# Difference between revisions of "Pretty Good Privacy"

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<li>At the very beginning, when Alice and Bob initially exchanged the key, the exchange could have been transparently intercepted by a third party (assume Alice and Bob were not using a secure channel to exchange the key because that is precisely what we are trying to build!). With a stolen key, a third party can eavesdrop on Alice or Bob, and even pretend to be Alice or Bob. | <li>At the very beginning, when Alice and Bob initially exchanged the key, the exchange could have been transparently intercepted by a third party (assume Alice and Bob were not using a secure channel to exchange the key because that is precisely what we are trying to build!). With a stolen key, a third party can eavesdrop on Alice or Bob, and even pretend to be Alice or Bob. | ||

− | <li>It is | + | <li>It is unwieldy for large groups of people to communicate privately, since the number of keys is polynomial with the number of people (recall the number of edges in a complete graph of ''n'' nodes): |

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## Revision as of 14:39, 24 June 2013

## Motivations

**Symmetric cryptography**—Alice wants to send Bob a secret message. They both agree on a single password to use as an encryption/decryption key. Alice can use that key to encrypt data to send to Bob, and Bob can use that key to decrypt data received from Alice. Mathematically, a symmetric cipher is a one-to-one function that is easily invertible—apply the function to encrypt data, or apply its inverse decrypt data. The key describes the characteristics of the function; without the key, one cannot determine the function or its inverse.

Symmetric cryptography has some disadvantages:

- At the very beginning, when Alice and Bob initially exchanged the key, the exchange could have been transparently intercepted by a third party (assume Alice and Bob were not using a secure channel to exchange the key because that is precisely what we are trying to build!). With a stolen key, a third party can eavesdrop on Alice or Bob, and even pretend to be Alice or Bob.
- It is unwieldy for large groups of people to communicate privately, since the number of keys is polynomial with the number of people (recall the number of edges in a complete graph of
*n*nodes):# people # keys 2 1 3 3 4 6 5 10 6 15 n n(n-1)/2

**Public-key (asymmetric) cryptography**—