From ba7dd5769758a953853200899289121b52ffb2a2 Mon Sep 17 00:00:00 2001
From: Hennadii Stepanov <32963518+hebasto@users.noreply.github.com>
Date: Mon, 11 Nov 2019 20:09:55 +0200
Subject: G refers to secp256k1 base point rather generator

---
 bip-schnorr.mediawiki | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'bip-schnorr.mediawiki')

diff --git a/bip-schnorr.mediawiki b/bip-schnorr.mediawiki
index 31a5904..cff066e 100644
--- a/bip-schnorr.mediawiki
+++ b/bip-schnorr.mediawiki
@@ -48,7 +48,7 @@ encodings and operations.
 
 === Design ===
 
-'''Schnorr signature variant''' Elliptic Curve Schnorr signatures for message ''m'' and public key ''P'' generally involve a point ''R'', integers ''e'' and ''s'' picked by the signer, and generator ''G'' which satisfy ''e = hash(R || m)'' and ''s⋅G = R + e⋅P''. Two formulations exist, depending on whether the signer reveals ''e'' or ''R'':
+'''Schnorr signature variant''' Elliptic Curve Schnorr signatures for message ''m'' and public key ''P'' generally involve a point ''R'', integers ''e'' and ''s'' picked by the signer, and the base point ''G'' which satisfy ''e = hash(R || m)'' and ''s⋅G = R + e⋅P''. Two formulations exist, depending on whether the signer reveals ''e'' or ''R'':
 # Signatures are ''(e, s)'' that satisfy ''e = hash(s⋅G - e⋅P || m)''. This supports more compact signatures, since [http://www.neven.org/papers/schnorr.pdf the hash ''e'' can be made as small as 16 bytes without sacrificing security], whereas an encoding of ''R'' inherently needs about 32 bytes. Moreover, this variant avoids minor complexity introduced by the encoding of the point ''R'' in the signature (see paragraphs "Encoding the sign of R" and "Implicit Y coordinate" further below in this subsection).
 # Signatures are ''(R, s)'' that satisfy ''s⋅G = R + hash(R || m)⋅P''. This supports batch verification, as there are no elliptic curve operations inside the hashes. Batch verification enables significant speedups.
 
@@ -100,7 +100,7 @@ The following conventions are used, with constants as defined for [https://www.s
 * Uppercase variables refer to points on the curve with equation ''y<sup>2</sup> = x<sup>3</sup> + 7'' over the integers modulo ''p''.
 ** ''is_infinite(P)'' returns whether or not ''P'' is the point at infinity.
 ** ''x(P)'' and ''y(P)'' are integers in the range ''0..p-1'' and refer to the X and Y coordinates of a point ''P'' (assuming it is not infinity).
-** The constant ''G'' refers to the generator, for which ''x(G) = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798'' and ''y(G) = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8''.
+** The constant ''G'' refers to the base point, for which ''x(G) = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798'' and ''y(G) = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8''.
 ** Addition of points refers to the usual [https://en.wikipedia.org/wiki/Elliptic_curve#The_group_law elliptic curve group operation].
 ** [https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication Multiplication (⋅) of an integer and a point] refers to the repeated application of the group operation.
 * Functions and operations:
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