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Conclusions for Chapter 5

Here, we are in a different world.

Before, it was possible to achieve any desired level of security merely by piling complication on top of complication.

Here, we are dealing with techniques that will not work at all for their intended purpose unless left in their pristine simplicity.

The only way to increase security is to use larger-sized numbers as keys. And all the security depends on the difficulty of a specific mathematical problem.

On top of that, these techniques seem only to offer a method of doing something that is useless and dangerous. They let you encrypt a document, so that its secrets are protected, which you are able now to send...to a complete stranger. Why else couldn't you have exchanged a secret key?

It is mainly the slowness of these techniques, and not any security considerations, that lead to them only being used when they are necessary.

A commonly cited advantage of public-key cryptography is that, with N users, only N keys are required for any pair of these users to communicate privately, while N(N-1)/2 keys (of the order of N^2) are required without public-key cryptography.

This does point to a real advantage of public-key cryptography, but the statement as commonly encountered needs some amplification to make this clear.

If N people are actively communicating with each other, each one needs to keep on file the keys of the other N-1 people. This is true whether they are agreed-upon secret keys, or public keys. But without the use of public-key methods, each person needs to have keys for communicating with everyone else at the start. With public-key methods, if each site simply has its own key, plus a certificate with which to demonstrate the authenticity of its public key, any two sites can later begin secure communications. If one site acts as a key server, even using conventional secret key methods, each site would only need initially a secret key to communicate with the key server; however, in that case, any two sites not having previously communicated would be dependent on the availability of the server to establish secure communications. It is in this that the advantage of having fewer keys to contend with actually consists.


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