Essentially they describe how if someone where to build a big enough computer to crack bitcoin in 2 minutes, say, maybe with a large "quantum computer", the bitcoin code can be upgraded to then make it near impossible again for that new machine to crack it. The code can always stay ahead of the hardware.
Nice to hear from someone who has also studied quantum mechanics though I agree with your analysis and input. Although with your last statement
about the code always being able to stay ahead of the machine is that necessarily true? As far as I know there aren't too many algorithms that would be suitable for use with Bitcoin because of some of the limitations and not too many have been developed in recent years however we seeing technology from a quantum computing aspect continue to develop at a rather impressive rate.
Yes, this will always be true. The concepts in computer science are clear. So it goes something like this:
You cannot write code for advanced hardware that doesn't exist yet. You can't run some fancy new hardware without the software to control it. So, the hardware is built first, then code can be written for it. But this new code for the fancy new hardware will surpass the hardware at some point. Maybe its best to explain with an example:
Some new machine is built but the largest number its register's can hold is 1,000,000. So we can't add two numbers, or multiply two numbers if the result is greater than 1,000,000. Along comes some code that can use linked lists to create bigger numbers. One link in the list can hold a number's large lower portion "900,000", the next link can hold the number's upper value of "1,000", put the two links together to get: "1,000,900,000". ... and the algorithms do the rest of adding, multiplying, manipulating those larger numbers even though the hardware can only handle numbers no greater than 1,000,000. ... And so, we've made code that has surpassed the hardware's capabilities.
I can't go into the details of bitcoin's algorithms since I don't work with those, but some of the comments made by others are easy enough to follow. I've read that bitcoin uses the family of SHA-2 algorithms, and at some point they can upgrade to the family of SHA-3 algorithms. ... The total number of private bitcoin addresses is 2^160, which is close to 2^256 (for discussion purposes). This number is close to 10^75, and for comparison there are about 10^78 atoms in the known universe. This gives a clue as to how large the search space for locating a private address can be.
From the thread I posted above: It would be possible to build a machine that can search for and find a non-empty private address.
If you build a Bremermann computer the size of Earth, you could crack a key in 2 minutes.
given the 2^256 search space. But if we simply made the search space bigger, say: 2^512, then we'd be back to requiring the Bremermann computer the size of the Earth to take as long as the age of the universe to try and find a private key.
My counter argument would be that a lot of time, money and energy is being put into quantum computers right now because its both exciting and useful however because currently there's nothing capable of breaking the majority of encryption algorithms out there we aren't necessarily looking to improve upon that yet because the current ones are good enough. Do you think the closer we get to quantum computers becoming a threat to encryption the more work that will be put into developing suitable algorithms?
Most of the work for the next levels of algorithms has already been done. What is left to do is a bit more testing, and then incorporation into the bitcoin core, this is not trivial. But with the current state of computers its not really necessary right now, there is plenty of time to get it right.
From my first comment above you can gather that I think the whole "quantum computer" thing is a bit of a silly pursuit, since current classical computers will eventually catch up to the proposed theoretical properties of quantum computers. But silly pursuits can sometimes hit upon new discoveries, and new technologies, so its not a total waste of time.
