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  Asymmetric or Public-Key-Cryptosystems

Here the keys for encryption and decryption differ. There needs to exist a private key, which is only known to the individual, and a public key, which is published. Every person has her or his own private key that is never published. It is used for decrypting only. Mathematically the different keys are linked to each other, still it is nearly impossible to derive the private key from the public one.
For sending a message to someone, one has to look up the other's public key and encrypt the message with it. The keyholder will use his/her private key to decrypt it. While everybody can send a message with the public key, the private key absolutely has to stay secret - and probably will.

"The best system is to use a simple, well understood algorithm which relies on the security of a key rather than the algorithm itself. This means if anybody steals a key, you could just roll another and they have to start all over." (Andrew Carol)

very famous examples for public-key systems are:

The RSA is probably one of the most popular public-key cryptosystems. With the help of RSA, messages can be encrypted, but also digital signatures are provided.
The mathematics behind are supposedly quite easy to understand (see: http://world.std.com/~franl/crypto/rsa-guts.html.

PGP is a public key encryption program. Most of all it is used for e-mail encryption.
It is supposed to be quite safe - until now.

PGPi is simply the international variation of PGP.

for further information about the RSA and other key-systems visit the RSA homepage:

All of those tools, like hash functions, too, can help to enhance security and prevent crime.
They can theoretically, but sometimes they do not, as the example of the published credit card key of France in March 2000 showed.
For more information see:

Still, cryptography can help privacy.
On the other hand cryptography is only one element to assure safe transport of data. It is especially the persons using it who have to pay attention. A key that is told to others or a lost cryptographic key are the end of secrecy.

browse Report:
-3   So what does cryptography mean?
-2   some essential definitions
-1   Key-Systems
0   Asymmetric or Public-Key-Cryptosystems
+1   Steganography
+2   Digital Signatures, Timestamps etc
+3   Another Question of Security