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((2^128) * (1.38064852 * ((10^(−16)) (ergs / K))) * (298 K)) / ((1361 (W / (m^2))) * (pi * (radius of Earth^2))) =ĭefinitely more on the plausible side, but we're already moving away from 128-bit crypto and there's a staggering number of generous assumptions being made here we aren't going to be getting thermodynamically ideal computers using a significant fraction of the total solar irradiance on the Earth any time soon. Using the same math as that article, but at room temperature, and taking the total solar irradiance on the Earth as an energy source, it would take this long to count up to 128 bits (calculated using Google): Add in the actual cost of compute and it just isn't happening, not in this galaxy.įor 128-bit crypto we can look at a more earthly calculation. There are circa 2^38 stars in the Milky Way, and they're not going to all go supernova.
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You'd need 2^36 supernovas to just count up to 2^256, never mind actually running SHA256.
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The total energy output of a supernova is enough to count up to 2^220, making a lot of generous (invalid) assumptions. However, here's a reference for the same kind of thing: I did the math myself at one point, but I lost the link. 128-bit keys should indeed be phased out entirely (and that seems to be well on the way anyway), and perhaps 256-bit too at some point (even if it's only the very paranoid or very long termers, it's also not big stretch on modern hardware at all, so eh), but fundamentally yes symmetric crypto is fine. Even 2^128 is still ridiculous, and going to a 512-bit key brings us right back to 2^256 which is impossible. Obviously this is utterly trivially countered by doubling the exponent.
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So a 128-bit symmetric key could be cracked on average like 2^64 or a 256-bit key like 2^128. "The math" here is just Grover's Algorithm, that lowers the cost of generic brute forcing to O(sqrt(n)). > I'm not sure if anyone has run the math But yes GP was totally wrong about "all methods are broken when compute becomes faster". There are a variety of post-quantum cryptographic algorithms under development including some ones that would be ugly slow but likely effective bandaids if required, but that's still a not totally unreasonable concern for certain threat profiles. It's public-key crypto that has always been the worry thanks to Shor's Algorithm, and all modern widely used crypto there is indeed vulnerable if an actual scalable general quantum computer could be constructed. Specifically, modern symmetric crypto (and hashing which is a related but different thing) is fine. Modern cryptography is not breakable via brute force any more
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