I guess I just strip it further back to the assumption that PQ sigs are even needed. My whole argument is that we need to verify the assumption of CQC again based on the physics Bitcoin demonstrates l...
if the compute and data size cost can be brought down to a reasonable distance from the elliptic curves, then it's a minimal cost for a guaranteed defense against successful building of a computer that can run shor's algorithm. it may not even be quantum computers that end up being able to run that algorithm, and the stickiness of the idea that you need qbits to do it, is not necessarily the case.
just look at what google did with systolic memory arrays. von neumann's computer architecture model has been dead since the introduction of parallel processing at commodity scale anyway.
there is always a possibility that someone will figure out a novel combination of materials that you can print onto regular silicon the same way as chips are made now, that provides a qbit that works well enough that a powerful cooler lowers teh noise level down to the point where it actually works.
not only that, the possibilities for novel geometries in conventional processors enabling thousands of small parallel compute units that specifically are built to run shor's algorithm is also possible, by making an ASIC for the job.
so, it's simply not the case. shor's algorithm has proofs. it just is currently impossible to implement a circuit that does it at sufficient scale or precision. like every technological advance that has ever happened before, it is probably one accidental discovery in some obscure little research lab somewhere in the boonies away from being a solved problem. it's not just the big expensive guys who are going to do it. look at AI itself - deepseek proved you can train LLMs on a fraction of the compute that was previously required. now moonshot has proven that you can lower the compute cost substantially with a pipelining system. what next? i mean, AIs could even stumble onto a way of shortcutting the computation of elliptic curve signatures such that it goes from geologic time per processor core to the point where a conventional supercomputer can undo pubkey derivation. it could happen tomorrow. it probably will happen, one way or another, by circuitry or by algorithm, and the more AIs we have the more likely it is to happen.
so, yeah. shor's algorithm is a thing. quantum may not be. the two things can be true at the same time.
just look at what google did with systolic memory arrays. von neumann's computer architecture model has been dead since the introduction of parallel processing at commodity scale anyway.
there is always a possibility that someone will figure out a novel combination of materials that you can print onto regular silicon the same way as chips are made now, that provides a qbit that works well enough that a powerful cooler lowers teh noise level down to the point where it actually works.
not only that, the possibilities for novel geometries in conventional processors enabling thousands of small parallel compute units that specifically are built to run shor's algorithm is also possible, by making an ASIC for the job.
so, it's simply not the case. shor's algorithm has proofs. it just is currently impossible to implement a circuit that does it at sufficient scale or precision. like every technological advance that has ever happened before, it is probably one accidental discovery in some obscure little research lab somewhere in the boonies away from being a solved problem. it's not just the big expensive guys who are going to do it. look at AI itself - deepseek proved you can train LLMs on a fraction of the compute that was previously required. now moonshot has proven that you can lower the compute cost substantially with a pipelining system. what next? i mean, AIs could even stumble onto a way of shortcutting the computation of elliptic curve signatures such that it goes from geologic time per processor core to the point where a conventional supercomputer can undo pubkey derivation. it could happen tomorrow. it probably will happen, one way or another, by circuitry or by algorithm, and the more AIs we have the more likely it is to happen.
so, yeah. shor's algorithm is a thing. quantum may not be. the two things can be true at the same time.
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