2 Public-key Cryptography

Secure transmission of private information is a crucial issue in today’s highly computerized world. Cryptographic algorithms are used to provide privacy of message transmission and to certify authenticity of sender and/or receiver of a message and message integrity as well as undeniability of transmitted messages (Menezes et al., 1996). The message that is sent by the sender is called the plaintext, the secured message is called the ciphertext. To get the ciphertext, the plaintext is encoded by the sender. The receiver reconstructs the plaintext from the ciphertext by decoding. For encoding and decoding so-called keys are used (Koblitz, 1994, p. 55). In the simplest setting, sender and receiver have agreed on a common private key, which is kept secret. This is called symmetric key cryptography. The secret private key is utilized for encoding and decoding messages sent between the two parties. For encoding the plaintext is XOR-ed with the secret key. The decoding is done in the same way using the ciphertext and the secret key on the receiver’s side (Menezes et al., 1996, p. 15). To be specific, if for example the plaintext message is given by the bit string 10011101 and the secret key is 11011100, the ciphertext is then given by 01000001. By using XOR-operations with ciphertext and key once more the plaintext is returned. Note that the XOR operation between two bit is defined as follows: 0 + 0 = 1 + 1 = 0, 1 + 0 = 0 + 1 = 1. If key length and length of plaintext do not coincide, the plaintext may be blocked. This leads to the concept of block ciphers (Menezes et al., 1996, p. 223). Symmetric key techniques generally can be implemented very efficiently. The corresponding algorithms are very fast. The problem, however, lies in the fact that two parties must have agreed on a common key before they can start to communicate and exchange messages. This would be highly impractical, for example, for transactions in electronic commerce (Menezes et al., 1996, p. 31).