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06:42 < andytoshi> sipa: ok, thanks!
06:42 < andytoshi> do you think you just need to look harder or that there's some algebraic reason stopping you?
06:43 < andytoshi> it may be more helpful to try to find consecutive 0s or triples of consecutive non-0 digits, rather than shaving a digit off the checksum
06:43 < andytoshi> although saving a digit is pretty damn helpful .. it saves the user work but also gives us an extra data digit while letting us store in a fixed-size cryptosteel
06:44 < sipa> i don't think it's impossible that a degree 12 one could exist
06:44 < andytoshi> although i notice the cryptosteel capsule now comes in 2-packs and can fit 123 characters https://cryptosteel.com/product/cryptosteel-capsule/
06:44 < sipa> but it's hard to say how much work it will take to find one
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07:56 < roconnor> andytoshi: I don't see how repeated digits allowed you to get x+x.
07:57 < sipa> so what precisely helps, and how much? i suspect that 0s and 1s in general help because they're trivial for multiplication; i suspect that fewer distinct coefficients helps because fewer tables/volvelles? what else?
07:58 < sipa> there was something roconnor said which i didn't quite get
07:58 < sipa> 22:59:30 < roconnor> To be more specific, I'm looking for a value such that a*x^13 + b*x^12 mod g(x) contains the sequence a b.
07:59 < roconnor> my lookup table proceeds 2 characters at a time.
07:59 < roconnor> and is a table for computing a*x^13 + b*x^12 mod g(x)
08:00 < roconnor> and if the subsequence a b occured in that result, then we chould shrink the lookup table by highlighting the index inside the answer.
08:00 < roconnor> which I thought would be kinda cool.
08:00 < sipa> i see
08:00 < sipa> i'm first going to try finding *a* degree 12 solution, which may not be possible/feasible in the first place
08:00 < sipa> before trying to bias
08:01 < roconnor> yes, getting a short code is probably the most important factor.
08:01 < sipa> ha, factor
08:02 < andytoshi> roconnor: later today i'll try to go through my example worksheet and highlight all the "convenient coincidences" that i encountered using this code, and maybe you infer what property of the code caused them to happen
08:02 < andytoshi> because it also was not obvious to me why they would happen
08:02 < andytoshi> i suppose, they could actually be coincidences ... but "a + b = c" followed by "b + c = a" happened *several* times
08:03 < andytoshi> also, all the checksum lookups were from odd rows of the table (which i noticed because in my table they're colored gray) until i got to the checksum rows, when suddenly they were from the even rows of the table
08:03 < andytoshi> again .. could be a coincidence, and i don't see any algebraic reason that that would happen
08:05 < roconnor> random input?
08:05 < andytoshi> yep, except that the start was 2ANDYS
08:05 < roconnor> *lol*
08:05 < roconnor> okay.
08:05 < sipa> also something vaguely related i learned this weekend: a BCH code can be uniquely identified using (base field F, irreducible polynomial over F, design distance, constant 'c')
08:05 < andytoshi> the 'randomness' was copied from one of my old worksheets, when i generated it using dice .. and with the old worksheet/code i did not get all these "coincidences"
08:05 < sipa> which factors out the choice of extension field entirely
08:06 < andytoshi> sipa: i'm a little surprised that the first two things aren't enough? is the "irreducible polynomial" the generator polynomial?
08:06 < andytoshi> oh, i guess the constant would be needed since that's the checksum you're supposed to compute?
08:06 < roconnor> andytoshi: if you are willing to paste or PM me your random data, I can run it on my postscript.
08:07 < sipa> andytoshi: (base field F, generator) is enough for encoding, and i guess you can probably infer the BCH design parameters from the generator too... though i'm not exactly sure how
08:07 < andytoshi> roconnor: yep for sure, one sec
08:08 < roconnor> sipa: because all extenion fields are isomorphic and that isomorphism maps powers of that irredicuble to themselves.
08:08 < sipa> andytoshi: but what i mean is this: before, i always characterized them using (base field F, modulus for extension field E, specific field element alpha in E, distance, c)
08:08 < roconnor> The wikipedia article hinted at this.
08:08 < andytoshi> roconnor: 2 ANDY S5GS 8YDX GMLU W34L EN0P RDAK 9GLL WZJC XRKY RHUC .... where the ending L WZJC XRKY RHUC are the checksum
08:08 < sipa> but the choice of alpha is actually immaterial; we only care about alpha to the extent that it affects minimal polynomials of its powers
08:09 < roconnor> "Using log notation which is independent on GF(24) isomorphisms"
08:09 < sipa> and it turns out that is conveyed entirely by just giving minpoly(alpha) itself
08:09 < sipa> and once you do that, the specific modulus used for your extension field doesn't matter anymore, because minpoly(alpha) uses base field coefficients
08:09 < andytoshi> sipa: ah! yep, there is no discernable difference between the different alphas
08:10 < sipa> oh, for a _specific_ extension field, the actual choice of alpha matters
08:10 < andytoshi> oh that surprises me actually
08:10 < sipa> but instead of specifying (extension field, alpha) you can just specify minpoly(alpha), which encapsulates the relevant information from both
08:11 < sipa> andytoshi: maybe it helps to see that not every alpha has the same multiplicative order
08:11 < roconnor> andytoshi: did you keep the implied HRP as dontonotusesss32 or whatever?
08:11 < andytoshi> roconnor: oh, no, i changed it to ms
08:11 < roconnor> ok
08:11 < roconnor> authentic
08:11 < andytoshi> 16:11 < sipa> andytoshi: maybe it helps to see that not every alpha has the same multiplicative order
08:11 < andytoshi> they don't??
08:12 < andytoshi> i believe you but it surprises me, and i have a call now and can't investigate
08:12 < sipa> well the multiplicative order of alpha is the design length of the code
08:12 < sipa> so for the generators i've suggested, alpha has multiplicative order 93
08:13 < sipa> for the BCH design properties of the code, only the order of alpha matters, not its choice
08:13 < sipa> but for properties beyond the design (computation distance), that's not enough either
08:35 < roconnor> andytoshi: the odd / even table entries thing has to be some kind of coincidence.  The table is sorted alphabetically, and the alphabetic order of the Bech32 character set is almost totally unrelated to any algebraic properties of anything.
08:40 < andytoshi> roconnor: good point
08:40 < andytoshi> sipa: when you say "not every alpha" what set of alphas are you talking about?
08:40 < andytoshi> i mean "every alpha that has the same minpoly"
08:41 < sipa> andytoshi: ah, yes! that's my point, all alphas with the same minpoly are identical, because they _result in the same generator_
08:41 < andytoshi> and i think those should have the same order, because you can extend to a splitting field for minpoly, and there is an automorphism of this field which maps "your alpha" to every other alpha
08:42 < andytoshi> ah perfect. ok, we agree :)
08:44 < roconnor> sipa: maybe you also can remind me the difference between a minimum polynomial and a characteristic polynomial.
08:45 < roconnor> andytoshi: I think your Q's are also just a coincidence.
08:46 < andytoshi> roconnor: could be. i should do this again with a fresh random secret
08:46 < roconnor> along with everything else.
08:46 < sipa> roconnor: i'd need to look that up
08:46 < roconnor> let's take your 0P 0P additions that are right next to each other as an example
08:47 < andytoshi> i might be able to do this today, i am with my gf's family and so have a new set of people who i can show off the volvelles to
08:47 < roconnor> the PPP's are there because of the XP lookup entry.
08:47 < roconnor> the repeated PPP
08:47 < sipa> the minimal polynomial for an element a of a field extension E/F is the unique monic polynomial with coefficients in F, which maps a to 0, of minimal degree
08:47 < roconnor> the repeated PPPs are by design.
08:47 < roconnor> but the repeated 0's are only there because of the 34 entry from your random string above.
08:48 < roconnor> and the XP is a function of the data from before the "34" entry.
08:48 < roconnor> The "34" is independent of the XP
08:48 < roconnor> so the fact that everything lines up there is a coincidence.
08:50 < roconnor> Similar argument applies to your repeated 4A 4A
08:51 < andytoshi> lol ok, cool
08:51 < roconnor> That said, the fact that the lookup table itself contains repeated characters faciliates this sort of coincidence.
08:51 < roconnor> by giving repeated characters in the lookup.
08:51 < andytoshi> one thing i've noticed with this worksheet is that it really triggers the "finding patterns in random noise" brain failure mode
08:52 < roconnor> but it doesn't cause repeated characters to appear in the partial checksums.
08:52 < roconnor> those appear randomly withtout any more frequency than with any other checksum.
08:53 < sipa> roconnor: i learn that the characteristic polynomial is always the same degree as the extension; the minimal polynomial may be of lower degree, and always divides the characteristic one
08:54 < andytoshi> ok, yeah, i guess we expect repeats pretty often in a 32-char alphabet
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08:56 < roconnor> The short of it is that the lookup entry isn't so random, we've manufactured repeated characters, but the data you are adding to it is always random and independent of the value we have looked up.
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08:57 < andytoshi> yeah, that makes sense
08:57 < andytoshi> and actually, my shitty dice rolling may be causing more repeats than expected in the "random" data
08:58 < roconnor> maybe.  You didn't run the debiasing.
08:58 < roconnor> though there aren't really any repeats in your string.
08:58 < roconnor> and I'm skeptical your dice is baised towards the selected generator.
09:12 < gene> check for magnets?
09:20 < andytoshi> yes, for real secret generation i will just run the debiasing
09:20 < andytoshi> it "felt like" the individual rolls had a lot of repeats and a lot of 5s
09:31 < gene> a mechanical tumbler or cup might help with increasing roll consistency/remove some bias (if rolling free hand)
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09:51 < roconnor> Right, one of those dice towers might be a good idea.  I tend to put my dice in a box and shake it a lot.
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10:29 < andytoshi> yeah. one difficulty is that when you're generating tons of bits in a row it's easy to get lazy/impatient
10:31 < andytoshi> i think, the debiasing technique will help just by involving 5 dice at once, which should tumble much more than a single die even if you're half-assing it
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10:42 < gene> +1, the more redundancy the better
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11:11 < roconnor> andytoshi: https://github.com/roconnor-blockstream/SSS32/pull/14 will be an easy fix.
11:12 < roconnor> https://github.com/roconnor-blockstream/SSS32/pull/14#issuecomment-974381008
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11:20 < jamesecombs> roconnor do you work for blockstream?
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16:54 < sipa> meshcollider: you may be interested in some of the BCH code discussion in scrollback here too
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--- Log closed Tue Nov 23 00:00:40 2021