1a0e13f94e
Use a different algorithm to minimize rejection. This is essentially the same algorithm implemented in the Linux kernel for __get_random_u32_below(), but written in a more readable way, and avoiding microopimizations that make it less readable. Which (the Linux kernel implementation) is itself based on Daniel Lemire's algorithm from "Fast Random Integer Generation in an Interval", linked below. However, I couldn't really understand that paper very much, so I had to reconstruct the proofs from scratch, just from what I could understand from the Linux kernel implementation source code. I constructed some graphical explanation of how it works, and why it is optimal, because I needed to visualize it to understand it. It is published in the GitHub pull request linked below. Here goes a wordy explanation of why this algorithm based on multiplication is better optimized than my original implementation based on masking. masking: It discards the extra bits of entropy that are not necessary for this operation. This works as if dividing the entire space of possible csrand() values into smaller spaces of a size that is a smaller power of 2. Each of those smaller spaces has a rejection band, so we get as many rejection bands as spaces there are. For smaller values of 'n', the size of each rejection band is smaller, but having more rejection bands compensates for this, and results in the same inefficiency as for large values of 'n'. multiplication: It divides the entire space of possible random numbers in chunks of size exactly 'n', so that there is only one rejection band that is the remainder of `2^64 % n`. The worst case is still similar to the masking algorithm, a rejection band that is almost half the entire space (n = 2^63 + 1), but for lower values of 'n', by only having one small rejection band, it is much faster than the masking algorithm. This algorithm, however, has one caveat: the implementation is harder to read, since it relies on several bitwise tricky operations to perform operations like `2^64 % n`, `mult % 2^64`, and `mult / 2^64`. And those operations are different depending on the number of bits of the maximum possible random number generated by the function. This means that while this algorithm could also be applied to get uniform random numbers in the range [0, n-1] quickly from a function like rand(3), which only produces 31 bits of (non-CS) random numbers, it would need to be implemented differently. However, that's not a concern for us, it's just a note so that nobody picks this code and expects it to just work with rand(3) (which BTW I tried for testing it, and got a bit confused until I realized this). Finally, here's some light testing of this implementation, just to know that I didn't goof it. I pasted this function into a standalone program, and run it many times to find if it has any bias (I tested also to see how many iterations it performs, and it's also almost always 1, but that test is big enough to not paste it here). int main(int argc, char *argv[]) { printf("%lu\n", csrand_uniform(atoi(argv[1]))); } $ seq 1 1000 | while read _; do ./a.out 3; done | grep 1 | wc -l 341 $ seq 1 1000 | while read _; do ./a.out 3; done | grep 1 | wc -l 339 $ seq 1 1000 | while read _; do ./a.out 3; done | grep 1 | wc -l 338 $ seq 1 1000 | while read _; do ./a.out 3; done | grep 2 | wc -l 336 $ seq 1 1000 | while read _; do ./a.out 3; done | grep 2 | wc -l 328 $ seq 1 1000 | while read _; do ./a.out 3; done | grep 2 | wc -l 335 $ seq 1 1000 | while read _; do ./a.out 3; done | grep 0 | wc -l 332 $ seq 1 1000 | while read _; do ./a.out 3; done | grep 0 | wc -l 331 $ seq 1 1000 | while read _; do ./a.out 3; done | grep 0 | wc -l 327 This isn't a complete test for a cryptographically-secure random number generator, of course, but I leave that for interested parties. Link: <https://git.kernel.org/pub/scm/linux/kernel/git/torvalds/linux.git/commit/?id=e9a688bcb19348862afe30d7c85bc37c4c293471> Link: <https://github.com/shadow-maint/shadow/pull/624#discussion_r1059574358> Link: <https://arxiv.org/abs/1805.10941> Cc: "Jason A. Donenfeld" <Jason@zx2c4.com> Cc: Cristian Rodríguez <crrodriguez@opensuse.org> Cc: Adhemerval Zanella <adhemerval.zanella@linaro.org> Cc: Björn Esser <besser82@fedoraproject.org> Cc: Yann Droneaud <ydroneaud@opteya.com> Cc: Joseph Myers <joseph@codesourcery.com> Cc: Sam James <sam@gentoo.org> Cc: Serge Hallyn <serge@hallyn.com> Cc: Iker Pedrosa <ipedrosa@redhat.com> [Daniel Lemire: Added link to research paper in source code] Cc: Daniel Lemire <daniel@lemire.me> Signed-off-by: Alejandro Colomar <alx@kernel.org> |
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TODO |
shadow-utils
Introduction
The shadow-utils package includes the necessary programs for converting UNIX password files to the shadow password format, plus programs for managing user and group accounts. The pwconv command converts passwords to the shadow password format. The pwunconv command unconverts shadow passwords and generates a passwd file (a standard UNIX password file). The pwck command checks the integrity of password and shadow files. The lastlog command prints out the last login times for all users. The useradd, userdel, and usermod commands are used for managing user accounts. The groupadd, groupdel, and groupmod commands are used for managing group accounts.
Sites
Contacts
There are several ways to contact us:
- the general discussion mailing list
- the #shadow IRC channel on libera.chat:
- irc://irc.libera.chat/shadow
Mailing archives
- the general discussion mailing list archive
- the commit mailing list archive, only used for historical purposes
Authors and maintainers
Authors and maintainers are listed in AUTHORS.md.