There is a sense of romanticization of "analog" computing. With air/fluids, with all kinds of techniques. This is nothing new as Scott Aaronson points out. Usually, these ideas tend to be novel (cool), but almost like one of those new perpetual machine ideas we constantly keep hearing about.
Quoting Scott:
> It’s important to realize that the idea of solving NP-complete problems in polynomial time using an analog device is far from new: computer scientists discussed such ideas extensively in the 1960s and 1970s. Indeed, the whole point of my NP-complete Problems and Physical Reality paper was to survey the history of such attempts, and (hopefully!) to serve as a prophylactic against people making more such attempts without understanding the history. For computer scientists ultimately came to realize that all proposals along these lines simply “smuggle the exponentiality” somewhere that isn’t being explicitly considered, exactly like all proposals for perpetual-motion machines smuggle the entropy increase somewhere that isn’t being explicitly considered.
With the exception of Quantum Computers, but in limited cases, quoting Scott:
> (Incidentally, quantum computing is interesting precisely because, out of all “post-Extended-Church-Turing” computing proposals, it’s the only one for which we can’t articulate a clear physical reason why it won’t scale, analogous to the reasons given above for memcomputing. With quantum computing the tables are turned, with the skeptics forced to handwave about present-day practicalities, while the proponents wield the sharp steel of accepted physical law. But as readers of this blog well know, quantum computing doesn’t seem to promise the polynomial-time solution of NP-complete problems, only of more specialized problems.)
From listening to Scott for many years, I don't have the expertise in this area to say it definitively, but most likely, your cool new analog computing idea isn't going to break the RSA anytime soon ;)
The suggestion is not an analogue computer at all. Did you read the article? But a digital computer produced from a different medium. Microfluidics is already being used in a really serious way in engineering automation of most biomolecular tech. Especially the latest generations of DNA sequencing machines. There the advantage of fluidics is you can mix and match the macroscopic logic domain with biomolecular function in a liquid phase.
First, cracking RSA is not believed to be NP complete. Second, even if it were, an analog computer could in theory provide a large constant factor speed up that would break current key sizes. But still, it seems very unlikely that an analog computer breaks RSA.
Quoting Scott:
> It’s important to realize that the idea of solving NP-complete problems in polynomial time using an analog device is far from new: computer scientists discussed such ideas extensively in the 1960s and 1970s. Indeed, the whole point of my NP-complete Problems and Physical Reality paper was to survey the history of such attempts, and (hopefully!) to serve as a prophylactic against people making more such attempts without understanding the history. For computer scientists ultimately came to realize that all proposals along these lines simply “smuggle the exponentiality” somewhere that isn’t being explicitly considered, exactly like all proposals for perpetual-motion machines smuggle the entropy increase somewhere that isn’t being explicitly considered.
With the exception of Quantum Computers, but in limited cases, quoting Scott:
> (Incidentally, quantum computing is interesting precisely because, out of all “post-Extended-Church-Turing” computing proposals, it’s the only one for which we can’t articulate a clear physical reason why it won’t scale, analogous to the reasons given above for memcomputing. With quantum computing the tables are turned, with the skeptics forced to handwave about present-day practicalities, while the proponents wield the sharp steel of accepted physical law. But as readers of this blog well know, quantum computing doesn’t seem to promise the polynomial-time solution of NP-complete problems, only of more specialized problems.)
https://www.scottaaronson.com/blog/?p=2212
From listening to Scott for many years, I don't have the expertise in this area to say it definitively, but most likely, your cool new analog computing idea isn't going to break the RSA anytime soon ;)
Further reading: https://www.scottaaronson.com/democritus/lec14.html