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I would say in this order: 1. DFI - DfiStarter Loan Platform (DLP) supports all Dfinity assets (D-Assets), giving traders the ability to access a wide range of credit types quickly and easily. 2. OCEAN - Unlocking the true potential of data requires a decentralized and secure infrastructure, which is what Ocean Protocol's OCEAN token aims to provide. It has the potential to empower individuals and businesses to harness the value of data in a transparent and privacy-preserving manner. 3. CARD - Cardstack is a full-stack technology framework with numerous open-sourced components. They are trying to make Web3 payments without gas fees and confirm each amount with your Face ID while keeping track of all transactions in your activity history. This is my fully underpriced gem bag at the moment. :)
> you just have to beat the Discrete Logarithm Problem. DLP for finite-field elliptic curves, to be exact, which may make a difference in how hard it is, assuming the solution isn't more general.
Of course Bitcoin can be hacked... you just have to beat the Discrete Logarithm Problem. Unlikely, but theoretically possible. But to be fair, beating DLP also means all internet security is gone. Usually when people ask such a question, I'm happy to answer, but I end up telling them that it's battle-tested. That's the best guarantee we have so far.
You're only focussing on a brute-force attack, which works by simply trying private keys until you hit the right one. That is not how one would break a private key in practice at all. Algorithms like Pollard's rho for discrete logarithms can compute a private key from a public key in roughly 2^128 steps. That's still a tremendously long time, but still immensely much faster than the 2^256 steps needed for a brute force attack. > A 256 qubit Quantum computer could hack Bitcoin in seconds. You need far more qubits than just the size of the curve to break DLP on a quantum computer (a few thousand logical qubits, if memory serves me right).