Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

musig-spec: address robot-dreams' comments #182

Merged
merged 1 commit into from
Apr 5, 2022
Merged

musig-spec: address robot-dreams' comments #182

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
16 changes: 8 additions & 8 deletions doc/musig-spec.mediawiki
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -214,13 +214,13 @@ Input:
* Let ''pk2 = GetSecondKey(pk<sub>1..u</sub>)''
* For ''i = 1 .. u'':
** Let ''P<sub>i</sub> = point(pk<sub>i</sub>)''; fail if that fails.
** Let ''a<sub>i</sub> = KeyAggCoeff'(pk<sub>1..u</sub>, pk<sub>i</sub>, pk2)''.
** Let ''a<sub>i</sub> = KeyAggCoeffInternal(pk<sub>1..u</sub>, pk<sub>i</sub>, pk2)''.
* Let ''Q<sub>0</sub> = a<sub>1</sub>⋅P<sub>1</sub> + a<sub>2</sub>⋅P<sub>1</sub> + ... + a<sub>u</sub>⋅P<sub>u</sub>''
* Fail if ''is_infinite(Q<sub>0</sub>)''.
* Let ''tacc<sub>0</sub> = 0''
* Let ''gacc<sub>0</sub> = 1''
* For ''i = 1 .. v'':
** Let ''(Q<sub>i</sub>, gacc<sub>i</sub>, tacc<sub>i</sub>) = Tweak(Q<sub>i-1</sub>, gacc<sub>i-1</sub>, tweak<sub>i</sub>, tacc<sub>i-1</sub>, is_xonly_t<sub>i</sub>)''; fail if that fails
** Let ''(Q<sub>i</sub>, gacc<sub>i</sub>, tacc<sub>i</sub>) = ApplyTweak(Q<sub>i-1</sub>, gacc<sub>i-1</sub>, tacc<sub>i-1</sub>, tweak<sub>i</sub>, is_xonly_t<sub>i</sub>)''; fail if that fails
* Return ''(Q<sub>v</sub>, gacc<sub>v</sub>, tacc<sub>v</sub>)''.

'''''HashKeys(pk<sub>1..u</sub>)''''':
Expand All @@ -234,15 +234,15 @@ Input:

'''''KeyAggCoeff(pk<sub>1..u</sub>, pk')''''':
* Let ''pk2 = GetSecondKey(pk<sub>1..u</sub>)'':
* Return ''KeyAggCoeff'(pk<sub>1..u</sub>, pk', pk2)''
* Return ''KeyAggCoeffInternal(pk<sub>1..u</sub>, pk', pk2)''

'''''KeyAggCoeff'(pk<sub>1..u</sub>, pk', pk2)''''':
'''''KeyAggCoeffInternal(pk<sub>1..u</sub>, pk', pk2)''''':
* Let ''L = HashKeys(pk<sub>1..u</sub>)''
* If ''pk' = pk2'':
** Return 1
* Return ''int(hash<sub>KeyAgg coefficient</sub>(L || pk')) mod n''<ref>The key aggregation coefficient is computed by hashing the public key instead of its index, which requires one more invocation of the SHA-256 compression function. However, it results in significantly simpler implementations because signers do not need to translate between public key indices before and after sorting.</ref>

'''''Tweak(Q<sub>i-1</sub>, gacc<sub>i-1</sub>, tweak<sub>i</sub>, tacc<sub>i-1</sub>, is_xonly_t<sub>i</sub>)''''':
'''''ApplyTweak(Q<sub>i-1</sub>, gacc<sub>i-1</sub>, tacc<sub>i-1</sub>, tweak<sub>i</sub>, is_xonly_t<sub>i</sub>)''''':
* If ''is_xonly_t<sub>i</sub>'' and ''not has_even_y(Q<sub>i-1</sub>)'':
** Let ''g<sub>i-1</sub> = -1 mod n''
* Else: let ''g<sub>i-1</sub> = 1''
Expand Down Expand Up @@ -333,7 +333,7 @@ Input:
* Let ''a = GetSessionKeyAggCoeff(session_ctx, P)''; fail if that fails
* Let ''gp = 1'' if ''has_even_y(P)'', otherwise let ''gp = -1 mod n''
* Let ''g<sub>v</sub> = 1'' if ''has_even_y(Q)'', otherwise let ''g<sub>v</sub> = -1 mod n''
* <div id="Sign negation"></div>Let ''d = g<sub>v</sub>⋅gacc<sub>v</sub>⋅gp⋅d' '' (See [[negation-of-the-secret-key-when-signing|Negation Of The Secret Key When Signing]])
* <div id="Sign negation"></div>Let ''d = g<sub>v</sub>⋅gacc<sub>v</sub>⋅gp⋅d' mod n'' (See [[negation-of-the-secret-key-when-signing|Negation Of The Secret Key When Signing]])
* Let ''s = (k<sub>1</sub> + b⋅k<sub>2</sub> + e⋅a⋅d) mod n''
* Let ''psig = bytes(s)''
* Let ''pubnonce = cbytes(k'<sub>1</sub>⋅G) || cbytes(k'<sub>2</sub>⋅G)''
Expand Down Expand Up @@ -402,10 +402,10 @@ Input:
* ''P'': a point
* The tweak ''t'': an integer with ''0 &le; t < n ''

'''''OrdinaryTweak(P, t)''''':
'''''ApplyOrdinaryTweak(P, t)''''':
* Return ''P + t⋅G''

'''''XonlyTweak(P, t)''''':
'''''ApplyXonlyTweak(P, t)''''':
* Return ''with_even_y(P) + t⋅G''

=== Negation Of The Secret Key When Signing ===
Expand Down