user7091: I've been reading about how BitCoin works for a few weeks now - and I'm trying to understand under-the-hood how the cryptography works. 
So i'll explain what I know at the moment - and if someone could clear it up for me? Or provide links to papers that may explain it a bit better (I've read the original bitcoin.pdf, but it is a bit vague)
Scenario:
I have an address (pk, sk).
I have a previous transaction tx that contains 1 bitcoin.
I create a new address (pk', sk') that I want to send the bitcoin too.
I hash the new public key pk' with the previous transaction tx such that hash(pk', tx) = h1. 
I sign the hashed transaction h1 using my secret key and some 'randomness' r. Sign"sk"(h1, r)
Then - this gets broadcasted and gets put inside a block by a Bitcoin miner? 

Also, if I was to send two 0.5 bitcoins to pk' I would do the following...
tx1 and tx2 are associated with 0.5 bitcoins. 
I then hash tx1 and tx2 with the new public key pk' such that hash(tx1, pk') = h1 and hash(tx2, pk') = h2. 
I then sign both of these hashes using the following function... Sign"sk"(h1, h2, r) or would it be Sign"sk"(h1,r), Sign"sk"(h2,r'). (different randomness for each signature)

This may be a silly question.. but I have been finding it difficult to get some clarity on how it works. I also understand that some characters (such as i and 0) are not included in the hash - does this refer to base 58 ? 

user4708: You probably would find it helpful to peruse the technical articles on the Bitcoin Wiki.  Here are some starting points based on your questions.
https://en.bitcoin.it/wiki/Address
https://en.bitcoin.it/wiki/Transaction
https://en.bitcoin.it/wiki/Script
https://en.bitcoin.it/wiki/Network
https://en.bitcoin.it/wiki/Block
One concept you did not mention but which is crucial to understanding how it works at a low level is the fact that transactions are verified by running Scripts (see link above).

7091: <p>I've been reading about how BitCoin works for a few weeks now - and I'm trying to understand under-the-hood how the cryptography works. </p>

<p>So i'll explain what I know at the moment - and if someone could clear it up for me? Or provide links to papers that may explain it a bit better (I've read the original bitcoin.pdf, but it is a bit vague)</p>

<p>Scenario:</p>

<p>I have an address (pk, sk).</p>

<p>I have a previous transaction tx that contains 1 bitcoin.</p>

<p>I create a new address (pk', sk') that I want to send the bitcoin too.</p>

<p>I hash the new public key pk' with the previous transaction tx such that hash(pk', tx) = h1. </p>

<p>I sign the hashed transaction h1 using my secret key and some 'randomness' r. Sign"sk"(h1, r)</p>

<p>Then - this gets broadcasted and gets put inside a block by a Bitcoin miner? </p>

<hr>

<p>Also, if I was to send two 0.5 bitcoins to pk' I would do the following...</p>

<p>tx1 and tx2 are associated with 0.5 bitcoins. </p>

<p>I then hash tx1 and tx2 with the new public key pk' such that hash(tx1, pk') = h1 and hash(tx2, pk') = h2. </p>

<p>I then sign both of these hashes using the following function... Sign"sk"(h1, h2, r) or would it be Sign"sk"(h1,r), Sign"sk"(h2,r'). (different randomness for each signature)</p>

<hr>

<p>This may be a silly question.. but I have been finding it difficult to get some clarity on how it works. I also understand that some characters (such as i and 0) are not included in the hash - does this refer to base 58 ? </p>
 4708: <p>You probably would find it helpful to peruse the technical articles on the Bitcoin Wiki.  Here are some starting points based on your questions.</p>

<p><a href="https://en.bitcoin.it/wiki/Address" rel="nofollow">https://en.bitcoin.it/wiki/Address</a></p>

<p><a href="https://en.bitcoin.it/wiki/Transaction" rel="nofollow">https://en.bitcoin.it/wiki/Transaction</a></p>

<p><a href="https://en.bitcoin.it/wiki/Script" rel="nofollow">https://en.bitcoin.it/wiki/Script</a></p>

<p><a href="https://en.bitcoin.it/wiki/Network" rel="nofollow">https://en.bitcoin.it/wiki/Network</a></p>

<p><a href="https://en.bitcoin.it/wiki/Block" rel="nofollow">https://en.bitcoin.it/wiki/Block</a></p>

<p>One concept you did not mention but which is crucial to understanding how it works at a low level is the fact that transactions are verified by running Scripts (see link above).</p>
