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Merge ElementsProject/secp256k1-zkp#182: musig-spec: address robot-dreams' comments

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b7f8ea2f2a828cb5a6804320a39750a77fffafba musig-spec: address robot-dreams' comments (Jonas Nick)

Pull request description:

  - KeyAggCoeff' -> KeyAggCoeffInternal for consistency
  - In Sign, add mod n when calculating d
  - In Tweak, reorder the parameters to (Q, gacc, tacc, tweak, is_xonly) because
    the first three are "state" arguments
  - Rename Tweak function to ApplyTweak to avoid confusion with tweak (the
    vector). This becomes apparent in the python reference code.

ACKs for top commit:
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    ACK b7f8ea2f2a828cb5a6804320a39750a77fffafba

Tree-SHA512: 6f9066af2f67b6d2769f38ebb2537769568e77bab18d487590a0095a695eab5c34a7177e4d299f27e3e30628dd07aff831f3f08db256cf2ae13ea0d92f3e18b8
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Tim Ruffing 2022-04-05 10:40:46 +02:00
commit 4469cad42f
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1 changed files with 8 additions and 8 deletions
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doc/musig-spec.mediawiki
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@ -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>)''''':
@ -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''
@ -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)''
@ -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 ===