An asymmetric-key (or public-key) cipher uses two keys: one private and one public. We discuss two algorithms: RSA and Diffie-Hellman.

**Asymmetric-Key Cryptography**

An asymmetric-key (or public-key) cipher uses two keys: one private and one public. We discuss two algorithms: RSA and Diffie-Hellman.

The most common public key algorithm is RSA, named for its inventors Rivest, Shamir, and Adleman (RSA). It uses two numbers, e and d, as the public and private keys.

Anyone who needs to send a message to Bob can use name *e.* For example, if Alice needs to send a message to Bob, she can change the message, usually a short one, to an integer. This is the plaintext. She then calculates the ciphertext, using *e* and *n.*

C=pe(mod n) Alice sends C, the ciphertext, to Bob.

Bob keeps Ð¤ and *d* private. When he receives the ciphertext, he uses his private key *d* to decrypt the message:

*P= *Cd(mod n)

For RSA to work the value of *P* must be less than the value of *n.* If *P* is a large number, the plaintext needs to be divided into blocks to make *P* less than *n.*

Although RSA can be used to encrypt and decrypt actual messages, it is very slow if the message is long. RSA, therefore, is useful for short messages such as a small message digest or a symmetric key to be used for a symmetric-key cryptosystem. In particular, we will see that RSA is used in digital signatures and other cryptosystems that often need to encrypt a small message without having access to a symmetric key.RSA is also used for authentication.

RSA is a public-key cryptosystem that is often used to encrypt and decrypt symmetric keys. Diffie-Hellman, on the other hand, was originally designed for key exchange. In the **Diffie-Hellman **cryptosystem, two parties create a symmetric session key to exchange data withouthaving to remember or store the key for future use. They do not have to meet to agree on the key; it can be done through the Internet.

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Computer Networks : Application Layer : Asymmetric Key Cryptography |

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