📅 Original date posted:2018-08-04
📝 Original message:I propose changing the verification equation from "Let *R = sG - eP*" to
Let *R = sG + eP*
This allows faster verification by avoiding negating a point (or a
coefficient).
If, instead of directly following the literal verification specification,
one is instead reconstructing R from r by finding a y coordinate that is a
quadratic residue, under the existing scheme one would verify
*sG - eP = R*
which is effectively verifying
0 = *sG - eP* - R or 0 = R - *sG + eP*
Either way one needs to negate at least one point (or one coefficient)
because of the opposite signs between sG and eP.
Under my proposed revised verification scheme, one would instead verify
0 = sG + eP + (-R).
While it seems that this requires negating R, it does not. Rather (-R) can
be directly constructed from r by finding a y coordinate that is *not* a
quadratic residue, which is precisely the same amount of work that
construction R from r was.
In either verification procedure, changing the verification equation to my
proposal removes one negation operation from the cost of doing verification.
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Russell O'Connor [ARCHIVE] /
npub1dw…8plrw
2023-06-07 18:13:55
in reply to nevent1q…hn2d
Author Public Key
npub1dw88wd5gqsqn6ufxhf9h03uk8087l7gfzdtez5csjlt6pupu4pwsj8plrwPublished at
2023-06-07 18:13:55Event JSON
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"content": "📅 Original date posted:2018-08-04\n📝 Original message:I propose changing the verification equation from \"Let *R = sG - eP*\" to\n\n Let *R = sG + eP*\n\nThis allows faster verification by avoiding negating a point (or a\ncoefficient).\n\n\nIf, instead of directly following the literal verification specification,\none is instead reconstructing R from r by finding a y coordinate that is a\nquadratic residue, under the existing scheme one would verify\n\n\n*sG - eP = R*\n\nwhich is effectively verifying\n\n 0 = *sG - eP* - R or 0 = R - *sG + eP*\n\nEither way one needs to negate at least one point (or one coefficient)\nbecause of the opposite signs between sG and eP.\n\n\nUnder my proposed revised verification scheme, one would instead verify\n\n 0 = sG + eP + (-R).\n\nWhile it seems that this requires negating R, it does not. Rather (-R) can\nbe directly constructed from r by finding a y coordinate that is *not* a\nquadratic residue, which is precisely the same amount of work that\nconstruction R from r was.\n\nIn either verification procedure, changing the verification equation to my\nproposal removes one negation operation from the cost of doing verification.\n-------------- next part --------------\nAn HTML attachment was scrubbed...\nURL: \u003chttp://lists.linuxfoundation.org/pipermail/bitcoin-dev/attachments/20180804/2fc635e5/attachment.html\u003e",
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