Skip to content

Commit 10e5f62

Browse files
authored
Merge pull request bitcoin#1592 from bigspider/bip-388-proposed
BIP-388: change status to 'Proposed'
2 parents 8256ea0 + 1d7f12d commit 10e5f62

File tree

2 files changed

+16
-16
lines changed

2 files changed

+16
-16
lines changed

README.mediawiki

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -1190,13 +1190,13 @@ Those proposing changes should consider that ultimately consent may rest with th
11901190
| Pieter Wuille, Ava Chow
11911191
| Informational
11921192
| Draft
1193-
|-
1193+
|- style="background-color: #ffffcf"
11941194
| [[bip-0388.mediawiki|388]]
11951195
| Applications
11961196
| Wallet Policies for Descriptor Wallets
11971197
| Salvatore Ingala
11981198
| Standard
1199-
| Draft
1199+
| Proposed
12001200
|-
12011201
| [[bip-0389.mediawiki|389]]
12021202
| Applications

bip-0388.mediawiki

Lines changed: 14 additions & 14 deletions
Original file line numberDiff line numberDiff line change
@@ -5,7 +5,7 @@
55
Author: Salvatore Ingala <[email protected]>
66
Comments-Summary: No comments yet.
77
Comments-URI: https://github.com/bitcoin/bips/wiki/Comments:BIP-0388
8-
Status: Draft
8+
Status: Proposed
99
Type: Standards Track
1010
Created: 2022-11-16
1111
License: BSD-2-Clause
@@ -78,14 +78,14 @@ Before a new policy is used for the first time, the user will register a wallet
7878
# After inspecting the policy and comparing it with a trusted source (for example a printed backup), the user approves the policy.
7979
# If stateful, the hardware signing device persists the policy in its permanent memory; if stateless, it returns a "proof of registration".
8080
81-
The proof of registration will allow the hardware signer to verify that a certain policy was indeed previously approved by the user, and is therefore safe to use without repeating the expensive user verification procedure. The details of how to create a proof of registration are out of scope for this document; using a Message Authentication Code on a hash committing to the wallet policy, its name and any additional metadata is an effective solution if correctly executed.
81+
The '''proof of registration''' will allow the hardware signer to verify that a certain policy was indeed previously approved by the user, and is therefore safe to use without repeating the expensive user verification procedure. The details of how to create a proof of registration are out of scope for this document; using a Message Authentication Code on a hash committing to the wallet policy, its name and any additional metadata is an effective solution if correctly executed.
8282

8383
Once a policy is registered, the hardware signing device can perform the typical operations securely:
8484
* generating receive and change addresses;
8585
* showing addresses on the secure screen;
8686
* sign transactions spending from a wallet, while correctly identifying change addresses and computing the transaction fees.
8787
88-
Before any of the actions mentioned above, the hardware signing device will retrieve the policy from its permanent storage if stateful; if stateless it will validate the '''proof of registration''' before using the wallet policy provided by the client.
88+
Before any of the actions mentioned above, the hardware signing device will retrieve the policy from its permanent storage if stateful; if stateless it will validate the proof of registration before using the wallet policy provided by the client.
8989

9090
Once the previously registered policy is correctly identified and approved by the user (for example by showing its name), and as long as the policy registration was executed securely, hardware signing devices can provide a user experience similar to the usual one for single-signature transactions.
9191

@@ -140,7 +140,7 @@ A ''wallet descriptor template'' is a <tt>SCRIPT</tt> expression.
140140
141141
The <tt>/**</tt> in the placeholder template represents commonly used paths for receive/change addresses, and is equivalent to <tt><0;1>/*</tt>.
142142

143-
Note that while [[bip-0389.mediawiki|BIP-389]] allows multipath `/<NUM;NUM;...;NUM>` expressions with an arbitrary number of options, this specification restricts it to exactly 2 choices (with the typical meaning of receive/change addresses).
143+
Note that while [[bip-0389.mediawiki|BIP-389]] allows multipath <tt>/<NUM;NUM;...;NUM></tt> expressions with an arbitrary number of options, this specification restricts it to exactly 2 choices (with the typical meaning of receive/change addresses).
144144

145145
The placeholder <tt>@i</tt> for some number ''i'' represents the ''i''-th key in the vector of key information items (which must be of size at least ''i + 1'', or the wallet policy is invalid).
146146

@@ -197,7 +197,7 @@ In order to allow supporting legacy derivation schemes (for example, using simpl
197197

198198
However, care needs to be taken in view of the following considerations:
199199

200-
* Allowing derivation schemes with a different length or cardinality in the same wallet policy would make it difficult to guarantee that there are no repeated pubkeys for every possible address generated by the policy. For example, `@0/<0;1>/*` and `@1/*` would generate the same pubkeys if the second public key in the key information vector is one of the first two unhardened children of the first public key. This could cause malleability with potential security implications (for example, in policies containing miniscript).
200+
* Allowing derivation schemes with a different length or cardinality in the same wallet policy would make it difficult to guarantee that there are no repeated pubkeys for every possible address generated by the policy. For example, <tt>@0/<0;1>/*</tt> and <tt>@1/*</tt> would generate the same pubkeys if the second public key in the key information vector is one of the first two unhardened children of the first public key. This could cause malleability with potential security implications (for example, in policies containing miniscript).
201201
* Allowing naked pubkeys with no <tt>/*</tt> suffix (for example a descriptor template like <tt>wsh(multi(2,@0,@1/<0;1>/*))</tt>) would cause a pubkey to be repeated in every output generated from the policy, which would result in a total loss of privacy.
202202
203203
== Examples ==
@@ -226,42 +226,42 @@ Some miniscript policies in <tt>wsh</tt>:
226226
[[bip-0044.mediawiki|BIP-44]], first account
227227
Descriptor template: pkh(@0/**)
228228
Keys info: ["[6738736c/44'/0'/0']xpub6Br37sWxruYfT8ASpCjVHKGwgdnYFEn98DwiN76i2oyY6fgH1LAPmmDcF46xjxJr22gw4jmVjTE2E3URMnRPEPYyo1zoPSUba563ESMXCeb"]
229-
Descriptor:pkh([6738736c/44'/0'/0']xpub6Br37sWxruYfT8ASpCjVHKGwgdnYFEn98DwiN76i2oyY6fgH1LAPmmDcF46xjxJr22gw4jmVjTE2E3URMnRPEPYyo1zoPSUba563ESMXCeb)
229+
Descriptor: pkh([6738736c/44'/0'/0']xpub6Br37sWxruYfT8ASpCjVHKGwgdnYFEn98DwiN76i2oyY6fgH1LAPmmDcF46xjxJr22gw4jmVjTE2E3URMnRPEPYyo1zoPSUba563ESMXCeb)
230230
<br>
231231
[[bip-0049.mediawiki|BIP-49]], second account
232232
Descriptor template: sh(wpkh(@0/**))
233233
Keys info: ["[6738736c/49'/0'/1']xpub6Bex1CHWGXNNwGVKHLqNC7kcV348FxkCxpZXyCWp1k27kin8sRPayjZUKDjyQeZzGUdyeAj2emoW5zStFFUAHRgd5w8iVVbLgZ7PmjAKAm9"]
234-
Descriptor:sh(wpkh([6738736c/49'/0'/1']xpub6Bex1CHWGXNNwGVKHLqNC7kcV348FxkCxpZXyCWp1k27kin8sRPayjZUKDjyQeZzGUdyeAj2emoW5zStFFUAHRgd5w8iVVbLgZ7PmjAKAm9))
234+
Descriptor: sh(wpkh([6738736c/49'/0'/1']xpub6Bex1CHWGXNNwGVKHLqNC7kcV348FxkCxpZXyCWp1k27kin8sRPayjZUKDjyQeZzGUdyeAj2emoW5zStFFUAHRgd5w8iVVbLgZ7PmjAKAm9))
235235
<br>
236236
[[bip-0084.mediawiki|BIP-84]], third account
237237
Descriptor template: wpkh(@0/**)
238238
Keys info: ["[6738736c/84'/0'/2']xpub6CRQzb8u9dmMcq5XAwwRn9gcoYCjndJkhKgD11WKzbVGd932UmrExWFxCAvRnDN3ez6ZujLmMvmLBaSWdfWVn75L83Qxu1qSX4fJNrJg2Gt"]
239-
Descriptor:wpkh([6738736c/84'/0'/2']xpub6CRQzb8u9dmMcq5XAwwRn9gcoYCjndJkhKgD11WKzbVGd932UmrExWFxCAvRnDN3ez6ZujLmMvmLBaSWdfWVn75L83Qxu1qSX4fJNrJg2Gt)
239+
Descriptor: wpkh([6738736c/84'/0'/2']xpub6CRQzb8u9dmMcq5XAwwRn9gcoYCjndJkhKgD11WKzbVGd932UmrExWFxCAvRnDN3ez6ZujLmMvmLBaSWdfWVn75L83Qxu1qSX4fJNrJg2Gt)
240240
<br>
241241
[[bip-0086.mediawiki|BIP-86]], first account
242242
Descriptor template: tr(@0/**)
243243
Keys info: ["[6738736c/86'/0'/0']xpub6CryUDWPS28eR2cDyojB8G354izmx294BdjeSvH469Ty3o2E6Tq5VjBJCn8rWBgesvTJnyXNAJ3QpLFGuNwqFXNt3gn612raffLWfdHNkYL"]
244-
Descriptor:tr([6738736c/86'/0'/0']xpub6CryUDWPS28eR2cDyojB8G354izmx294BdjeSvH469Ty3o2E6Tq5VjBJCn8rWBgesvTJnyXNAJ3QpLFGuNwqFXNt3gn612raffLWfdHNkYL)
244+
Descriptor: tr([6738736c/86'/0'/0']xpub6CryUDWPS28eR2cDyojB8G354izmx294BdjeSvH469Ty3o2E6Tq5VjBJCn8rWBgesvTJnyXNAJ3QpLFGuNwqFXNt3gn612raffLWfdHNkYL)
245245
<br>
246246
[[bip-0048.mediawiki|BIP-48]] P2WSH multisig
247247
Descriptor template: wsh(sortedmulti(2,@0/**,@1/**))
248248
Keys info: ["[6738736c/48'/0'/0'/2']xpub6FC1fXFP1GXLX5TKtcjHGT4q89SDRehkQLtbKJ2PzWcvbBHtyDsJPLtpLtkGqYNYZdVVAjRQ5kug9CsapegmmeRutpP7PW4u4wVF9JfkDhw", "[b2b1f0cf/48'/0'/0'/2']xpub6EWhjpPa6FqrcaPBuGBZRJVjzGJ1ZsMygRF26RwN932Vfkn1gyCiTbECVitBjRCkexEvetLdiqzTcYimmzYxyR1BZ79KNevgt61PDcukmC7"]
249-
Descriptor:wsh(sortedmulti(2,[6738736c/48'/0'/0'/2']xpub6FC1fXFP1GXLX5TKtcjHGT4q89SDRehkQLtbKJ2PzWcvbBHtyDsJPLtpLtkGqYNYZdVVAjRQ5kug9CsapegmmeRutpP7PW4u4wVF9JfkDhw,[b2b1f0cf/48'/0'/0'/2']xpub6EWhjpPa6FqrcaPBuGBZRJVjzGJ1ZsMygRF26RwN932Vfkn1gyCiTbECVitBjRCkexEvetLdiqzTcYimmzYxyR1BZ79KNevgt61PDcukmC7))
249+
Descriptor: wsh(sortedmulti(2,[6738736c/48'/0'/0'/2']xpub6FC1fXFP1GXLX5TKtcjHGT4q89SDRehkQLtbKJ2PzWcvbBHtyDsJPLtpLtkGqYNYZdVVAjRQ5kug9CsapegmmeRutpP7PW4u4wVF9JfkDhw,[b2b1f0cf/48'/0'/0'/2']xpub6EWhjpPa6FqrcaPBuGBZRJVjzGJ1ZsMygRF26RwN932Vfkn1gyCiTbECVitBjRCkexEvetLdiqzTcYimmzYxyR1BZ79KNevgt61PDcukmC7))
250250
<br>
251251
Miniscript: A 3-of-3 that becomes a 2-of-3 after 90 days
252252
Descriptor template: wsh(thresh(3,pk(@0/**),s:pk(@1/**),s:pk(@2/**),sln:older(12960)))
253253
Keys info: ["[6738736c/48'/0'/0'/100']xpub6FC1fXFP1GXQpyRFfSE1vzzySqs3Vg63bzimYLeqtNUYbzA87kMNTcuy9ubr7MmavGRjW2FRYHP4WGKjwutbf1ghgkUW9H7e3ceaPLRcVwa", "[b2b1f0cf/44'/0'/0'/100']xpub6EYajCJHe2CK53RLVXrN14uWoEttZgrRSaRztujsXg7yRhGtHmLBt9ot9Pd5ugfwWEu6eWyJYKSshyvZFKDXiNbBcoK42KRZbxwjRQpm5Js", "[a666a867/44'/0'/0'/100']xpub6Dgsze3ujLi1EiHoCtHFMS9VLS1UheVqxrHGfP7sBJ2DBfChEUHV4MDwmxAXR2ayeytpwm3zJEU3H3pjCR6q6U5sP2p2qzAD71x9z5QShK2"]
254-
Descriptor:wsh(thresh(3,pk([6738736c/48'/0'/0'/100']xpub6FC1fXFP1GXQpyRFfSE1vzzySqs3Vg63bzimYLeqtNUYbzA87kMNTcuy9ubr7MmavGRjW2FRYHP4WGKjwutbf1ghgkUW9H7e3ceaPLRcVwa/<0,1>/*),s:pk([b2b1f0cf/44'/0'/0'/100']xpub6EYajCJHe2CK53RLVXrN14uWoEttZgrRSaRztujsXg7yRhGtHmLBt9ot9Pd5ugfwWEu6eWyJYKSshyvZFKDXiNbBcoK42KRZbxwjRQpm5Js/<0,1>/*),s:pk([a666a867/44'/0'/0'/100']xpub6Dgsze3ujLi1EiHoCtHFMS9VLS1UheVqxrHGfP7sBJ2DBfChEUHV4MDwmxAXR2ayeytpwm3zJEU3H3pjCR6q6U5sP2p2qzAD71x9z5QShK2/<0,1>/*),sln:older(12960)))
254+
Descriptor: wsh(thresh(3,pk([6738736c/48'/0'/0'/100']xpub6FC1fXFP1GXQpyRFfSE1vzzySqs3Vg63bzimYLeqtNUYbzA87kMNTcuy9ubr7MmavGRjW2FRYHP4WGKjwutbf1ghgkUW9H7e3ceaPLRcVwa/<0,1>/*),s:pk([b2b1f0cf/44'/0'/0'/100']xpub6EYajCJHe2CK53RLVXrN14uWoEttZgrRSaRztujsXg7yRhGtHmLBt9ot9Pd5ugfwWEu6eWyJYKSshyvZFKDXiNbBcoK42KRZbxwjRQpm5Js/<0,1>/*),s:pk([a666a867/44'/0'/0'/100']xpub6Dgsze3ujLi1EiHoCtHFMS9VLS1UheVqxrHGfP7sBJ2DBfChEUHV4MDwmxAXR2ayeytpwm3zJEU3H3pjCR6q6U5sP2p2qzAD71x9z5QShK2/<0,1>/*),sln:older(12960)))
255255
<br>
256256
Miniscript: A singlesig wallet with automatic inheritance to a timelocked 2-of-3 multisig
257257
Descriptor template: wsh(or_d(pk(@0/**),and_v(v:multi(2,@1/**,@2/**,@3/**),older(65535))))
258258
Keys info: ["[6738736c/48'/0'/0'/100']xpub6FC1fXFP1GXQpyRFfSE1vzzySqs3Vg63bzimYLeqtNUYbzA87kMNTcuy9ubr7MmavGRjW2FRYHP4WGKjwutbf1ghgkUW9H7e3ceaPLRcVwa", "[b2b1f0cf/44'/0'/0'/100']xpub6EYajCJHe2CK53RLVXrN14uWoEttZgrRSaRztujsXg7yRhGtHmLBt9ot9Pd5ugfwWEu6eWyJYKSshyvZFKDXiNbBcoK42KRZbxwjRQpm5Js", "[a666a867/44'/0'/0'/100']xpub6Dgsze3ujLi1EiHoCtHFMS9VLS1UheVqxrHGfP7sBJ2DBfChEUHV4MDwmxAXR2ayeytpwm3zJEU3H3pjCR6q6U5sP2p2qzAD71x9z5QShK2", "[bb641298/44'/0'/0'/100']xpub6Dz8PHFmXkYkykQ83ySkruky567XtJb9N69uXScJZqweYiQn6FyieajdiyjCvWzRZ2GoLHMRE1cwDfuJZ6461YvNRGVBJNnLA35cZrQKSRJ"]
259-
Descriptor:wsh(or_d(pk([6738736c/48'/0'/0'/100']xpub6FC1fXFP1GXQpyRFfSE1vzzySqs3Vg63bzimYLeqtNUYbzA87kMNTcuy9ubr7MmavGRjW2FRYHP4WGKjwutbf1ghgkUW9H7e3ceaPLRcVwa),and_v(v:multi(2,[b2b1f0cf/44'/0'/0'/100']xpub6EYajCJHe2CK53RLVXrN14uWoEttZgrRSaRztujsXg7yRhGtHmLBt9ot9Pd5ugfwWEu6eWyJYKSshyvZFKDXiNbBcoK42KRZbxwjRQpm5Js,[a666a867/44'/0'/0'/100']xpub6Dgsze3ujLi1EiHoCtHFMS9VLS1UheVqxrHGfP7sBJ2DBfChEUHV4MDwmxAXR2ayeytpwm3zJEU3H3pjCR6q6U5sP2p2qzAD71x9z5QShK2,[bb641298/44'/0'/0'/100']xpub6Dz8PHFmXkYkykQ83ySkruky567XtJb9N69uXScJZqweYiQn6FyieajdiyjCvWzRZ2GoLHMRE1cwDfuJZ6461YvNRGVBJNnLA35cZrQKSRJ),older(65535))))
259+
Descriptor: wsh(or_d(pk([6738736c/48'/0'/0'/100']xpub6FC1fXFP1GXQpyRFfSE1vzzySqs3Vg63bzimYLeqtNUYbzA87kMNTcuy9ubr7MmavGRjW2FRYHP4WGKjwutbf1ghgkUW9H7e3ceaPLRcVwa),and_v(v:multi(2,[b2b1f0cf/44'/0'/0'/100']xpub6EYajCJHe2CK53RLVXrN14uWoEttZgrRSaRztujsXg7yRhGtHmLBt9ot9Pd5ugfwWEu6eWyJYKSshyvZFKDXiNbBcoK42KRZbxwjRQpm5Js,[a666a867/44'/0'/0'/100']xpub6Dgsze3ujLi1EiHoCtHFMS9VLS1UheVqxrHGfP7sBJ2DBfChEUHV4MDwmxAXR2ayeytpwm3zJEU3H3pjCR6q6U5sP2p2qzAD71x9z5QShK2,[bb641298/44'/0'/0'/100']xpub6Dz8PHFmXkYkykQ83ySkruky567XtJb9N69uXScJZqweYiQn6FyieajdiyjCvWzRZ2GoLHMRE1cwDfuJZ6461YvNRGVBJNnLA35cZrQKSRJ),older(65535))))
260260
<br>
261261
Taproot wallet policy with sortedmulti_a and a miniscript leaf
262262
Descriptor template: tr(@0/**,{sortedmulti_a(1,@0/<2;3>/*,@1/**),or_b(pk(@2/**),s:pk(@3/**))})
263263
Keys info: ["[6738736c/48'/0'/0'/100']xpub6FC1fXFP1GXQpyRFfSE1vzzySqs3Vg63bzimYLeqtNUYbzA87kMNTcuy9ubr7MmavGRjW2FRYHP4WGKjwutbf1ghgkUW9H7e3ceaPLRcVwa", "xpub6Fc2TRaCWNgfT49nRGG2G78d1dPnjhW66gEXi7oYZML7qEFN8e21b2DLDipTZZnfV6V7ivrMkvh4VbnHY2ChHTS9qM3XVLJiAgcfagYQk6K", "xpub6GxHB9kRdFfTqYka8tgtX9Gh3Td3A9XS8uakUGVcJ9NGZ1uLrGZrRVr67DjpMNCHprZmVmceFTY4X4wWfksy8nVwPiNvzJ5pjLxzPtpnfEM", "xpub6GjFUVVYewLj5no5uoNKCWuyWhQ1rKGvV8DgXBG9Uc6DvAKxt2dhrj1EZFrTNB5qxAoBkVW3wF8uCS3q1ri9fueAa6y7heFTcf27Q4gyeh6"]
264-
Descriptor:tr([6738736c/48'/0'/0'/100']xpub6FC1fXFP1GXQpyRFfSE1vzzySqs3Vg63bzimYLeqtNUYbzA87kMNTcuy9ubr7MmavGRjW2FRYHP4WGKjwutbf1ghgkUW9H7e3ceaPLRcVwa/<0;1>/*,{sortedmulti_a(1,xpub6FC1fXFP1GXQpyRFfSE1vzzySqs3Vg63bzimYLeqtNUYbzA87kMNTcuy9ubr7MmavGRjW2FRYHP4WGKjwutbf1ghgkUW9H7e3ceaPLRcVwa/<2;3>/*,xpub6Fc2TRaCWNgfT49nRGG2G78d1dPnjhW66gEXi7oYZML7qEFN8e21b2DLDipTZZnfV6V7ivrMkvh4VbnHY2ChHTS9qM3XVLJiAgcfagYQk6K/<0;1>/*),or_b(pk(xpub6GxHB9kRdFfTqYka8tgtX9Gh3Td3A9XS8uakUGVcJ9NGZ1uLrGZrRVr67DjpMNCHprZmVmceFTY4X4wWfksy8nVwPiNvzJ5pjLxzPtpnfEM/<0;1>/*),s:pk(xpub6GjFUVVYewLj5no5uoNKCWuyWhQ1rKGvV8DgXBG9Uc6DvAKxt2dhrj1EZFrTNB5qxAoBkVW3wF8uCS3q1ri9fueAa6y7heFTcf27Q4gyeh6/<0;1>/*))})
264+
Descriptor: tr([6738736c/48'/0'/0'/100']xpub6FC1fXFP1GXQpyRFfSE1vzzySqs3Vg63bzimYLeqtNUYbzA87kMNTcuy9ubr7MmavGRjW2FRYHP4WGKjwutbf1ghgkUW9H7e3ceaPLRcVwa/<0;1>/*,{sortedmulti_a(1,xpub6FC1fXFP1GXQpyRFfSE1vzzySqs3Vg63bzimYLeqtNUYbzA87kMNTcuy9ubr7MmavGRjW2FRYHP4WGKjwutbf1ghgkUW9H7e3ceaPLRcVwa/<2;3>/*,xpub6Fc2TRaCWNgfT49nRGG2G78d1dPnjhW66gEXi7oYZML7qEFN8e21b2DLDipTZZnfV6V7ivrMkvh4VbnHY2ChHTS9qM3XVLJiAgcfagYQk6K/<0;1>/*),or_b(pk(xpub6GxHB9kRdFfTqYka8tgtX9Gh3Td3A9XS8uakUGVcJ9NGZ1uLrGZrRVr67DjpMNCHprZmVmceFTY4X4wWfksy8nVwPiNvzJ5pjLxzPtpnfEM/<0;1>/*),s:pk(xpub6GjFUVVYewLj5no5uoNKCWuyWhQ1rKGvV8DgXBG9Uc6DvAKxt2dhrj1EZFrTNB5qxAoBkVW3wF8uCS3q1ri9fueAa6y7heFTcf27Q4gyeh6/<0;1>/*))})
265265
<br>
266266

267267
=== Invalid policies ===
@@ -281,7 +281,7 @@ Remark: some of the examples of invalid descriptor templates may be valid via op
281281

282282
== Backwards Compatibility ==
283283

284-
The <tt>@</tt> character used for key placeholders is not part of the syntax of output script descriptors, therefore any valid descriptor with at least one `KEY` expression is not a valid descriptor template. Vice versa, any descriptor template with at least one key placeholder is not a valid output script descriptor.
284+
The <tt>@</tt> character used for key placeholders is not part of the syntax of output script descriptors, therefore any valid descriptor with at least one <tt>KEY</tt> expression is not a valid descriptor template. Vice versa, any descriptor template with at least one key placeholder is not a valid output script descriptor.
285285

286286
Adoption of wallet policies in software and hardware wallets is opt-in. Conversion from wallet policies to the corresponding descriptors is programmatically extremely easy, and conversion from descriptors to wallet policies (when respecting the required patterns) can be automated. See the reference implementation below for some examples of conversion.
287287

0 commit comments

Comments
 (0)