--- Log opened Wed May 06 00:00:14 2020
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03:25 < elichai2> Is it true that any 256bit number has a ~50% of being a valid X coordinate?
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05:32 < real_or_random> elichai2: yes, half of the non-zero scalars are valid x coords
06:44 < sipa> more precisely, it has ((N-1)/2)/(2^256) chance of being a valid X coordinate
06:48 < real_or_random> I wonder if f(random curve C in our field, x) = is x a valid x-coordinate on C is a PRF
06:49 < real_or_random> so can you predict other x-coords after seeing a few x-coords? I guess that's hard. not sure if anyone looked seriously into the hardness
06:51 < sipa> so the curve equation is the "key" ?
06:51 < real_or_random> right
06:52 < real_or_random> may be an efficient PRF inside a circuit
06:54 < real_or_random> it's just one bit but you could use H(x, 1), ... H(x, n) instead of x directly, and it's possible to compute the hashes outside the circuit
06:56 < sipa> feels related to the quadratic residuosity prf
07:07 < real_or_random> oh indeed
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--- Log closed Thu May 07 00:00:14 2020