In ECDSA, why is (r,−s mod n) complementary to…
Clash Royale CLAN TAG#URR8PPP
I am trying to find resources in previous malleability posts, but couldn’t find derivations/proofs of this fact or how the exact lows value is derived. Any pointers would greatly appreciated.
add a comment 
I am trying to find resources in previous malleability posts, but couldn’t find derivations/proofs of this fact or how the exact lows value is derived. Any pointers would greatly appreciated.
add a comment 
I am trying to find resources in previous malleability posts, but couldn’t find derivations/proofs of this fact or how the exact lows value is derived. Any pointers would greatly appreciated.
I am trying to find resources in previous malleability posts, but couldn’t find derivations/proofs of this fact or how the exact lows value is derived. Any pointers would greatly appreciated.
add a comment 
add a comment 
1 Answer
1
active
oldest
votes
ECDSA signatures are pairs (r,s) such that r = x(m/sG + r/sP) mod n, where P is the public key and m is the message digest. x() in that equation means “the X coordinate of”.
In that equation, if you substitute s = s’, you get *r = x(m/(s’)*G + r/(s)P) mod n, or *r = x((m/s’*G + r/s’P)).
However, it is true that for any point Q, x(Q) = x(Q), as negating a point only affects the Y coordinate. Thus, *r = x(m/s’*G + r/s’P) mod n, or (r,s’) is valid signature whenever (r,s) is.

Thank you very much. I understand negating a scalar over ff, but not why that negated scalar * point will result in a point with the same xcoord as scalar * point.
– James C.
Jan 5 at 22:31
add a comment 
Your Answer
StackExchange.ready(function() {
var channelOptions = {
tags: “”.split(” “),
id: “308”
};
initTagRenderer(“”.split(” “), “”.split(” “), channelOptions);
StackExchange.using(“externalEditor”, function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using(“snippets”, function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: ‘answer’,
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: “”,
imageUploader: {
brandingHtml: “Powered by u003ca class=”iconimgurwhite” href=”https://imgur.com/”u003eu003c/au003e”,
contentPolicyHtml: “User contributions licensed under u003ca href=”https://creativecommons.org/licenses/bysa/3.0/”u003ecc bysa 3.0 with attribution requiredu003c/au003e u003ca href=”https://stackoverflow.com/legal/contentpolicy”u003e(content policy)u003c/au003e”,
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: “.discardanswer”
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave(‘#loginlink’);
});
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin(‘.newpostlogin’, ‘https%3a%2f%2fbitcoin.stackexchange.com%2fquestions%2f83408%2finecdsawhyisr%25e2%2588%2592smodncomplementarytors%23newanswer’, ‘question_page’);
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
ECDSA signatures are pairs (r,s) such that r = x(m/sG + r/sP) mod n, where P is the public key and m is the message digest. x() in that equation means “the X coordinate of”.
In that equation, if you substitute s = s’, you get *r = x(m/(s’)*G + r/(s)P) mod n, or *r = x((m/s’*G + r/s’P)).
However, it is true that for any point Q, x(Q) = x(Q), as negating a point only affects the Y coordinate. Thus, *r = x(m/s’*G + r/s’P) mod n, or (r,s’) is valid signature whenever (r,s) is.

Thank you very much. I understand negating a scalar over ff, but not why that negated scalar * point will result in a point with the same xcoord as scalar * point.
– James C.
Jan 5 at 22:31
add a comment 
ECDSA signatures are pairs (r,s) such that r = x(m/sG + r/sP) mod n, where P is the public key and m is the message digest. x() in that equation means “the X coordinate of”.
In that equation, if you substitute s = s’, you get *r = x(m/(s’)*G + r/(s)P) mod n, or *r = x((m/s’*G + r/s’P)).
However, it is true that for any point Q, x(Q) = x(Q), as negating a point only affects the Y coordinate. Thus, *r = x(m/s’*G + r/s’P) mod n, or (r,s’) is valid signature whenever (r,s) is.

Thank you very much. I understand negating a scalar over ff, but not why that negated scalar * point will result in a point with the same xcoord as scalar * point.
– James C.
Jan 5 at 22:31
add a comment 
ECDSA signatures are pairs (r,s) such that r = x(m/sG + r/sP) mod n, where P is the public key and m is the message digest. x() in that equation means “the X coordinate of”.
In that equation, if you substitute s = s’, you get *r = x(m/(s’)*G + r/(s)P) mod n, or *r = x((m/s’*G + r/s’P)).
However, it is true that for any point Q, x(Q) = x(Q), as negating a point only affects the Y coordinate. Thus, *r = x(m/s’*G + r/s’P) mod n, or (r,s’) is valid signature whenever (r,s) is.
ECDSA signatures are pairs (r,s) such that r = x(m/sG + r/sP) mod n, where P is the public key and m is the message digest. x() in that equation means “the X coordinate of”.
In that equation, if you substitute s = s’, you get *r = x(m/(s’)*G + r/(s)P) mod n, or *r = x((m/s’*G + r/s’P)).
However, it is true that for any point Q, x(Q) = x(Q), as negating a point only affects the Y coordinate. Thus, *r = x(m/s’*G + r/s’P) mod n, or (r,s’) is valid signature whenever (r,s) is.

Thank you very much. I understand negating a scalar over ff, but not why that negated scalar * point will result in a point with the same xcoord as scalar * point.
– James C.
Jan 5 at 22:31
add a comment 

Thank you very much. I understand negating a scalar over ff, but not why that negated scalar * point will result in a point with the same xcoord as scalar * point.
– James C.
Jan 5 at 22:31
Thank you very much. I understand negating a scalar over ff, but not why that negated scalar * point will result in a point with the same xcoord as scalar * point.
– James C.
Jan 5 at 22:31
Thank you very much. I understand negating a scalar over ff, but not why that negated scalar * point will result in a point with the same xcoord as scalar * point.
– James C.
Jan 5 at 22:31
add a comment 
Thanks for contributing an answer to Bitcoin Stack Exchange!
 Please be sure to answer the question. Provide details and share your research!
But avoid …
 Asking for help, clarification, or responding to other answers.
 Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave(‘#loginlink’);
});
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin(‘.newpostlogin’, ‘https%3a%2f%2fbitcoin.stackexchange.com%2fquestions%2f83408%2finecdsawhyisr%25e2%2588%2592smodncomplementarytors%23newanswer’, ‘question_page’);
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave(‘#loginlink’);
});
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave(‘#loginlink’);
});
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave(‘#loginlink’);
});
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown