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musig-spec: fix unnecessary O(n^2) KeyAgg runtime

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Jonas Nick 2022-03-23 14:24:03 +00:00
parent d13429e28c
commit ef537b2065
1 changed files with 11 additions and 6 deletions
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doc/musig-spec.mediawiki
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@ -90,9 +90,10 @@ The algorithm '''''KeyAgg(pk<sub>1..u</sub>, tweak<sub>1..v</sub>, is_xonly_t<su
* Return ''bytes(Q)''. * Return ''bytes(Q)''.
The algorithm '''''KeyAggInternal(pk<sub>1..u</sub>, tweak<sub>1..v</sub>, is_xonly_t<sub>1..v</sub>)''''' is defined as: The algorithm '''''KeyAggInternal(pk<sub>1..u</sub>, tweak<sub>1..v</sub>, is_xonly_t<sub>1..v</sub>)''''' is defined as:
* Let ''pk2 = GetSecondKey(pk<sub>1..u</sub>)''
* For ''i = 1 .. u'': * For ''i = 1 .. u'':
** Let ''a<sub>i</sub> = KeyAggCoeff(pk<sub>1..u</sub>, pk<sub>i</sub>)''.
** Let ''P<sub>i</sub> = point(pk<sub>i</sub>)''; fail if that fails. ** 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 ''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>'' * 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>)''. * Fail if ''is_infinite(Q<sub>0</sub>)''.
* Let ''tacc<sub>0</sub> = 0'' * Let ''tacc<sub>0</sub> = 0''
@ -104,15 +105,19 @@ The algorithm '''''KeyAggInternal(pk<sub>1..u</sub>, tweak<sub>1..v</sub>, is_xo
The algorithm '''''HashKeys(pk<sub>1..u</sub>)''''' is defined as: The algorithm '''''HashKeys(pk<sub>1..u</sub>)''''' is defined as:
* Return ''hash<sub>KeyAgg list</sub>(pk<sub>1</sub> || pk<sub>2</sub> || ... || pk<sub>u</sub>)'' * Return ''hash<sub>KeyAgg list</sub>(pk<sub>1</sub> || pk<sub>2</sub> || ... || pk<sub>u</sub>)''
The algorithm '''''IsSecond(pk<sub>1..u</sub>, pk')''''' is defined as: The algorithm '''''GetSecondKey(pk<sub>1..u</sub>)''''' is defined as:
* For ''j = 1 .. u'': * For ''j = 1 .. u'':
** If ''pk<sub>j</sub> &ne; pk<sub>1</sub>'': ** If ''pk<sub>j</sub> &ne; pk<sub>1</sub>'':
*** Return ''true'' if ''pk<sub>j</sub> = pk' '', otherwise return ''false''. *** Return ''pk<sub>j</sub>''
* Return ''false'' * Return ''bytes(0)''
The algorithm '''''KeyAggCoeff(pk<sub>1..u</sub>, pk')''''' is defined as: The algorithm '''''KeyAggCoeff(pk<sub>1..u</sub>, pk')''''' is defined as:
* Let ''L = HashKeys(pk<sub>1..u</sub>)''. * Let ''pk2 = GetSecondKey(pk<sub>1..u</sub>)'':
* If ''IsSecond(pk<sub>1..u</sub>, pk')'': * Return ''KeyAggCoeff'(pk<sub>1..u</sub>, pk', pk2)''
The algorithm '''''KeyAggCoeff'(pk<sub>1..u</sub>, pk', pk2)''''' is defined as:
* Let ''L = HashKeys(pk<sub>1..u</sub>)''
* If ''pk' = pk2'':
** Return 1 ** Return 1
* Return ''int(hash<sub>KeyAgg coefficient</sub>(L || pk')) mod n'' * Return ''int(hash<sub>KeyAgg coefficient</sub>(L || pk')) mod n''