Comparing Asymmetric and symmetric Encryption Systems Public-key systems provide several advantages over private-key (symmetric) encryption methods. First, the combination of keys required to provide private messages between enormous numbers of people is small. n people want to share information with one another, then only n unique public-key pairs are required-far fewer person's equivalent private-key system. Second, key is not a problem. Each public key can be posted anywhere and does not require any special handling to This Third, public-key systems make implementation of digital signatures possible. means that an electronic document can be signed and sent to any recipient with nonrepudiation That with public-key techniques, it is not possible for anyone other than the signer to produce the signature electronically; in addition, the signer cannot later deny signing the electronic document. Public-key systems have disadvantages. One disadvantage is that public-key encryption and decryption are significantly slower than private-key systems. This extra time can add up quickly as individuals and organizations conduet commerce on the Internet. Public-key systems do not replace private-key systems but serve as a complement to them. Publie-key systems are used to transmit private keys to Internet participants so that additional, more efficient communication can occur in a secure Internet session. Figure 10-9 shows a graphical comparison of the hash coding, private- key, and public-key encryption methods: Figure 10-9a shows hash coding: Figure 10-9b depicts private-key encryption; and Figure 10-9o illustrates public-key encryption.