--- Log opened Tue Mar 22 00:00:32 2022
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09:47 < halosghost> I have what I believe is another stupid qeustion
09:47 < halosghost> s/eu/ue/
09:52 < halosghost> is there an exposed function to determine if a public key / point is even/odd?
10:01 < sipa> just look at the first character of the compressed encoding, or the last of an uncompressed
10:04 < halosghost> that's kind of what I thought
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10:14 < halosghost> sipa: and given that I'm working with compressed points, the test is genuinely as simple as the first byte being equal to either 0x03 or 0x02 (for odd or even)?
10:14 < sipa> tes
10:14 < sipa> yes
10:15 < sipa> (of the serialization)
10:15 < halosghost> right
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12:44 < halosghost> is there a good place for me to read further on what secp256k1_fe_is_quad_var() does / how it works?
12:44 < sipa> It tests whether a field element is the square of another field element.
12:44 < roconnor> AFAIU it has been removed.
12:45 < halosghost> mm
12:46 < sipa> Half of the non-zero field elements (and zero) are the square of a field element. The other half are the negation of a square of a field element.
12:46 < sipa> And indeed, it was removed.
12:48 < halosghost> andytoshi: can you clarify for me why `pedersen_commitment_serialize()` does this: output[0] = 9 ^ secp256k1_fe_is_quad_var(&ge.y) ?
12:48 < halosghost> (I'm struggling to figure out what that would be doing
12:48 < halosghost> )
12:49 < roconnor> ... I guess maybe it is still in -zkp.
12:50 < andytoshi> yes, we still use quadness in -zkp for pedersen commitments. it would hardfork liquid to change this
12:51 < andytoshi> halosghost: the first byte of pedersen commitments is 8 or 9, depending on parity
12:51 < roconnor> not parity, squareness.
12:51 < roconnor> ... depending on your definition of parity.
12:54 < halosghost> oh, interesting
12:54 < halosghost> that's very clarifying
12:54 < halosghost> andytoshi: thank you!
12:55 < sipa> In this regard field element are pretty similar to real numbers: half of them are the square (the positive ones), the other half are the negation of squares.
12:55 < roconnor> It might be helpful to note there are three way of dividing up the pairs of points with the same x-coordiante.
12:55 < sipa> * are a square
12:55 < roconnor> 1) base on even / oddness
12:55 < roconnor> 2) based on upper half or lower half of the field elements.
12:56 < roconnor> 3) based on squareness or nonsquareness
12:57 < roconnor> (of course you can invent other arbitrarly complicated schemes as well on top of these 3)
12:57 < sipa> Well all three have the property that negating an element changes the character.
12:58 < sipa> I guess (oddness XOR upperhalfness XOR squareness) also has that property.
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