user4803: I know each user has a public key and private key. The users signs the transaction with his private key and sends it to a Bitcoin address. What prevents me from claiming his coins? I read something about verification with the private key but I didn't really understand. How does Bitcoin ensure that only the eligible person can spend the bitcoin? More specifically I didn't understand the verify and sign part in Satoshi's paper in the diagram on page 2.
Also from this diagram, how is it that a secret key can act as a key to lock a lock, but the public key can open the lock only but can't lock it back? How is this implemented technically?

user3056: Read about Public-key cryptography and Digital signature.
For bitcoins you need the private key to spend (by signing) the coins that were "sent" to the address associated with a public key.

4803: <p>I know each user has a public key and private key. The users signs the transaction with his private key and sends it to a Bitcoin address. What prevents me from claiming his coins? I read something about verification with the private key but I didn't really understand. How does Bitcoin ensure that only the eligible person can spend the bitcoin? More specifically I didn't understand the verify and sign part in Satoshi's paper in the diagram on page 2.</p>

<p>Also from <a href="http://thumbnails.visually.netdna-cdn.com/bitcoin-infographic_5029189c9cbaf.jpg" rel="nofollow">this diagram</a>, how is it that a secret key can act as a key to lock a lock, but the public key can open the lock only but can't lock it back? How is this implemented technically?</p>
 3056: <p>Read about <a href="http://en.wikipedia.org/wiki/Public-key_cryptography" rel="nofollow">Public-key cryptography</a> and <a href="http://en.wikipedia.org/wiki/Digital_signature" rel="nofollow">Digital signature</a>.</p>

<p>For bitcoins you need the private key to spend (by signing) the coins that were "sent" to the address associated with a public key.</p>
