Benjamin_Loison/Variable_MLS
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Update on Overleaf.

Browse Source
This commit is contained in:
Benjamin Loison
2023-06-22 08:56:12 +00:00
committed by node
parent 240e4a57c8
commit ed07c403a8
2 changed files with 7 additions and 6 deletions
Download Patch File Download Diff File Expand all files Collapse all files

10
ccs-body.tex
View File

@@ -17,8 +17,8 @@ Consensus data includes consensus-critical information such as proof-of-work or
Everything that is part of the block header is considered consensus data.
While application data can grow or shrink depending on the implementation, consensus data grows boundlessly at a constant linear rate in time~\cite{kiayias2021mining}.
Recently, Kiayias~\textit{et al.}~\cite{kiayias2021mining} have proposed a blockchain protocol to reduce storage and communication complexity of blockchains to $O(polylog(n))$.
However, the security of their protocol was only proven if a fixed PoW difficulty is assumed for ll blocks. This is not a realistic assumption in practice. For example the block difficulty in Bitcoin has shown exponential growth in the past decade.
Recently, Kiayias~\textit{et al.}~\cite{kiayias2021mining} have proposed a blockchain protocol to reduce storage and communication complexity of PoW blockchains to $O(polylog(n))$.
However, the security of their protocol was only proven if a fixed PoW difficulty is assumed for all blocks. This is not a realistic assumption in practice. For example the block difficulty in Bitcoin has shown exponential growth in the past decade.
In this work, we address this important issue and present XX (un petit nom ??), a scheme to construct a succinct representation of the blockchain using Non-Interactive Proofs-of-Proof-of-Works (NIPoPoWs) that also operates in $O(\polylog(n))$ storage complexity and $O(\polylog(n))$ communication complexity and handles a variable difficulty for the blocks of the blockchain. The main idea of our construction is to XXXXXXXX
@@ -66,7 +66,7 @@ The application state at the end of the blockchain can then be computed by start
The second school argues for storing both transactions and the state after these transactions have been applied (called a snapshot), in each block.
In such a system, the application state at the end of the blockchain does not need to be computed by applying the blocks.
Instead, a block near the end of the chain can simply be inspected, and the application state within extracted.
Instead, a block near the end of the chain can simply be inspected, and the application state within it extracted.
This can result in faster queries and simpler implementation of certain types of smart contracts.
However, this approach requires more storage space and can make synchronization of the network more complex.
@@ -123,7 +123,7 @@ However, the adversary remains computationally bounded. Hence, it cannot, in a p
% Second, we assume that \hash{.} values are uniformly distributed over the \(\llbracket 0 ; 2^{\ell} -1\rrbracket \)interval.
% Finally, we assume that \hash{.} is collision free in the sense that given two blocks \(b_1, b_2\) we have \(b_1 = b_2 \Leftrightarrow \) \hash{b_1} = \hash{b_2}.
% \textcolor{blue}{je ne suis pas completement sûre que la suite fasse partie du modèle. En fait il faut mettre toute cette partie là où on va expliquer notre solution}
% \textcolor{blue}{je ne suis pas completement sûre que la suite fasse partie du modèle. En fait il faut mettre toute cette partie là où on va expliquer notre solution}
% In addition to the application specifications, a block \(b\) is valid if it can be appended to a prefix of the current blockchain.
% Note that a block is not required to extend the best blockchain. On the contrary, it can happen that this addition may change the best blockchain.
% PoW systems rely on two additional functions, namely \diff{.} and \target{.}.
@@ -294,7 +294,7 @@ Flyclient~\cite{9152680} allows a succinct and secure construction of proofs in
Another approach to build succinct proofs is to rely on SNARKS (for Succinct Non-Interactive Argument of Knowledge). Coda~\cite{coda2020} is such a construction. Coda compresses a chain to polylogarithmic size and updates the proof with new blocks. However, leveraging SNARKs requires a trusted setup for the common reference string.
Kiayias et al.~\cite{10.1007/978-3-662-53357-4_5} introduced and formalized an interactive proof mechanism, \emph{Proofs-of-Proof-of-Work} (PoPoW) based on superblocks that allows a client to verify a chain in sublinear time and communication complexity. However, the authors later showed the existence of an attack on the scheme and proposed a non-interactive alternative (NIPoPoWs)~\cite{10.1145/3460120.3484784}. However, the proposed solution did not address the size of the blockchain that needed to be stored by any miner. The authors further used NIPoPoWs to develop a scheme that also allows the miners to operate in $O(\polylog(n))$ storage and communication complexity while reducing the security tolerance to a Byzantine adversary that controls strictly less than a third of the total computation power and limiting itself to operate in an environment with a fixed difficulty~\cite{10.1145/3460120.3484784}.
Kiayias et al.~\cite{10.1007/978-3-662-53357-4_5} introduced and formalized an interactive proof mechanism, \emph{Proofs-of-Proof-of-Work} (PoPoW) based on superblocks that allows a client to verify a chain in sublinear time and communication complexity. However, the authors later showed the existence of an attack on the scheme and proposed a non-interactive alternative (NIPoPoWs)~\cite{10.1145/3460120.3484784}, but the proposed solution did not address the size of the blockchain that needed to be stored by any miner. The authors further used NIPoPoWs to develop a scheme that also allows the miners to operate in $O(\polylog(n))$ storage and communication complexity while reducing the security tolerance to a Byzantine adversary that controls strictly less than a third of the total computation power and limiting itself to operate in an environment with a fixed difficulty~\cite{10.1145/3460120.3484784}.
The authors in~\cite{jain2022extending} propose a scheme to construct a succinct representation of the blockchain using NIPoPoWs that also operates in $O(\polylog(n))$ storage complexity and $O(\polylog(n))$ communication complexity and which provably achieves security against a Byzantine adversary that controls strictly less than half of the total computational power.
%