From 0144413e91bf5d71b54126783acaf339422abe7e Mon Sep 17 00:00:00 2001
From: Jonas Nick <jonasd.nick@gmail.com>
Date: Mon, 20 Jun 2022 13:16:27 +0000
Subject: bip-0340: clarify that lift_x fails with out-of-range inputs

Without this commit, it's not defined what happens if x is not in range 0..p-1.
However, lift_x may easily be called with out of range values. The reference
implementation of lift_x correctly returns failure in such cases.
---
 bip-0340.mediawiki | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

(limited to 'bip-0340.mediawiki')

diff --git a/bip-0340.mediawiki b/bip-0340.mediawiki
index 9573846..a67afe3 100644
--- a/bip-0340.mediawiki
+++ b/bip-0340.mediawiki
@@ -109,8 +109,9 @@ The following conventions are used, with constants as defined for [https://www.s
 ** The function ''bytes(P)'', where ''P'' is a point, returns ''bytes(x(P))''.
 ** The function ''int(x)'', where ''x'' is a 32-byte array, returns the 256-bit unsigned integer whose most significant byte first encoding is ''x''.
 ** The function ''has_even_y(P)'', where ''P'' is a point for which ''not is_infinite(P)'', returns ''y(P) mod 2 = 0''.
-** The function ''lift_x(x)'', where ''x'' is an integer in range ''0..p-1'', returns the point ''P'' for which ''x(P) = x''<ref>
-    Given a candidate X coordinate ''x'' in the range ''0..p-1'', there exist either exactly two or exactly zero valid Y coordinates. If no valid Y coordinate exists, then ''x'' is not a valid X coordinate either, i.e., no point ''P'' exists for which ''x(P) = x''. The valid Y coordinates for a given candidate ''x'' are the square roots of ''c = x<sup>3</sup> + 7 mod p'' and they can be computed as ''y = &plusmn;c<sup>(p+1)/4</sup> mod p'' (see [https://en.wikipedia.org/wiki/Quadratic_residue#Prime_or_prime_power_modulus Quadratic residue]) if they exist, which can be checked by squaring and comparing with ''c''.</ref> and ''has_even_y(P)'', or fails if no such point exists. The function ''lift_x(x)'' is equivalent to the following pseudocode:
+** The function ''lift_x(x)'', where ''x'' is a 256-bit unsigned integer, returns the point ''P'' for which ''x(P) = x''<ref>
+    Given a candidate X coordinate ''x'' in the range ''0..p-1'', there exist either exactly two or exactly zero valid Y coordinates. If no valid Y coordinate exists, then ''x'' is not a valid X coordinate either, i.e., no point ''P'' exists for which ''x(P) = x''. The valid Y coordinates for a given candidate ''x'' are the square roots of ''c = x<sup>3</sup> + 7 mod p'' and they can be computed as ''y = &plusmn;c<sup>(p+1)/4</sup> mod p'' (see [https://en.wikipedia.org/wiki/Quadratic_residue#Prime_or_prime_power_modulus Quadratic residue]) if they exist, which can be checked by squaring and comparing with ''c''.</ref> and ''has_even_y(P)'', or fails if ''x'' is greater than ''p-1'' or no such point exists. The function ''lift_x(x)'' is equivalent to the following pseudocode:
+*** Fail if ''x &ge; p''.
 *** 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''.
-- 
cgit v1.2.3

