it sounds like you can share your public address, and there will be no security breach if you keep the private key to yourself.
That is correct.
Frankly speaking, how are they intending to build a secure digital network currency if the encryption method is due for a breach within its lifetime?
There is no guarantee that ECDSA will ever be "breached", but there is no guarantee that it won't either. That is the nature of cryptography. A cryptographic function is secure until someone finds a way to make it insecure, then people move to a newer secure function. Fortuntately, as long as it is used properly, bitcoin layers 3 different cryptographic functions between your private key and your public address. It is extremely unlikely that a weakness will be found in all three functions simultaneously. This means there is time to replace a function in the protocol while bitcoins are still protected by the other two functions. Bitcoin can there fore grow and change to adapt to new cryptographic discoveries.
So my question then is, couldn't you use an offline wallet and use something like Armory to conduct offline transactions using proprietary keys? Wouldn't this prevent both your public and private keys of your offline saving wallets from ever being exposed?
Describe these "offline transactions"? Explain exactly how ownership of the bitcoins (which reside as an output on the blockchain) will be transfered to another individual using your "offline wallet and something like Armory" without the public key being exposed?
Another idea: couldn't I just open up a separate offline wallet on my offline PC to send small funds to so that those bitcoins can be used freely?
Send small funds from where?
This also preserves the secure state of my offline savings wallet, correct?
That depends. Will you be spending/sending any of the bitcoins that are received at that offline savings wallet? Or will it be exclusively receiving bitcoins. As soon as you try to get any bitcoins out of that offline savings, you are back where we started.
I am not a big fan of paper, they are basically like paper money to me.
Which has worked very well for many, many years. What is it about paper money that you don't like?
In my eyes, it's tantamount to keeping cash in my mattress,
Well, I'd hope you'd secure it a bit better than that.
or a safe which will targeted by hoodlums,
So, you'd rather that the hoodlums attack you directly to get at your bitcoins than to attack a safe? You prefer to be beaten to a bloody pulp and tortured beyond belief for the sake of some money? Personally, I'd rather they just took my money and moved on. My life, and health are far more valuable to me than any amount of money could ever be.
or keeping it at a bank deposit, which I thought was the direction we were trying to steer away from with this new paradigm shift.
A paper wallet is absolutely nothing like that. Where did you get that idea?
Or it could just get lost or destroyed by fire.
And your memory can't get lost or destroyed by fire? or illness? or fall or other injury? Just store two copies in two separate secure locations.
I am a big fan of memory, that is the securest method in my opinion.
I can tell.
As I'll explain later, I think my brainwallet passphrase is going to be amazing,
And I disagree.
I can share the brainwallet with my trusted family members in case anything happens to me.
And you can be 100% that none of them will go against your wishes behind your back and write it down so they don't forget it?
I agree, vast majority, but my circumstances put me in the category of those who will benefit most from a brainwallet, while significantly mitigating its risks.
You're just not like "other people", right?
What I meant originally was that if my passphrase does get hacked, no one will ever be able to support a brainwallet ever again once I've shared my compromised passphrase on the internets.
I suspect you are wrong about that, but I've already indicated that I'm already generally against the idea of a brain wallet in most cases anyhow.
As mentioned earlier, I could use offline transactions, or set up another wallet as a middle man.
Which most likely demonstrates that you have no idea what you are talking about and are just making stuff up in hopes that you can do what you want without someone telling you that it is a bad idea.
One technique I've seen is someone type a bunch of BS letters over 1000 characters long into a brainwallet to generate keys. That seems pretty secure.
No. It really doesn't. That is a bad idea. You want a good idea? Grab a handful of very well balanced dice (perhaps from your local casino?). Roll the dice a bunch of times (until you've rolled at least 62 dice) and then convert from base 6 to get a private key.
So I learned after all of this, is to never let my offline savings wallet's public address ever hit the network. A pain in the ass, but good to know.
So you've learned nothing then? You still haven't even bothered to learn the difference between an address and a public key? Why do I even bother if you aren't going to make an effort?
I guess my only other question is: should I just memorize the friggin' private key?
Sure, you could do that if you like. How will you generate the private key? And will you memorize a new private key every time you spend funds?