Analysis Of RSA Algorithm Communications Essay

Analysis Of RSA Algorithm Communications EssayTo protect and wrap up data from malicious labializeer and irrelevant mankind is the fundamental prerequisite of a security system. So for this reason for hiding data legion(predicate) cryptographic primitives like symmetric and unsymmetrical cryptography, digital signatures, hash functions etcetera The symmetric cryptography consists of same appoint for write in codeing and also for decrypting the data. Where as lop alignd cryptography takes advantage of a pair of underlyings to figure and decrypt the message. These blushers ar habitual strike and a private place. The pro nominate which is distributed to other and which is publicly known is known as a public key and the key which is kept secret is known as private key. These dickens keys argon needed simultaneously both for encrypting and decrypting the data. Public key will encrypt the data where as private key is used to decrypt the data. crooked cryptographic shoul d satisfy undermentioned(a) properties. They beKey generation unconscious process must be computation aloney efficient.By using the public key of the liquidator the seter must be able to process the fancy text for any assumption message.By using the private key the decryption of cipher text into gauze-like text should be through by the receiver.It will be impossible to compute like encrypt or decrypt the data with extinct either of the key.RSA was designed by Ronald Rivest, Adi Shamir, and Len Adleman. It is an asymmetric cryptographic technology. As in asymmetric cryptographic encryption the public key is known by everyone where as the private key is kept undisclosed. For decryption of data which is encrypted with the public key, private key must just now be used. Integers between 0 to n-1 where n is the modernisticulus are taken as cipher and plain text. This n is gener all(prenominal)y 1024 bits. But the suggested length of n is 2048 bits instead of 1024 bits because it is no farsighteder secure.Algorithm of Key generationThe following stairs describe how a set of keys are generated.Two distinct prime numbers are selected which are not equal. Say p and q. this numbers are of same bit length.Determine modulus n where n=p.qProcess or calculate (pq) =(p1)(q1). Here is totient.Select an integer which is public exponent e, such that 1Calculate d. This scum bag be cipher by using modular arithmetic. This should satisfy de=1. Now this ed-1 should be every bit divided by (p-1)(q-1) .Here (n,e) is the public key which is used for encryption and (n,d) is a private key which is used for decryption. Encryption The following steps describe the how encryption is through with(p) in RSA algorithmic rule. It is illustrated with an example where in 2 imaginary characters are described Alice and Bob. As we know that public key is (n,e) this is transmitted by Alice to Bob by keeping her private key secret. A message say M is wished by Bob to send to Alice . Before sending the message M it is converted into an integer 0Get the public key which is (n,e)Plain text integer is delineate by m.Calculate cipher text as shown c=me zipper text c is send to the receiver.Decryption Now when Alice receives the message displace by Bob, she regains the original message m from cipher text c by utilizing her private key exponent d. this can be done by cd=m (mod n). Now she can recover M once she regains m by using Padding aim. This is shown as cd = (me)d = med (mod n). Since , med = m1+kq(n) =m(mq(n))k =m (mod n) . By this we get the original message back. This can be shown in following steps.Private key (n,d) is used by receiver to calculate m=cd mod n.The plaintext m is extracted.Computational issues of RSA pick of the two prime numbers p q In the very scratch line step p is selected from a set of hit-or-miss number. After this it is ensured that p is odd by setting its highest and lowest bit. Finally p is do prime by applying a Miller Rabi n algorithm. Choosing the value of e By choosing a prime number for e, the mathematical equation can be satisfied. That is gcd(e,p-1) = q. Among these three numbers which are 3, 17 and 65537 e is chosen for truehearted modular exponentiation. Calculating the value d It is determined by leng then(prenominal)ed Euclidean Algorithm which is equivalent to d = e-1 (mod q(n)). Modular exponentiation algorithm This step of RSA is calculated by following mathematical equation AB mod n = ( Security of RSARSA cryptosystems security system is not so perfect. Many attacks are present like Brute Force attack, clipping Attack, chosen Ciphertext attack and Mathematical attack are some bragging(a) attack. Brute Force Attack In this attack the attacker figures all possible mode of combinations to condition the private key. If the length of the key is long then it will be difficult for Brute force attackers to break the key as the possible combinations will exponentially increases rather then linearly. RSA uses a short secret key to avoid the long computations for encrypting and decrypting the data. If the key is long the process will become little slow because of these computations. Since RSA uses a short secret key Bute Force attack can slowly break the key and hence make the system insecure. Mathematical Attacks Since RSA algorithm is mathematical, the most prominent attack against RSA is Mathematical Attack. In the following way an attacker can attack the mathematical properties of RSA algorithm.* By finding out the values of p and q which are prime factors of modulus n, the (n)= (p-1)(q-1) can be found out. By finding out this it will be easy to find d = e-1(mod (n)). d = e-1(mod (n)). Can be directly calculated by determining the value of totient (n) without figuring the values of p and q.d can be figured out directly without first collusive the (n).This attack can be circumvented by using long length of key. By doing this it would be difficult to find out pri me factors. That is the reason why it was recommended to use size of modulus as 2048 bits. Timing Attack one of the side channel attack is time attack in which attackers calculate the time variation for implementation. Attackers can easily determine d by calculating the time variations that take place for computation of Cd (mod n) for a given cipher text C. Many countermeasures are developed against such timing attacks. Following explains the way which this attack can be counteractedIf the time for all computations is made constant this attack can be counteracted but the hassle in doing this is it can degrade the computational efficiency. By artificially viewing noise to the attacker which can be produced by including a random delay to the exponentiation algorithm. This noise is virtual but appears real to the attacker.If we cover a random number to the cipher text it will hold on the attacker from bit by bit scrutiny.Chosen Ciphertext Attack RSA is hypersensitized to chosen c ipher text attack due to mathematical blank space me1me2 = (m1m2)e (mod n) product of two plain text which is resultant of product of two cipher text. For example c = me (mod n) which is cipher text is decrypted in following steps Calculate x = (c x 2e) mod n.Receive y = xd (mod n) by submitting x as a chosen cipher text.multiplicative property is then applied which is x = (c mod n) x (2c mod n) = (mc mod n ) x (2c mod n) = (2m)c mod n. By this attacker can calculate m by using y = (2m). By padding the plain text at the implementation level this simple mindedness can be easily solved. Several mutants of RSA cryptography standard are been implemented. PKCS Public Key Cryptography standards are in style(p) version. The previous version was proven to be porn to Adaptive Chosen Ciphertext attack (CCA2). This adaptive chosen cipher text can be prevented by latest version which is Optimal Asymmetric Encryption Padding (OAEP). Bellare and Rogway introduced this OAEP. To process the pla in text before encryption the OAEP uses a pair of casual oracles G and H which is Feistel network. Following two goals are satisfied by OAEP. OAEP embroider PROCEDUREDue to addition of random numbers the probabilistic scheme are being replaced instead of the deterministic encryption scheme. If the attacker is unable to invert the trapdoor one way permutation then the partial decryption of the cipher text is prevented.