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in Encryption and decryption same key is use to to convert plan text to cipher and cipher to plan text. so why in public key cryptograpy method sender Encrypt using receiver public key and receiver decrypt using his own private key ?

user207421
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What you initially refer to is symmetric encryption (shared key), which allows 2 entities to communicate securely based on a single shared key that is only known to the two entities. This key can be exchanged several ways, but can't be publicized for obvious reasons.

Asymmetric encryption (public/private key) allows 2 entities to communicate securely as follows:

If one party wants to accept secure (encrypted) information, they need a key that isn't visible to the world (private), but they also have to be able to provide a key to anyone who wants to send encrypted information (public).

So I can give my public key out to the whole world and know the data is secure since only I have the private key, therefore I'm the only one who can decrypt it.

See Asymmetric Encryption in this Microsoft article: http://support.microsoft.com/kb/246071

Matt
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    You may want to point out that the type of encryption the asker is implying is referred to as symmetric encryption, as a point of comparison. – 101100 Dec 10 '12 at 20:58
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Because it wouldn't be secure the other way around, or feasible either. Only the recipient has his private key, so nobody else can use it.

user207421
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