SPEED AND SECURITY ENHANCEMENT
THROUGH
PUBLIC KEY CRYPTOGRAPHY
J.SAIGEETHA Lecturer in Computer Science,
Nehru Memorial College, Puthanampatti Trichy.621007 Tamilnadu.India.
V.SELVI
Lecturer in Computer Science , Nehru Memorial College,
Puthanampatti. Trichy.621007 Tamilnadu.India.
Abstract
It is true that the transfer of data is essential in the fast developing world. It is equally true that the transfer of data to be taken place with much security by not giving groom to the intruders. This paper presents the analysis of the security of information with enhanced the speed of encryption and decryption process. This process uses public key cryptography via RSA algorithm with some modification. There are two keys used in RSA algorithm for effectiveness in the aspect of security one being the public key used for all and the other being the secret key. The implementation is done in the JAVA language and crypt analysis is performed to check the level of protection and speed.
Keywords: Public key Cryptography, Encryption, Decryption, RSA algorithm, Cryptanalysis
1. Introduction
1.1 The concept of public key cryptography
Two keys are used in public key cryptography. With the public key one could encrypt messages, and Decrypt them with the private key. Thus the owner of the private key would be the only one who could decrypt the messages, but anyone knowing another idea that was observed was that of a key exchange. In a two-party communication it would be useful to generate a common secret key for bulk encryption using a secret key cryptosystem; public could send them in privacy.
The public key cryptosystem algorithms have the following important characteristics
It is computationally infeasible for a intruder to determine the decryption key given by the owner, even with knowledge of the cryptographic algorithm and the encryption key.
Either one of the two related key can be used for encryption, while the other used for decryption.
Prerequisite to Work
1. one algorithm is used for encryption and decryption with a pair of keys, one for encryption and one for decryption
2. The sender and receiver must each have one of the matched pair of keys.
Prerequisite for Security:
1. One of the two keys must be kept secret.
3. Knowledge of the algorithm plus one of the keys plus samples the cipher text must be insufficient to determine the other key.
The public key is common to all and the secret is kept secret. It can be illustrated in the following figure 1
:
figure 1
2.RSA Algorithm 2.1 - Key Generation.
1. Select TWO PRIME NUMBERS P,Q. 2. Calculate n=p*q.
3. Calculatef(n)=(p-1)*(q-1)
4. Select integers e; gcd(f(n),e)=1;1<e<f(n). 5. Calculate d; d=e-1 mod f(n)
6. Public key KU ={e,n} 7. Private key KR ={d,N}.
Encryption:
Plain text : M<n
Cipher text : C= Me (mod n).
Decryption:
Cipher text : CPlain text : M=Cd (mod n). These operations are explained in the following figure 2
Plain Text(M)
Encryption
Cipher Text ( C
)
Decryption
Plain Text(M) Figure 2
2.2 Problems in RSA
1. The alphabets in the plain text are represented by numbers ranging from 1 to 26. Hence it is not possible to represent the special; characters in the plain text.
2. The encryption and decryption technique is applied to each and every character of a text, even though the character is repeated in the plain text. So it requires more time for the redundant calculation.
3. As the calculation result is repeated in the cipher text, it will be ease for the intruders to identify the corresponding characters, thus by trapping the message in a easier way, which results in security lapses
Solution:
The above mentioned problems are being resolved by the following manner:
1. Instead of numbers, the characters in the plain text are represented by UNICODE which can be able to represent the special characters;
2. The second one is to be solved by the back substitution. Once the result is computer, it cannot be repeated again. For this purpose, the results are maintained and will be reused in upcoming calculation.
Sender1
Sender2
Sender3
Public key
Receiver Public key
Public key
Public key
Sender C=Me mod n
3. In case of numbers in cipher text, the intruders may able to detect the characters easily. So the symbols are also used in cipher text representation the symbol is substitute exactly once with a particular number. For the next occurrence, some other symbols are used to represent the same number. Finally the entire cipher text is in the form of symbols instead of numbers.
3. Procedure
3.1 RSA Algorithm
The RSA algorithm provides security for the data, which is transferred in a network. the algorithm consists of the following steps.
1. calculate public and secret key. The computation includes the following steps. a. Generate two prime numbers p and q randomly.
b. Computer n=p*q. c. Calculate z=(p-1)*(q-1).
d. Choose a number relatively prime to z and call it d.
e. Find e such that e* d=1 mod z where e is the public key and d is secret key. 2. Encode the plain text to be encrypted as a UNICODE.
3. In encryption, the plain text is converted to the cipher text by using this formula C=pe mod n
where p is the plain text in UNICODE. C is the cipher text
E is the encryption key
4. In decryption, the cipher text is converted into UNICODE by using this formula P= Cd mod n
Where d is the decryption key.
5. The UNICODE version is finally converted into plain text.
Disadvantage in RSA
The encryption and decryption technique is applied to each and every character even though the character is repeated in the plain text. So it requires more time for the redundant calculation. Since the algorithm uses the UNICODE representation, the intruders may trap the message very easily.
3.2 RSA1 Algorithm
The refined RSA1 eliminate the redundant calculation in encryption and decryption. This algorithm also uses the same methodology for the secret and public key generation. It also eliminates the redundancy by using the previously calculated result, if the character is repeated.
1.The plain text is represented using UNICODE.
2.The UNICODE represented is used instead to plaintext in encryption technique.
3.In encryption, the plain text is converted to the cipher text by using this formula if the character is not already exists in the text.
C=pe mod n
Where p is the plain text in UNICODE. C is the cipher text
E is the encryption key
4.In decryption, the cipher text is converted into UNICODE by using this formula if the character is not already exists in the text.
P= Cd mod n
Where d is the decryption key.
5.The UNICODE version is finally converted into plain text.
Advantages :
Disadvantages :
In spite of rapid processing, it lacks security.
It occupies more storage space for maintaining the previous results.
3.3 RSA2 Algorithm
The main intention of this algorithm is to improve security. This algorithm utilizes the same procedure for key generation.
1. The plain text is represented by using UNICODE.
2. The UNICODE represented is used instead of plain text in encryption technique. 3. In encryption, the plaint text is converted to the cipher text by using this formula. C=pe mod n
Where p is the plain text in UNICODE. C is the cipher text
E is the encryption key
4. Encode the cipher text as represented by symbols.
5. Before Decryption, Decode the symbols in the form of cipher text.
6. In decryption, the cipher text is converted into UNICODE by using this formula. P=Cd mod n
Where d is the decryption key
7. The UNICODE version is finally converted into plain text.
4. System Flow Diagram
The entire problem is described in the following figure
Figure 3
5. Results & Conclusion
The algorithms RSA, RSA1 and RSA2 are compared based on their execution time. The same set of data is applied to test the speed of each algorithm. Since in all the test cases, the value of encryption key is larger than the value of decryption key. The encryption time is comparatively higher than the decryption time.
Public Key Cryptography
RSA Algorithm
Existing RSA Algorithm
Refined RSA RSA1
Algorithm
In RSA, the execution time primarily depends on the file size. As the file size increases, the execution time will be increased automatically. In RSA1, the execution time is purely based on the repetition of each character in the test data. If the number of the occurrences of a character increases (as the same is being represented by the same number) the execution time will get reduced with in turn enhance the performance of the system. Even for an increased file size the execution time may remain same due to the duplication of characters.
In RSA2 the speed depends on the file size. But this algorithm is a highly secured one when compared to RSA and RSA1 algorithms. However the time consumption of this algorithm will be relatively higher. In this algorithm, the encrypted message is again encrypted; the cipher text is represented by the way of symbols in stead of numbers.
The observed results are tabulated in table 1
Table 1
File Size (Bytes)
Algorithms Encryption Time (Sec) Decryption Time (sec) Execu tion Time (sec) 394 RSA RSA1 RSA2 29 4 45 2 1 3 31 5 48 1011 RSA RSA1 RSA2 85 5 113 4 1 5 89 6 118 2705 RSA RSA1 RSA2 237 6 291 9 1 12 246 7 303 3114 RSA RSA1 RSA2 265 6 331 11 1 12 276 7 443 4933 RSA
RSA1 RSA2 437 6 615 18 1 19 455 7 634
The above values are represented in the graph given in figure 4. The file size is taken to be in X axis and the execution time in Y axis. The execution time of all the algorithms are represented simultaneously in chart.
RSA ANALYSIS CHART
0 200 400 600 800
394 1011 2705 3114 4933
File Size
Executi
on Ti
m
e
RSA RSA1 RSA2
Figure 4
In this chart, three different lines are displayed. From this graph, the RSA1 has high speed when compared to RSA and RSA2. The RSA2 requires more time for execution.
It is observed that RSA1 gives better performance based on the execution time whereas the RSA2 is better based on security. The time is directly proportional to the file size.
Thus the new algorithm introduced to support both the speed and security is known as refined RSA algorithm.
6. References
[1] Algorithms for software implementations of RSA, A.Mitchell C.Trinity coll., Cambridge as appears Computers and Digital Techniques, IEEE May 1989 (Vol 136, No:3-PP 166-170)
[2] RSA Speedup with chinese Remainder Theorem Immune against Hardware Fault cryptanalysis, December 11-15, 2000 - New Orleans, Louisiana Sung-Ming Yen, Sang-Jae
[3] On optimizing RSA algorithm implementation on signal processor regarding asymmetric private key length –2003 IEEE International Symposium on 4-6 Sept 2003
[4] Computer Networks by Andrew S.Tanenbaum
[5] Data Communication and Network by Behrouz A Forouzan [6] Cryptography and Network Security by William Stalling
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