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From: Salvatore Ingala <salvatore.ingala@gmail.com>
Date: Mon, 8 Jun 2020 11:28:28 +0200
Message-ID: <CAMhCMoELX-=9N08KE499yjPNzH6xPqBB+gAKgQMTxbnsWQuV1w@mail.gmail.com>
To: bitcoin-dev@lists.linuxfoundation.org
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Subject: [bitcoin-dev] Hash-based accumulators with quick insertion
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Dear all,

I have been working on some constructions for cryptographic accumulators
that optimise for quick insertion.

As a brief background, an accumulator is a data structure that maintains
compact commitments to a potentially very large (and dynamic) set, while
keeping proofs of membership short. Unsurprisingly, they are getting more
popular, and one notable application in Bitcoin is to create light-weight
full nodes that do not need to store the UTXO set (Utreexo accumulator[1]).

In this work, I focus on additive accumulators that supports adding new
elements, but not removing them. My motivation is to support extending
Script with access to an arbitrarily large portion of the blockchain
history and state (e.g., past blocks, txids, or any more complex state
obtained from them - with all due care). The additional storage and
computation cost for nodes is small, and the cost (in additional bytesize)
for any transaction that wishes to access state committed in the
accumulator should be just slightly bigger than typical Merkle proofs.

I have focused on:
- An accumulator with insertion time O(1) and proof size O(log^2 n)
- A construction with insertion time O(log log n) and proof size O(log n
log log n)

All the performance metrics above are in "number of hashes".

You can find:
- draft writeup:
https://github.com/bigspider/accumulator/blob/master/docs/paper-draft.pdf
- sample python code (only for the first construction at this time):
https://github.com/bigspider/accumulator

While this is still an unfinished work, the ideas in the draft are
hopefully clear enough and easy to understand. I wanted to share it at this
stage as it can benefit from comments to improve the constructions, to
cover any related work or to find potential applications in Bitcoin (e.g.
Script, layer2, side chains, etc).

Best,
Salvatore Ingala

[1] - Thaddeus Dryja, Utreexo: A dynamic hash-based accumulator optimized
for the Bitcoin UTXO set - https://eprint.iacr.org/2019/611.pdf

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<div dir=3D"ltr">Dear all,<br><br>I have been working on some constructions=
 for cryptographic accumulators that optimise for quick insertion. <br><br>=
As a brief background, an accumulator is a data structure that maintains co=
mpact commitments to a potentially very large (and dynamic) set, while keep=
ing proofs of membership short. Unsurprisingly, they are getting more popul=
ar, and one notable application in Bitcoin is to create light-weight full n=
odes that do not need to store the UTXO set (Utreexo accumulator[1]).<br><b=
r>In this work, I focus on additive accumulators that supports adding new e=
lements, but not removing them. My motivation is to support extending Scrip=
t with access to an arbitrarily large portion of the blockchain history and=
 state (e.g., past blocks, txids, or any more complex state obtained from t=
hem - with all due care). The additional storage and computation cost for n=
odes is small, and the cost (in additional bytesize) for any transaction th=
at wishes to access state committed in the accumulator should be just sligh=
tly bigger than typical Merkle proofs.<br><br>I have focused on: <br>- An a=
ccumulator with insertion time O(1) and proof size O(log^2 n)<br>- A constr=
uction with insertion time O(log log n) and proof size O(log n log log n)<d=
iv><br></div><div>All the performance metrics above are in &quot;number of =
hashes&quot;.<br><br>You can find:<br>- draft writeup: <a href=3D"https://g=
ithub.com/bigspider/accumulator/blob/master/docs/paper-draft.pdf">https://g=
ithub.com/bigspider/accumulator/blob/master/docs/paper-draft.pdf</a><br>- s=
ample python code (only for the first construction at this time): <a href=
=3D"https://github.com/bigspider/accumulator">https://github.com/bigspider/=
accumulator</a><br><br>While this is still an unfinished work, the ideas in=
 the draft are hopefully clear enough and easy to understand. I wanted to s=
hare it at this stage as it can benefit from comments to improve the constr=
uctions, to cover any related work or to find potential applications in Bit=
coin (e.g. Script, layer2, side chains, etc).<br><br>Best,<br>Salvatore Ing=
ala<br><br>[1] - Thaddeus Dryja, Utreexo: A dynamic hash-based accumulator =
optimized for the Bitcoin UTXO set - <a href=3D"https://eprint.iacr.org/201=
9/611.pdf">https://eprint.iacr.org/2019/611.pdf</a><br></div></div>

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