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14:06 < jeremyrubin> why is it that taproot_tweak_pubkey rejects tweaks over the curve order, and not over the prime field?
14:09 < jeremyrubin> i.e.:      `if t >= SECP256K1_ORDER:` is what's in the spec and not     `if t >= SECP256K1_P:`
14:10 < pinheadmz> jeremyrubin: aren't the tweaks scalars like private keys? So they'd come from the group of integers modulo the order of the curve ?
14:10 < pinheadmz> Whereas the field size is the modulus for the group of EC points
14:11 < pinheadmz> But I'm just learning so this is a good Q for me to wonder out loud
14:18 < jeremyrubin> well I guess if it's 2^128 out of 2^256 points, so 1 in 2^128 odds to generate a random point above the threshold that would be invalid?
14:21 < pinheadmz> I thought the order was way higher than that, another big prime but not quite as big as the field size
14:22 < pinheadmz> And that's why in bip32 derivation there's like a 1:1^128 chance of hitting a number between the order and field size which wouldn't be usable
14:24 < jeremyrubin> well it is big, but the funny thing with big numbers is the order is a big number, but so is the gap between the prime field and the order
14:25 < jeremyrubin> but the gap is "small enough" relative to the order itself
14:27 < pinheadmz> Heh sure but the odds of picking a 256 bit int *between* order and field size is like 2^-128
14:28 < pinheadmz> Anyway do you think I'm right about taproot tweaks and curve order?
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15:26 < andytoshi> jeremyrubin: the prime field never appears in the "api" of the secp265k1 curve
15:27 < andytoshi> it's an implementation detail of how addition works. but it's not a visible property of the group
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17:57 < pinheadmz> andytoshi: i thought the field size is an explicit parameter of the curve?
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19:54 < andytoshi>  pinheadmz: it's part of the definition of the curve. but in cryto you just treat the curve as a group
19:54 < andytoshi> and as a group, there the field order is not a visible property
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--- Log closed Sat Aug 23 00:00:18 2025