advertisement

International Journal of Engineering Trends and Technology (IJETT) – Volume 31 Number 1 - January 2016 Threshold Sr2n Public key Cryptosystem Dr.M.Sreedevi, Assistant Professor,Dept.of Computer Science,S.V.University, Tirupati ABSTRACT RSA places a vital role in Asymmetric key cryptography. Many cryptosystems has been proposed with modifications to original RSA by improving security, performance of various phases of algorithm. SRNN is one of the extension of RSA. In this paper we propose SR2N algorithm which uses extremely large number that has two prime factors along with two natural numbers in pair of keys (Public key and PrivateKey). These natural numbers increases the security of the cryptosystem which will with stand various attacks as they are selected randomly. Keywords: Cryptography, SRNN, Symmetric and Asymmetric key cryptography. II.SRNN CRYPTOSYSTEM I. INTRODUCTION Symmetric-key cryptography is based on the usage of single key by sender and receiver for exchange of messages securely. The sender uses the secret key to encrypt the message and the receiver uses the same secret key to decrypt it. The main problem of symmetric key cryptography is getting the sender and receiver to agree on the same secret key without third party intervention. Because all keys in a symmetric key cryptosystem must remain secret, symmetric key cryptography often has difficulty providing secure key management, especially in open systems with a large number of users. To solve this problem, Diffie and Hellman introduced a new approach to cryptography and, in effect, challenged cryptologists to come up with a cryptographic algorithm that met the requirements for public-key systems. Public-key cryptography is used where each user has a pair of keys, one called the public key and the other private key. Each user’s public key is published while the private key is kept secret and thereby the need for the sender and the receiver to share secret information (key) is eliminated. The only requirement is that public keys are associated with the users in a trusted (authenticated) manner using a public key infrastructure (PKI). The public key cryptosystems are the most popular, due to both confidentiality and authentication facilities. So in this paper we have proposed new cryptosystem SR2N which is a PKI. Short Range Natural Number (SR2N) Cryptography is one of the best known public key cryptosystems for ISSN: 2231-5381 key exchange or digital signatures or encryption of blocks of data. RSA uses a variable size encryption block and a variable size key. The key pair is derived from very large number n, i.e. the product of two prime numbers chosen according to special rules. These primes may be 100 or more digits in length each, yielding an n with roughly twice as many digits as the prime factors. In SRNN cryptosystem the public key information includes n and a derivative of one of the factors of n, an attacker cannot determine the prime factors of n and therefore the private key from this information alone. And all values are declared as global with less security and low work by proposing SR2N Algorithm declaring some local and global variables with more processing speed in multi user environment. SRNN Algorithm has some important parameters affecting its level of security and speed. By increasing the modulus length plays an important role in increasing the complexity of decomposing it into its factors. This will increase the length of private key and hence difficult to be decrypted without knowing the decryption key. When the length of message is changed then the length of encrypted message is will are selected to obtained larger encrypted message to increase the security of the data. Key Generation, Encryption, Decryption Process : II.a. Key Generation Process: The following steps determine the values of e,d and n. Choose two very large (100+digit) prime numbers p and q. Compute n=p*q Compute phi=(p-1)(q-1) Choose integer e (1<e<phi) such that GCD of (e,phi)=1 Compute secret exponent d (1<d<phi) such that (exd) mod phi=1 Choose Short Range Natural Number U randomly such that U<phi-1 Choose another Short Range Natural Number such that phi>a>U Compute Ua Find d such that e*d mod phi=1 The private key is(n,e,Ua) and the private key (d,a,U) http://www.ijettjournal.org Page 15 International Journal of Engineering Trends and Technology (IJETT) – Volume 31 Number 1 - January 2016 II.b.Encryption Process IV Implementation of SR2N Algorithm Obtains the recipient’s public key (n,e,ua) Represents the plain text message as a positive integer m Computes the cipher text c=(m ua)e mod n Sends the cipher text c to recipient II.c.Decryption Process Use private key (d,a,u) to compute m=(ve c)d mod n where v=uphi-a mod n Extracts the plain text from the integer representative m. III Proposed SRNN Public key Cryptosystem – SR2N Algorithm The SR2N Algorithm is based on SRNN with some modifications. SR2N Algorithm is also public key cryptography algorithm. This modification increases the security of cryptosystem. Key Generation, Encryption, Decryption Process 3.1. Key Generation Process Choose two prime numbers p,q such that (4p+1) and (4q+1) are primes Compute n=(4p+1) * (4q+1) Compute phi=24 pq Choose integer e (1<e<phi)such that GCD of (e,phi)=1 Compute secret exponent d, (1<d<phi) such that (exd) mod phi=1 Choose another short range natural number a such that phi(n)>a>2 Find d such that e*d mod phi=1 The public key is(n,e,2a ) and the private key (n,d,a) 3.2.Encryption Process Obtains the recipients public key (n,e,2a) Represents the plain text message as a positive integer m Computes the cipher text c=(n,e)mod n Sends the cipher text x to recipient Here programs are implemented using java library functions. We have implemented the SR2N cryptosystem in two forms: A console mode implementation, as well as a user friendly GUI Implementation. We focus on the user friendly GUI mode implementation here. We start default values of input file name, encrypt file name, decrypt file name, key_size, message block size or chunk size, prime numbers p and q are used and user have flexibility to change these values when required. If user wants to generate new public and private keys then new frame is appeared to select new keys. Any practical implementation of the SR2NN cryptosystem would involve working with large integers. One way of dealing with this requirement to write our own library that handles all the required functions but we use Big integer library (Java) in Java. Here use of natural numbers make it more secure algorithm. V. Comparison Between SRNN Algorithm and SR2N Algorithm Table:1 shows the general comparison between SRNN and our proposed algorithm SR2N we found that by increasing modulus length n security increase, speed decrease and when chunk size m increases both security and speed increases. From key generation point of view SR2N algorithm is bit of slower when compared with SRNN algorithm. From encryption point of view both algorithms are working almost same. In case of SRNN algorithm only one multiplication operation is additional for each chunk calculation. So when chunk size increases we found both algorithms are giving almost same time. From decryption point of view SRNN algorithm is much slower than SR2N algorithm. Overall performance we found that SR2N algorithm provides better security with more processing speed. Sl. No 1 SRNN Algorithm SR2N Algorithm All Values Global 2 Security is less when compare to SR2N Process speed is slow It is best suited for multi-user environment Some Values are Local and some Values are Global. Global Values are p,q,e ,plain text Using package security is more (DOS Shell etc) 3.3.Decryption Process Use private key(n,d,a) to compute m = (ve c) d mod n where v=2phi-a mod n Extracts the plain text from the integer representative m ISSN: 2231-5381 3 4 http://www.ijettjournal.org are Process speed is fast It is also best suited for multi user environment Page 16 International Journal of Engineering Trends and Technology (IJETT) – Volume 31 Number 1 - January 2016 5 Partition possible is not It is possible to utilize for group security & partition Author : V. Conclusion In this paper we have proposed a threshold publickey cryptosystem whose security rests in part on the difficulty of factoring large numbers which not only uses primes but also natural numbers in encryption process. Once the method has withstood all attacks for sufficient length of time it may be used with a reasonable amount of confidence. Currently RSA with modulus length 1024 bits with chunk size 512 bits is better in speed but some weaker in security. In case of SRNN algorithm if we generate randomly small range of natural numbers u and a session to session will be a better solution for balance between speed and security. If we take SRNN with modulus length 1024 bits with chunk size 512 is a feasible solution from speed as well as security. In this way SRNN with modulus length 1024 bits may be a optimize solution which make balance between speed and security. Dr. M. SreedeviM.CA,M.Phil,Ph.D Currently Workin as a Assistant Professor,Department of ComputerScience, S.V.University, Tirupati,A.P since 3rd July 2007 to Till-to-date. REFERENCES [1].”InKesi-Increased Key Size Method in SRNN Public Key Cryptography Algorithm”, K.Sheela, E.George Dharma Prakash Raj Vol.2, Issue,8 August 2013,Pg219-223. [2].“Modified RSA Public Key Cryptosystem Using Short Range Natural Number Algorithm”, Mr.Sonal Sharma, Mr.Jitendra Singh Yadav, Mr.Prashant Sharma, Volume 2, issue 8, August 2012 [3]. “An Efficient Implementation of digital Signature Algorithm with SRNN Public key Cryptography”, Mr.Hemath Kumar, Dr.Ajit Singh, volume-1 issue-1, june 2012. [4]. William Stallings, Cryptography and Network security, pearson Education, hird Edition. AD97 M. Ajtai and C.Dwork, A public-key cryptosystem with worst case/average-case equivalence, Proc.29th ACM STOC (1997), 284-297. [5].Gary C, Kessler “An Overview on Cryptography” June 2010 [6]. Carnegie Mellon Software Engineering Institute “Public key Cryptography”. [7]. A fast implementation of the RSA algorithm using the GNU MP library. By Anirban Banerjee, IIT-Calcutta [8]. Wikipedia, the free encyclopedia: Natural Numbers. [9]. Performance Comaprision, Desion and implementation of RC5 Symmetric Encryption Core using Reconfigurable Hardware by Omar Elkeelany and AdegokeOlabisi Journal of computers, vol.3 No 3 march 2008. [10]. Fast Implementation of RSA 1993. [11].An Efficient Implementation of RSA Digital Signature Algorithm , Young-yu Cao, Chong Fu. ISSN: 2231-5381 http://www.ijettjournal.org Page 17