n g Sy stem u s ed f o r w r i t i n g t h e c o d e f o u n d i n t h i s f i l e i s Windows 8 // SCILAB v e r s i o n 5 . 5 . 2 // |−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− // | T hi s wo rked o u t e xa m pl e f o u n d i n Page No : 17 o f t h e book w i l l do t h e f o l l o w i n g o p e r a t i o n s | // | 1 . F ind t h e r e m a i n d e r when t h e d i v i d e n d i s negative // | 2 . T ake t h e d i v i d e n d a s −255 and d i v i s o r a s 11 and f i n d t h e r e m a i n d e r // | 3 . P r i n t t h e r e s u l t i n t h e s c i l a b command l i n e clc ; 11

17 18 19 20 21 22 23 24 25 26 27

clear ; a = -255; n =11; q = int ( a / n ) ; r =a -n * q; printf ( ” B e f o r e : \ n%d = ( %d x %d ) + %d\n ” ,a , q ,n ,r ) ; if a , %d | %d\n ” ,r1 ,n1 , a1 ) ; printf ( ”%d = ( %d x %d ) + %d\n ” ,a2 ,q2 , n2 , r2 ) ; printf ( ” r=%d => , %d + %d” , r2 , n2 , a2 );

Scilab code Exa 2.5 Division properties // C h a pt er No : 2 E x e r c i s e Number : 2 . 5 o f t h e Book Name : C r y p t o g r a p h y and N etwo rk S e c u r i t y by B eh r ou z Fo ro uz an , S p e c i a l I n d i a n E d i t i o n , 2 00 7 2 // T h i s f i l e must be us ed u nd er t h e t er m s o f t h e CeCILL . 3 // T h i s s o u r c e f i l e i s l i c e n s e d a s d e s c r i b e d i n t h e f i l e COPYING, w h ic h 4 // you s h o u l d h av e r e c e i v e d a s p a r t o f t h i s

1

13

5 6 7

8 9 10 11

12

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

d i s t r i b u t i o n . The te r m s // a r e a l s o a v a i l a b l e a t // h t t p : / /www . c e c i l l . i n f o / l i c e n c e s / L ic en c e C eC I L L V 2 −en . t x t // T hi s S o u r c e f i l e i s W r i t te n by S t u d e n t S h r e ya R a j i v Somkuwar ( 1 5 BCE1225 ) , S t u d en t J Ro bin Raj ( 1 5 BCE1325 ) G uided by Dr . T . S u bb u l ak s hm i , P r o f e s s o r // S c h o o l o f Computing S c i e n c e and E n g i n e e r i n g , VIT U n i v e r s i t y C h enn a i // The O p e r a t i n g Sy stem u s ed f o r w r i t i n g t h e c o d e f o u n d i n t h i s f i l e i s Windows 8 // SCILAB v e r s i o n 5 . 5 . 2 // |−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− // | T hi s wo rked o u t e xa m pl e f o u n d i n Page No : 18 o f t h e book w i l l do t h e f o l l o w i n g o p e r a t i o n s | // | 1 . S o l v e and p r o v e f o r 13 | 7 8 , 7 | 9 8 , −6 | 2 4 , 4 | 4 4 , 11 | ( −33) // | 2 . S o l v e and p r o v e f o r 1 3 + 2 7 , 7 + 5 0 , −6 + 2 3 , 4 + 4 1 , 11 + ( −32) // | 3 . P r i n t t h e r e s u l t i n t h e s c i l a b command l i n e clc ; clear ; a =78 n =13 printf ( ” %d | %d , s i n c e %d = ( %d x %d ) + %d\n ” ,a , n ,a , int ( a /n ) ,n ,a - int ( a / n ) * n ) ; a =98; n =7; printf ( ” %d | %d , s i n c e %d = ( %d x %d ) + %d\n ” ,a , n ,a , int ( a /n ) ,n ,a - int ( a / n ) * n ) ; a =24; n = -6; printf ( ” %d | %d , s i n c e %d = ( %d x %d ) + %d\n ” ,a , n ,a , int ( a /n ) ,n ,a - int ( a / n ) * n ) ; a =44; 14

28 n =4; 29 printf ( ” %d | %d , s i n c e %d = ( %d x %d ) + %d\n ” ,a , 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

n ,a , int ( a /n ) ,n ,a - int ( a / n ) * n ) ; a = -33 n =11; printf ( ” %d | %d , s i n c e %d = ( %d x %d ) + n ,a , int ( a /n ) ,n ,a - int ( a / n ) * n ) ; a =27; n =13; printf ( ” %d + %d , s i n c e %d = ( %d x %d ) + n ,a , int ( a /n ) ,n ,a - int ( a / n ) * n ) ; a =50; n =7; printf ( ” %d + %d , s i n c e %d = ( %d x %d ) + n ,a , int ( a /n ) ,n ,a - int ( a / n ) * n ) ; a =23; n = -6; printf ( ” %d + %d , s i n c e %d = ( %d x %d ) + n ,a , abs ( int ( a /n )) ,n ,a - abs ( int ( a / n ) ) * n ) ; a =41; n =4; printf ( ” %d + %d , s i n c e %d = ( %d x %d ) + n ,a , int ( a /n ) ,n ,a - int ( a / n ) * n ) ;

%d\n ” ,a ,

%d\n ” ,a ,

%d\n ” ,a ,

%d\n ” ,a ,

%d\n ” ,a ,

Scilab code Exa 2.6 Positive integer division // C h a pt er No : 2 E x e r c i s e Number : 2 . 6 o f t h e Book Name : C r y p t o g r a p h y and N etwo rk S e c u r i t y by B eh r ou z Fo ro uz an , S p e c i a l I n d i a n E d i t i o n , 2 00 7 2 // T h i s f i l e must be us ed u nd er t h e t er m s o f t h e CeCILL . 3 // T h i s s o u r c e f i l e i s l i c e n s e d a s d e s c r i b e d i n t h e f i l e COPYING, w h ic h 4 // you s h o u l d h av e r e c e i v e d a s p a r t o f t h i s d i s t r i b u t i o n . The te r m s

1

15

5 6 7

8 9 10 11

12

13 14 15 16 17 18 19 20 21 22 23 24

// a r e a l s o a v a i l a b l e a t // h t t p : / /www . c e c i l l . i n f o / l i c e n c e s / L ic en c e C eC I L L V 2 −en . t x t // T hi s S o u r c e f i l e i s W r i t te n by S t u d e n t S h r e ya R a j i v Somkuwar ( 1 5 BCE1225 ) , S t u d en t J Ro bin Raj ( 1 5 BCE1325 ) G uid...