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# 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.

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.

## RSA

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. ### Encryption

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.

### Decryption

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

P= Cd(mod n)

### Restriction

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.

### Applications

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.

## Diffie-Hellman

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. Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

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