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Renovated RSA Cryptosystem for Secure Data Transmission International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 24 (2017) pp. 15179-15186 © Research India Publications. http://www.ripublication.com Renovated RSA Cryptosystem for secure Data Transmission P.Sri Ram Chandra1*, Dr. G.Venkateswara Rao2 and Dr.G.V.Swamy3 1Research Scholar (Computer Science and Engineering Department), Gandhi Institute of Technology and Management (GITAM), Visakhapatnam, Andhra Pradesh, India and Faculty member in Computer Science and Engineering, Godavari Institute of Engineering and Technology (A), Rajahmundry, Andhra Pradesh, India. *Corresponding Author (1ORCID: 0000-0002-9546-1314) 2Associate Professor, Information Technology, 3Professor and Head, Electronics and Physics Department, 1,2,3, Gandhi Institute of Technology and Management (GITAM), Visakhapatnam, Andhra Pradesh, India. Abstract one for key generation, one for encryption, and the other for decryption. They are classified as Symmetric key Cryptographic techniques are the principal means to provide Cryptosystem (same encryption key is used for decryption), information security, RSA (Rivest–Shamir–Adleman) is one Asymmetric key Cryptosystem (different keys for encryption of the first practical public-key cryptosystems and is widely and decryption are used). used for secure data transmission. The first part of this paper describes the functionality of RSA and its attacks, identified Before the introduction of asymmetric-key cryptography by ‘factoring the N’ is the most common one. Now authors have Diffie and Hellman [3], at first both the users has to come up proposed the Renovated RSA (RRSA) cryptosystem through with an agreement in regard of the encryption and decryption the use of Armstrong prime number(r) in addition to the processes there after they can communicate in private with existing two prime numbers (p, q) to generate the public (e) encrypted messages sent between them, said as symmetric key and private (d) keys. The theoretical proof of the newly cryptography. An asymmetric-key cryptosystem is one in developed cryptosystem was shown to ensure the functionality which each user places an encryption procedure E into a of the original RSA not to be disturbed. In the second part of public file, each user has a corresponding decryption this paper, strength of RRSA cryptosystem was analysed over procedure D, the details of which the user does not reveal to size of the variable N, in such a way that it cannot be factored anyone else. The key to ensure the security of asymmetric-key i.e., N with more than 232 decimal digits. The theoretical cryptosystem is for it to be extremely difficult to derive the samples considered as per the algorithm requirements, decryption key from the publicly available encryption key [2]. revealed that the size of the variable N in RRSA can go The cryptosystem developed should ensure the few principles beyond 232 decimal digits by using an Armstrong prime (r) of security like confidentiality, authentication, integrity, non- even with the less number of digits in p, q when compared to repudiation [5]. Considering the data transmission between RSA. A series of algorithms were also discussed to perform two entities A and B, ‘if A ensures that none expect B gets the the calculations involved in the encryption and decryption data’ is termed to be as confidentiality. Integrity states that processes at a faster rate even with several hundred digits both A and B will undergo an agreement such that, none of there in e, d, N. them would tamper the data further [1]. ‘B assures that the Keywords: Cryptosystem, Armstrong prime number, Prime data was sent by A only’ designated as authentication. Non- number, Factorization Complexity, Encryption, Decryption, repudiation does not allow the sender of a message to refuse Co-Prime, Public Key, Private Key, Intruder. the claim of not sending the message [1]. INTRODUCTION THE RSA ALGORITHM We are in the era of business on internet where the computer The vital feature of RSA public-key cryptosystem is that the applications were developed to handle the data related to encryption and decryption procedure are done with two crucial areas like finance, banking, army and government. In different keys - public key and private key respectively. Its transferring such significant data across the network may security is based on the issues like difficulty of the large sometimes get into the hands of the intruders who may tamper number prime factorization, which is a well-known the contents of the data [1]. In this regard the security mathematical problem that has no effective solution [6]. The measures are to be taken to protect the data. Cryptography is following algorithm1 gives the result of RSA [5]. one of the best suitable platforms to ensure secure data transmission where the data encryption and decryption processes are involved with or without a secret key [1]. In cryptography, a cryptosystem is a suite of three algorithms: 15179 International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 24 (2017) pp. 15179-15186 © Research India Publications. http://www.ripublication.com Algorithm 1 milliseconds, or 5027, days to cycle through all possible messages on one computer [14]. Mitigation Step1.Key Generation The simple solution to overcome this attack is to send the Step2: Encryption large messages preferably the size greater than 18 characters Step3: Decryption [14], which in turn the time to cycle all through the plaintext messages grows exponentially. Further this would become an insurmountable task for the intruder to crack the original Procedure for Step1 (Key Generation): message. Select two distinct prime numbers p and q. Calculate N = p * q. Common modulus Calculate ⱷ (n) = (p -1) * (q-1). In common modulus attack, the intruder detects the plaintext message without factoring N or finding the secret decryption Select an integer e whose gcd (ⱷ (n), e) = 1; 1<e< ⱷ exponent d [14]. Imagine a scenario where John would like to (n) send the message M to Alice and Bob individually. To do this Determine d (using modular arithmetic) which Alice gives John her public key (N, e1) and Bob gives John his satisfies the congruence relation .d*e ≡1 (mod ⱷ (n)). d is kept public key (N, e2) where e1 and e2 are relatively prime. The as private key component problem arises because Alice and Bob are both using the same e1 modulus N. John sends C1 = M (mod N) to Alice and C2 = Public key = {e, N}. Me2 (mod N) to Bob. Now suppose an eavesdropper Eve intercepts and . Since , Eve can use the Private Key = {d, N}. C1 C2 gcd (e1, e2) = 1 Euclidean Algorithm to get integers x and y such that 1 = e1x+e2y. Exactly one of x or y will be negative. Without loss of generality assume is negative. Eve can now calculate Procedure for Step2 (Encryption): C = Me mod N. x -1 -x x y (C1 ) (C2) = C1 C2 e1 x e2 y Procedure for Step3 (Decryption): M = Cd mod N. = (M ) (M ) e1x+e2y = M 1 Where, C - Cipher text, M - Message, p and q - Prime = M Numbers, N - Common Modulus, e and d - Public and Private = M (mod N) Keys Respectively. Thus, Eve can detect the plaintext message without factoring N or uncovering the decryption exponent d [14]. The Attacks on RSA public-key Cryptosystem Mitigation The saying "A chain is no stronger than its weakest link" is In order to make the RSA free from this attack, two individual very suitable for describing attacks on cryptosystems. Most of users in the same channel of communication should have the attackers’ instinct is to go for the weakest link of the chain unique modulus value N. which includes key generation, key management, the cryptographic algorithm and the cryptographic protocol. The consequent sections briefly describe the attacks on RSA and Low exponent value for e. the factored values of RSA-N. Most of the times RSA cryptosystem uses the lower exponent value viz., e=3 for making the encryption faster. However, there is a vulnerability that if the same message is encrypted 3 Searching the Message Space times with different keys i.e., same exponent with different One of the appearing weaknesses of RSA is that one has to moduli then the intruder can retrieve the message [17]. give away everybody the algorithm that encrypts the messages. Considering the message space is small i.e., less Mitigation than 9 characters and we are using English as our plaintext Instead of selecting the lower exponent value for e, it is that gives us 269 = 5429503678976 possible plaintext preferred to use the larger exponent value and an efficient messages. If it takes 0.18 milliseconds to encrypt a message computing machine which can do encryption at a faster rate. using RSA 1024, then it should take 434360294318.08 15180 International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 24 (2017) pp. 15179-15186 © Research India Publications. http://www.ripublication.com Man-In-The-Middle Attacks y) (x - y). If (x + y) or (x - y) are not prime numbers, then Fermat’s method can be repeated with those values. A ‘man-in-the-middle’ attack is a kind of active attack where the attacker furtively relays and perhaps amends the For example N =1121, the Fermat’s method starts by conversation or keys between the two entities who believe considering x as square root of N i.e., x≈34. Now construct the they are directly communicating with each other [18]. The table1 with two columns x and x2- N incrementing the value of Mail-Man can listen in our conversations and collect the x by one till the x2- N can be perfect square. information we disclose. He could also fabricate any information in order to take control over the communication channel.
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