aren't there also "shortcuts" for doing multiplication and thus exponentials?
Discussion
Yes in multiplication. No in division.
In naive multiplication, you repeat addition over and over. So 5 x 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5
You can reduce the number of steps by converting the multiplicand to binary, and then going through the 0’s and 1’s. At each digit, you double the previous number (bit shift), then add it again if the digit is a 1. This shortcut works in elliptic curve math to make multiplication fast.
Division, the inverse operation, has no known comparable shortcut. The security of Bitcoin keys rests on such a shortcut not existing, or at least not being discovered.
Part of the hubbub over quantum computing is that, at sufficient scale, it would offer such a shortcut. The search space of the large prime field is too large for a conventional computer to search. But a sufficiently advanced quantum computer could, in principle, test all values in parallel.
this makes Sense, thanks for sharing
The idea that a singular centralized entity can even perform a meaningful computation with qubits is entirely speculative and has not been proven real.
Not to mention the inherent flawed approach by attempting to compute via a singular computer (node) with a singular observer (miner) and a forced consensus mechanism. Yet physicists still think they can solve decoherence that way 😂.
Bitcoins been here for 16 years; all
UTXOs remain coherent.
Agreed that there is a lot of hype around quantum. Hard to predict if/how/when practical applications will be developed.
The history of cryptographic systems shows that they tend to fall over long enough time scales. For this reason, my baseline expectation (Baysian prior) is that weaknesses in ECDSA will eventually be found and exploited. Whether by conventional computing or quantum.
As long as these weaknesses are discovered and exploited slowly, #Bitcoin can adapt. We can soft-fork in new signature schemes. The bulk of existing UTXOs can be migrated, even if a few get cracked in the process.
A zero-day fast crack of ECDSA would break “your keys, your coins”. This is the only existential threat to Bitcoin that I know of. Fortunately, it seems incredibly unlikely.
Yeah I see it much differently. Bitcoin is the missing language to quantum mechanics; it’s the same system of rules as Bitcoin. Like identical. A peer to peer electron(ic) cash system just is the transactional mechanics which uphold conservation of energy.
There’s a quantum computer, it’s called Bitcoin. There is no second best. The most important thing for a quantum computer to compute is perfect money, that’s already been computed….No one wants to admit we’ve all been wrong for 16 years. We as users compute the meaning to our UTXOs, not central authority.
I believe ECDSA is a mathematical and universal thermodynamic limit. The premise of quantum computing is that you can force close state and brute force coherence via artificial temperature without any recognition of the energy required to for a shared resolution process.
It’s attempting to break Planck Time, yet Bitcoin and Lightning specifically highlights the ability for unresolved states to exist between Blocks. It’s fiat.
Bitcoins biggest vulnerability is in the social domain, where users are convinced to adopt a BIP/hardfork to protect against something the universe fundamentally doesn’t allow. Trust the physicists; we’re too stupid to understand quantum mechanics.