--- Day changed Wed Aug 29 2018
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08:07 < gmaxwell> Erik Aronesty's response to it being pointed out that his scheme is broken ( https://bitcointalk.org/index.php?topic=4973123.0 ) is apparently just to post it to new places (see bitcoin dev mailinglist).
08:10 < sipa> i think he's not posting about his own scheme, but pointing out that the existing only only supports interactive thresholds
08:12 < gmaxwell> sipa: he posted two messages, the second links to https://medium.com/@simulx/an-m-of-n-bitcoin-multisig-scheme-e7860ab34e7f which is a copy of what he posted on bitcointalk.
08:13 < sipa> ok
08:13 < gmaxwell> He claims that signing is completely non-interactive (but doesn't actually describe something with that property).
08:13 < sipa> sigh :)
09:50 < roconnor> Is it correct to say that both affine coordinates and jacobian coordinates are types of projective coordinates?
09:58 < andytoshi> you mean, both jacobian and projective coordinates are types of projective coordinates?
09:58 < andytoshi> affine coordinates cannot express the line at infinity
09:59 < andytoshi> but there is a bijection between jacobian and projective coordinates
10:00 < roconnor> hmm, maybe I'm confused as to what affine coordinates mean.
10:01 < andytoshi> so, the affine plane and the projective plane are actually different objects
10:02 < andytoshi> our affine coordinates are coordinates onto the plane, plus a flag "infinity" which says that actually we have some point that doesn't exist on the plane
10:02 < roconnor> okay I think I was confusing affine coordinates with projective coordinates.
10:02 < andytoshi> (and we're exploiting the fact that we only care about points on our curve, so there's only one such point)
10:03 < andytoshi> ah
10:03 < andytoshi> yes, the projective plane is a much nicer object (it's topologically compact and so is the elliptic curve embedded in it; furthermore there is a group law on the elliptic curve that doesn't require patching a "point at infinity" into it)
10:03 < roconnor> I think what I meant to ask was " Is it correct to say that both homogenous coordinates and jacobian coordinates are types of projective coordinates?"
10:03 < andytoshi> and both projective and jacobian coordinates are coordinate maps of projective space
10:04 < andytoshi> ah yep
10:04 < andytoshi> then the answer is yes
10:04 < roconnor> whew. Thanks.
10:04 < roconnor> I was in fact confused, just not in the way I thought I was confused.
10:05 < andytoshi> heh, you're not alone ... i once tried to google this and found that every answer was confused gibberish
10:05 < andytoshi> so i asked an algebraic geometer, who replied with a series of very simple questions until he'd figured out what the hell i was saying
10:05 < roconnor> :)
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10:59 < sipa> roconnor: i'm not sure; i think homogeneous coordinates are just another way of representing the affine plane (and don't have a point at infinity included)
10:59 < sipa> projective coordinates are homogeneous coordinates, with the addition of points at infinity
10:59 < sipa> (this may be just a terminology issue)
11:00 < sipa> but jacobian coordinates and projective coordinates are different ways of representing the same set of points for sure
11:02 < andytoshi> i think it's a terminology issue .. i've never heard "homogenous coordinates" used to describe affine coordinates, but i guess they could be
11:03 < andytoshi> s/they/it/
11:07 < sipa> no, no
11:07 < sipa> homogeneous coordinates are (x,y,z) coordinates, but don't include z=0 points
11:08 < sipa> so they're another representation for the same set of points as the affine ones
11:08 < andytoshi> ohh right derp
11:08 < sipa> while projective coordinates are the same sort of coordinate system, but for the set of points that includes infinity (which have z=0 in projective coordinates)
12:31 < roconnor> https://en.wikipedia.org/wiki/Homogeneous_coordinates
12:31 < roconnor> ". They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates"
12:31 < roconnor> This suggests that homogeneous coordinates includes points at infinity.
12:32 < sipa> roconnor: ok, not what i learned in high school :)
12:33 < roconnor> I've been trying to remember the terminology we used at university for computer graphics.
12:33 < roconnor> (though since this was a CS course, everything was a little wishy-washy)
12:35 < sipa> 1wei'm sure my high school class on projective geometry was wishy-washy too :D