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The current fast_mix() function is a piece of classic mailing list crypto, where it just sort of sprung up by an anonymous author without a lot of real analysis of what precisely it was accomplishing. As an ARX permutation alone, there are some easily searchable differential trails in it, and as a means of preventing malicious interrupts, it completely fails, since it xors new data into the entire state every time. It can't really be analyzed as a random permutation, because it clearly isn't, and it can't be analyzed as an interesting linear algebraic structure either, because it's also not that. There really is very little one can say about it in terms of entropy accumulation. It might diffuse bits, some of the time, maybe, we hope, I guess. But for the most part, it fails to accomplish anything concrete. As a reminder, the simple goal of add_interrupt_randomness() is to simply accumulate entropy until ~64 interrupts have elapsed, and then dump it into the main input pool, which uses a cryptographic hash. It would be nice to have something cryptographically strong in the interrupt handler itself, in case a malicious interrupt compromises a per-cpu fast pool within the 64 interrupts / 1 second window, and then inside of that same window somehow can control its return address and cycle counter, even if that's a bit far fetched. However, with a very CPU-limited budget, actually doing that remains an active research project (and perhaps there'll be something useful for Linux to come out of it). And while the abundance of caution would be nice, this isn't *currently* the security model, and we don't yet have a fast enough solution to make it our security model. Plus there's not exactly a pressing need to do that. (And for the avoidance of doubt, the actual cluster of 64 accumulated interrupts still gets dumped into our cryptographically secure input pool.) So, for now we are going to stick with the existing interrupt security model, which assumes that each cluster of 64 interrupt data samples is mostly non-malicious and not colluding with an infoleaker. With this as our goal, we have a few more choices, simply aiming to accumulate entropy, while discarding the least amount of it. We know from <https://eprint.iacr.org/2019/198> that random oracles, instantiated as computational hash functions, make good entropy accumulators and extractors, which is the justification for using BLAKE2s in the main input pool. As mentioned, we don't have that luxury here, but we also don't have the same security model requirements, because we're assuming that there aren't malicious inputs. A pseudorandom function instance can approximately behave like a random oracle, provided that the key is uniformly random. But since we're not concerned with malicious inputs, we can pick a fixed key, which is not secret, knowing that "nature" won't interact with a sufficiently chosen fixed key by accident. So we pick a PRF with a fixed initial key, and accumulate into it continuously, dumping the result every 64 interrupts into our cryptographically secure input pool. For this, we make use of SipHash-1-x on 64-bit and HalfSipHash-1-x on 32-bit, which are already in use in the kernel's hsiphash family of functions and achieve the same performance as the function they replace. It would be nice to do two rounds, but we don't exactly have the CPU budget handy for that, and one round alone is already sufficient. As mentioned, we start with a fixed initial key (zeros is fine), and allow SipHash's symmetry breaking constants to turn that into a useful starting point. Also, since we're dumping the result (or half of it on 64-bit so as to tax our hash function the same amount on all platforms) into the cryptographically secure input pool, there's no point in finalizing SipHash's output, since it'll wind up being finalized by something much stronger. This means that all we need to do is use the ordinary round function word-by-word, as normal SipHash does. Simplified, the flow is as follows: Initialize: siphash_state_t state; siphash_init(&state, key={0, 0, 0, 0}); Update (accumulate) on interrupt: siphash_update(&state, interrupt_data_and_timing); Dump into input pool after 64 interrupts: blake2s_update(&input_pool, &state, sizeof(state) / 2); The result of all of this is that the security model is unchanged from before -- we assume non-malicious inputs -- yet we now implement that model with a stronger argument. I would like to emphasize, again, that the purpose of this commit is to improve the existing design, by making it analyzable, without changing any fundamental assumptions. There may well be value down the road in changing up the existing design, using something cryptographically strong, or simply using a ring buffer of samples rather than having a fast_mix() at all, or changing which and how much data we collect each interrupt so that we can use something linear, or a variety of other ideas. This commit does not invalidate the potential for those in the future. For example, in the future, if we're able to characterize the data we're collecting on each interrupt, we may be able to inch toward information theoretic accumulators. <https://eprint.iacr.org/2021/523> shows that `s = ror32(s, 7) ^ x` and `s = ror64(s, 19) ^ x` make very good accumulators for 2-monotone distributions, which would apply to timestamp counters, like random_get_entropy() or jiffies, but would not apply to our current combination of the two values, or to the various function addresses and register values we mix in. Alternatively, <https://eprint.iacr.org/2021/1002> shows that max-period linear functions with no non-trivial invariant subspace make good extractors, used in the form `s = f(s) ^ x`. However, this only works if the input data is both identical and independent, and obviously a collection of address values and counters fails; so it goes with theoretical papers. Future directions here may involve trying to characterize more precisely what we actually need to collect in the interrupt handler, and building something specific around that. However, as mentioned, the morass of data we're gathering at the interrupt handler presently defies characterization, and so we use SipHash for now, which works well and performs well. Cc: Theodore Ts'o <tytso@mit.edu> Cc: Greg Kroah-Hartman <gregkh@linuxfoundation.org> Reviewed-by: Jean-Philippe Aumasson <jeanphilippe.aumasson@gmail.com> Signed-off-by: Jason A. Donenfeld <Jason@zx2c4.com> |
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| Documentation | ||
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| fs | ||
| include | ||
| init | ||
| ipc | ||
| kernel | ||
| lib | ||
| LICENSES | ||
| mm | ||
| net | ||
| samples | ||
| scripts | ||
| security | ||
| sound | ||
| tools | ||
| usr | ||
| virt | ||
| .clang-format | ||
| .cocciconfig | ||
| .get_maintainer.ignore | ||
| .gitattributes | ||
| .gitignore | ||
| .mailmap | ||
| COPYING | ||
| CREDITS | ||
| Kbuild | ||
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| README | ||
Linux kernel
============
There are several guides for kernel developers and users. These guides can
be rendered in a number of formats, like HTML and PDF. Please read
Documentation/admin-guide/README.rst first.
In order to build the documentation, use ``make htmldocs`` or
``make pdfdocs``. The formatted documentation can also be read online at:
https://www.kernel.org/doc/html/latest/
There are various text files in the Documentation/ subdirectory,
several of them using the Restructured Text markup notation.
Please read the Documentation/process/changes.rst file, as it contains the
requirements for building and running the kernel, and information about
the problems which may result by upgrading your kernel.