Quote from: Mezzmarr on January 21, 2014, 06:47:26 PM

There are at least three theories I've come across to not re-use [addresses].

1. Once a key is used, it is technically part of the block chain, and while it may be encrypted, the fact is hackers could work enormous calculations to crack it. The reason your bank login is safer, is your bank will likely allow three attempts and lock it down. By comparison, anyone can download the blockchain and run infinite cracks to dissever the private key data, possibly enabling theft. Keep in mind, hackers do not need your address, only the private key which contains your public address within it.

Your address becomes a part of the blockchain as soon as you receive bitcoins at the address. It doesn't matter if you "re-use" it or not. Fortunately the private keys are protected by 3 layers of cryptography (and no encryption at all).

To calculate a private key from a bitcoin address:

You would first have to figure out a way to reverse the RIPEMD-160 hash function. A bitcoin address is really just a representation of the output of a RIPEMD-160 hash on a 256 bit number. Therefore, you have to find a 256 bit number that results in the bitcoin address when you perform RIPEMD-160 on it.

Next, you would have to figure out a way to reverse the SHA-256 hash function. The 256 bit number that is hashed with RIPEMD-160 is the output of a SHA-256 hash on a 256 bit public key. Therefore, you have to find a 256 bit public key that results in the desired 256 bit hash.

Finally, you would have to figure out a way to reverse the ECDSA digital signature algorithm when using the Secp256k1 curve to calculate the private key from the public key.

At the moment there is no known way to reverse ANY of those three functions, so it doesn't really matter how many attempts the hacker uses.

Again, the address is available on the blockchain as soon as you receive bitcoins, so you don't get any protection against knowledge of your bitcoin address by avoiding re-using addresses.

Quote from: Mezzmarr on January 21, 2014, 06:47:26 PM

2. Once you transmit your key over the internet to "use" it legitimately in the blockchain to send Bitcoin, although encrypted, it is subject to capture and hacking.

Your private key is not "transmitted" over the internet to send bitcoins (not even encrypted), so it is not subject to capture or hacking.

Quote from: Mezzmarr on January 21, 2014, 06:47:26 PM

3. With common virus distributed key stroke loggers (etc.) your copy and paste of the private key to use it, could be detected compromising your wallet security.

If you are using a proper bitcoin wallet (such as Bitcoin-Qt, Electrum, Armory, MultiBit, etc), then you should never have to enter your private key. The wallet should have created it, and should use it without your even needing to know what it is. As such, a keylogger shouldn't have access to it. A virus could access wherever the wallet stores the private keys, but it can do that even if you don't re-use addresses. Therefore avoiding re-using addresses does not protect you from viruses.

Quote from: Mezzmarr on January 21, 2014, 06:47:26 PM

Again, all theories,

All theories that are based on imagination and a complete lack of understanding about how bitcoin works. While your advice ("Don't re-use addresses") might be good advice, your reasoning is flawed and unconvincing.