Give a clear explanation of RSA cryptography and why it works. Solution RSA stands for Rivest-Shamir-Adleman cruptography, that is an internet incryption and authetication system that uses two mathematical keys, one public that can be shared publically and one private that is kept secret. It in both key can encrypt a message . If public key encrpts a message, private key decript it or vice versa and because of this feature only, RSA is widely used asymmetric algorithm now -a-days . This asymmetry is based on practical difficulty of product of two large prime numbers, called factoring problem. In it user uses these two prime numbers to create and publish a public key that has an auxillary value also. These prime numbers are kept secret. And this publishing method is used to encript any message, if key is large enough then sufficieint knowlege of prime number is necessary to decode the messay. Thus this system ensures confidentiality, integratiy, autheticity and non-reputability of data that is cummunication electronically and data storage.Thus it is use to protect information travelling back and fourth over the net. Thus RSA uses following four steps : key generation, key distribution, encription and decription. Why RSA works : Here we find the answers of following three questions actually : (i) Why opposite keys are used :In it both key encript the message and if message is to be descripted, then the opposite key that was used to encript it, should be used to descript it also. In it the Identity of the particular person is important. Because of this feature only, services like elctronic voting ,mix nets and digital signature are so widely used. (ii ) Why RSA satisfies the correctness equation : This equation states that ciphertext c that originates from message m should be equal to m after decryption. Or decrypting the ciphertext must product the original message. (iii) Why to use inverse of a key to calculate with respect to Totient : RSA works on the fact that it is difficult to deduce the given secret what is public and reason is that deducing what is secret from what is public, can not be impossible because security relies upton a problem that is considered hard..