# CSC8419 | RSA Algorithm | Information Technology

Home Assignment Answers CSC8419 | RSA Algorithm | Information Technology

RSA Algorithm is generally used for the encryption method in order to encrypt the data before sending it to the network. This algorithm is widely used to secure the sensitive data which is transmitted over an insecure network like the internet. RSA algorithm is also known as cryptosystem for public-key encryption. RSA Algorithm was first described in 1977 by Ron Rivest, Adi Shamir and Leonard Adleman of Massachusetts Institute of Technology. The public key Cryptography encryption is also known as symmetric cryptography, and it involves to mathematically linked keys such as private key and a public key which are required to encrypt and decrypt the data and information. In RSA Algorithm, the public and private key both are used to encrypt a message, and the key opposite to it is used to decrypt the message. Because of this advantage of RSA algorithm, it has become widely used asymmetric algorithm because it provides different methods to ensure the confidentiality, integrity, availability, authenticity and repeatability of electronic communication and data storage over the network. There are many different protocols like OpenPGP, OpenSSL that rely on RSA Algorithm for encryption and digital signature functions over the data to secure it from intruders. RSA Algorithm is also used in the browser to make them unable to make a secure connection over an insecure network like internet and validate digital signature for transactions or transmission of data.

Security of RSA Algorithm

As discussed earlier just security of RSA Algorithm relies on the computational difficulty of factoring large integers. As computing power increases and more efficient factory algorithms are discovered with the time, the ability to calculate larger and larger number also becomes easy. The strength of the encryption is directly related to the key size and increasing the length of the provisions an exponential increase in the strength of encryption method. This will make the data more difficult to breach over the network by the intruders. RSA Algorithm keys are typically 1024 or 2048 bit long, but according to some of researchers and experts, it is believed that 1024 bit keys could be broken in the future. UFO many of the private and government industries are moving to use 2048 Bit long keys in order to provide robust security of encryption to the data of the network. When is security experts are in favour to use RSA Algorithm to implement public key cryptography on the data to make it secure from different threats and issues? Most of hardware and software in modern time are ECC-ready, and the popularity is likely to grow as it can deliver equivalent security with lower computing power and battery resource usage. This makes RSA Algorithm more suitable for the mobile applications.

RSA Algorithm in cryptography

RSA Algorithm is a Cryptography algorithm that means it worked on two different keys that is a public key and private key. The public key is given to the public in order to access Limited amount of data, and the private key is kept private in order to encrypt the data and provide access to the unlimited person.

Example of RSA Algorithm in cryptography

• A client sends its public key to the server request to accept the data.
• the server encrypts the data by using the public key of the client and send the encrypted data to the client to access.
• blind receives the data from the server with encryption and decrypt the encrypted data with the use of a public key.

In RSA Algorithm, no third party except the browser can decrypt the data which is transmitted between the client and server. The main reason behind the development of RSA Algorithm is factorization of large integers. The public consists of two numbers in which one number is a multiplication of two large prime numbers and in private key is obtained from same prime numbers. Therefore, the strength of cryptography or encryption in RSA Algorithm totally lies on the strength of key size. Larger the number of key size battle the encryption security to the data.

Generation of public and private key in RSA Algorithm

Public key

• Select two prime no's. Suppose P = 53 and Q = 59. Now First part of the Public key: n = P*Q = 3127.
• We also need a small exponent say e: But e Must be
• An integer.
• Not be a factor of n.
• 1 < e < Φ(n) [Φ(n) is discussed below], Let us now consider it to be equal to 3.
• Our Public Key is made of n and e

Private key

• We need to calculate Φ(n) : Such that Φ(n) = (P-1)(Q-1) so, Φ(n) = 3016
• Now calculate Private Key, d : d = (k*Φ(n) + 1) / e for some integer k For k = 2, value of d is 2011.

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