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Return a point from lift_x()

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John Newbery 2019-05-18 13:38:00 -04:00 • committed by Pieter Wuille
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@ -107,7 +107,7 @@ The following convention is used, with constants as defined for secp256k1:
*** Let ''c = x<sup>3</sup> + 7 mod p''.
*** Let ''y = c<sup>(p+1)/4</sup> mod p''.
*** Fail if ''c &ne; y<sup>2</sup> mod p''.
*** Return ''(r, y)''.
*** Return the unique point ''P'' such that ''x(P) = x'' and ''y(P) = y''.
** The function ''point(x)'', where ''x'' is a 32-byte array, returns the point ''P = lift_x(int(x))''.
** The function ''hash(x)'', where ''x'' is a byte array, returns the 32-byte SHA256 hash of ''x''.
** The function ''jacobi(x)'', where ''x'' is an integer, returns the [https://en.wikipedia.org/wiki/Jacobi_symbol Jacobi symbol] of ''x / p''. It is equal to ''x<sup>(p-1)/2</sup> mod p'' ([https://en.wikipedia.org/wiki/Euler%27s_criterion Euler's criterion])<ref>For points ''P'' on the secp256k1 curve it holds that ''jacobi(y(P)) &ne; 0''.</ref>.