Elliptic Curves in Public Key Cryptography

Elliptic Curves in Public Key Cryptography: The Diffie Hellman Key Exchange Protocol and its relationship to the Elliptic Curve Discrete Logarithm Problem Public Key Cryptography Public key cryptography is a modern form of cryptography that allows different parties to exchange information securely over an insecure network, without having first to agree upon some secret key. The main use of public key cryptography is to provide information security in computer science, for example to transfer securely email, credit card details or other secret information between sender and recipient via the internet. There are three steps involved in transferring information securely from person A to person B over an insecure network. These are encryption of the original information, called the plaintext, transfer of the encrypted message, or ciphertext, and decryption of the ciphertext back into plaintext. Since the transfer of the ciphertext is over an insecure network, any spy has access to the ciphertext and thus potentially has access to the original information, provided he is able to decipher the message. Thus, a successful cryptosystem must be able encrypt the original message in such a way that only the intended receiver can decipher the ciphertext. The goal of public key cryptography is to make the problem of deciphering the encrypted message too difficult to do in a reasonable time (by say brute-force) unless certain key facts are known. Ideally, only the intended sender and receiver of a message should know these certain key facts. Any certain piece of information that is essential in order to decrypt a message is known as a key. A key(s) specifies the particular function that transforms the original message into ciphertext and vice versa. Public key cryptography relies on two keys, a

private key and a public key. The public key is published in a place where anyone has access to it. However, each individual person or computer also chooses a private key that should

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