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From: shymaa arafat <shymaa.arafat@gmail.com>
Date: Fri, 12 Nov 2021 00:28:39 +0200
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Subject: [bitcoin-dev] Providing "non-inclusion proofs" to "append to the
 right Merkles" with minimized overhead
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Dear Bitcoin Developers,
Hi everybody,
Please allow me to suggest this idea, hope you find it worth reading &
commenting....

While append to the right UTXO Merkles have the much needed advantage of
locality of reference that leads to shorter batch proofs, they're
criticized by some for not providing non-inclusion proofs. This is a
suggestion to slightly change the needed anyway map/dictionary to map the
UTXOS to their positions as leaves given their hash value, so that it can
provide non-inclusion proofs....

1-A 2=E2=81=B6=E2=81=B4 (could be tuned*) pointer vector is allocated to pu=
t the  UTXO in a
bucket according to its hash.
2-Due to the Cryptographic hash robustness & bit randomness UTXO hashes
should fall uniformly as all buckets are equiprobable and each bucket is
expected to contain 1-2 UTXOS (less than Go lang map load factor which is
6.5-8, 2=C2=B3=C2=B2 entry may lead to the same)
3-Insertion is adding a node (in order)to the bucket linked list, deletion
is deleting a node from the bucket list; the vector bucket pointer maybe
adjusted in the process from or to NULL value.
.
The strucutre should be as in attached figure:
Vector of pointers to buckets that could be linked lists with the following
fields in each node:
-A pointer to the UTXO leaf in the main Merkle
-The value of the remaining hash bits, or could be omitted with its value
with the leaf node.
-two bit flag that will be explained shortly.
.
4-To save computation time, we may calculate and send the accumulated root
value of this secondary tree only once per block; either at the end if
valid or when encountering an invalid UTXO to send the non-inclusion proof
and abort the whole block. Like the Tx Merkle, maybe no need to store the
tree or maybe it will save time for the non changed parts (experimental).
5-The non-inclusion proof will be send according to the previous block
accumulated root, so during batch preparation a newly inserted  UTXO will
be flagged 1, a deleted UTXO is  flagged -1, and 0 means value the same as
previous block.
6-If the block is valid, update and reset flags to 0 while computing the
new root. A hash of a bucket is the concatenation of all its nodes(expected
to be2), and empty buckets are substituted by a default NULL hash value.
7-If we had an invalid UTXO, we have two cases:
a)-The hash doesn't exist in any case ( not even with a deleted flag), in
this case we send the usual non-inclusion proof considering old status
before any UTXO from this block.
b)-The UTXO hash is there, but has a deleted flag (it was spent before
during this block); ie, a double spend within the same block.
Now, in this case I do have some doubts and suggestions or comments are
welcomed:
I think we should resend the previous inclusion proof along saying
something like "TX ID ....spent it with proof...."
I guess this an implementation detail of how to point out to a previous
proof in the same block
( I assume such a block is going to be aborted anyways after the invalid
UTXO and old status will be resumed, if this is wrong please say so)
.
That's all, thank you for your time,
Shymaa M. Arafat

--000000000000fe95f605d08add8e
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"auto"><div dir=3D"auto">Dear Bitcoin Developers,</div><div dir=
=3D"auto">Hi everybody,</div><div dir=3D"auto">Please allow me to suggest t=
his idea, hope you find it worth reading &amp;=C2=A0 commenting....</div><d=
iv dir=3D"auto"><br></div>While append to the right UTXO Merkles have the m=
uch needed advantage of locality of reference that leads to shorter batch p=
roofs, they&#39;re criticized by some for not providing non-inclusion proof=
s. This is a suggestion to slightly change the needed anyway map/dictionary=
 to map the UTXOS to their positions as leaves given their hash value, so t=
hat it can provide non-inclusion proofs....<div dir=3D"auto"><br></div><div=
 dir=3D"auto">1-A 2=E2=81=B6=E2=81=B4 (could be tuned*) pointer vector is a=
llocated to put the=C2=A0 UTXO in a bucket according to its hash.</div><div=
 dir=3D"auto">2-Due to the Cryptographic hash robustness &amp; bit randomne=
ss UTXO hashes should fall uniformly as all buckets are equiprobable and ea=
ch bucket is expected to contain 1-2 UTXOS (less than Go lang map load fact=
or which is 6.5-8, 2=C2=B3=C2=B2 entry may lead to the same)</div><div dir=
=3D"auto">3-Insertion is adding a node (in order)to the bucket linked list,=
 deletion is deleting a node from the bucket list; the vector bucket pointe=
r maybe adjusted in the process from or to NULL value.</div><div dir=3D"aut=
o">.</div><div dir=3D"auto">The strucutre should be as in attached figure:<=
/div><div dir=3D"auto">Vector of pointers to buckets that could be linked l=
ists with the following fields in each node:</div><div dir=3D"auto">-A poin=
ter to the UTXO leaf in the main Merkle</div><div dir=3D"auto">-The value o=
f the remaining hash bits, or could be omitted with its value with the leaf=
 node.</div><div dir=3D"auto">-two bit flag that will be explained shortly.=
</div><div dir=3D"auto">.</div><div dir=3D"auto">4-To save computation time=
, we may calculate and send the accumulated root value of this secondary tr=
ee only once per block; either at the end if valid or when encountering an =
invalid UTXO to send the non-inclusion proof and abort the whole block. Lik=
e the Tx Merkle, maybe no need to store the tree or maybe it will save time=
 for the non changed parts (experimental).</div><div dir=3D"auto">5-The non=
-inclusion proof will be send according to the previous block accumulated r=
oot, so during batch preparation a newly inserted=C2=A0 UTXO will be flagge=
d 1, a deleted UTXO is=C2=A0 flagged -1, and 0 means value the same as prev=
ious block.</div><div dir=3D"auto">6-If the block is valid, update and rese=
t flags to 0 while computing the new root. A hash of a bucket is the concat=
enation of all its nodes(expected to be2), and empty buckets are substitute=
d by a default NULL hash value.</div><div dir=3D"auto">7-If we had an inval=
id UTXO, we have two cases:</div><div dir=3D"auto">a)-The hash doesn&#39;t =
exist in any case ( not even with a deleted flag), in this case we send the=
 usual non-inclusion proof considering old status before any UTXO from this=
 block.</div><div dir=3D"auto">b)-The UTXO hash is there, but has a deleted=
 flag (it was spent before during this block); ie, a double spend within th=
e same block.</div><div dir=3D"auto">Now, in this case I do have some doubt=
s and suggestions or comments are welcomed:</div><div dir=3D"auto">I think =
we should resend the previous inclusion proof along saying something like &=
quot;TX ID ....spent it with proof....&quot;</div><div dir=3D"auto">I guess=
 this an implementation detail of how to point out to a previous proof in t=
he same block=C2=A0</div><div dir=3D"auto">( I assume such a block is going=
 to be aborted anyways after the invalid UTXO and old status will be resume=
d, if this is wrong please say so)</div><div dir=3D"auto">.</div><div dir=
=3D"auto">That&#39;s all, thank you for your time,</div><div dir=3D"auto">S=
hymaa M. Arafat</div><div dir=3D"auto"><br></div></div>

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