From b44fc0d6ec646e873ee1bf1ac9705f7e1ad7c3d7 Mon Sep 17 00:00:00 2001 From: Hamy Ratoanina Date: Fri, 17 Nov 2023 18:18:47 -0500 Subject: [PATCH] Add specs for KeccakSponge (#1366) * Add specs for KeccakSponge * Apply comments --- evm/spec/tables/keccak-sponge.tex | 66 +++++++++++++++++++++++++++++- evm/spec/zkevm.pdf | Bin 189454 -> 199514 bytes 2 files changed, 64 insertions(+), 2 deletions(-) diff --git a/evm/spec/tables/keccak-sponge.tex b/evm/spec/tables/keccak-sponge.tex index 29f71ba1..a712335b 100644 --- a/evm/spec/tables/keccak-sponge.tex +++ b/evm/spec/tables/keccak-sponge.tex @@ -1,4 +1,66 @@ -\subsection{Keccak sponge} +\subsection{KeccakSponge} \label{keccak-sponge} -This table computes the Keccak256 hash, a sponge-based hash built on top of the Keccak-f[1600] permutation. +This table computes the Keccak256 hash, a sponge-based hash built on top of the Keccak-f[1600] permutation. An instance of KeccakSponge takes as input a Memory address $a$, +a length $l$, and computes the Keccak256 digest of the memory segment starting at $a$ and of size $l$. An instance can span many rows, each individual row being a single call to +the Keccak table. Note that all the read elements must be bytes; the proof will be unverifiable if this is not the case. Following the Keccak specifications, the input string is padded to the next multiple of 136 bytes. +Each row contains the following columns: +\begin{itemize} + \item Read bytes: + \begin{itemize} + \item 3 address columns: \texttt{context}, \texttt{segment} and the offset \texttt{virt} of $a$. + \item \texttt{timestamp}: the timestamp which will be used for all memory reads of this instance. + \item \texttt{already\_absorbed\_bytes}: keeps track of how many bytes have been hashed in the current instance. At the end of an instance, we should have absorbed $l$ bytes in total. + \item \texttt{KECCAK\_RATE\_BYTES} \texttt{block\_bytes} columns: the bytes being absorbed at this row. They are read from memory and will be XORed to the rate part of the current state. + \end{itemize} + \item Input columns: + \begin{itemize} + \item \texttt{KECCAK\_RATE\_U32S} \texttt{original\_rate\_u32s} columns: hold the rate part of the state before XORing it with \texttt{block\_bytes}. At the beginning of an instance, they are initialized with 0. + \item \texttt{KECCAK\_RATE\_U32s} \texttt{xored\_rate\_u32s} columns: hold the original rate XORed with \texttt{block\_bytes}. + \item \texttt{KECCAK\_CAPACITY\_U32S} \texttt{original\_capacity\_u32s} columns: hold the capacity part of the state before applying the Keccak permutation. + \end{itemize} + \item Output columns: + \begin{itemize} + \item \texttt{KECCAK\_DIGEST\_BYTES} \texttt{updated\_digest\_state\_bytes columns}: the beginning of the output state after applying the Keccak permutation. At the last row of an instance, they hold the computed hash. +They are decomposed in bytes for endianness reasons. + \item \texttt{KECCAK\_WIDTH\_MINUS\_DIGEST\_U32S} \texttt{partial\_updated\_state\_u32s} columns: the rest of the output state. They are discarded for the final digest, but are used between instance rows. + \end{itemize} + \item Helper columns: + \begin{itemize} + \item \texttt{is\_full\_input\_block}: indicates if the current row has a full input block, i.e. \texttt{block\_bytes} contains only bytes read from memory and no padding bytes. + \item \texttt{KECCAK\_RATE\_BYTES} \texttt{is\_final\_input\_len} columns: in the final row of an instance, indicate where the final read byte is. If the $i$-th column is set to 1, it means that +all bytes after the $i$-th are padding bytes. In a full input block, all columns are set to 0. + \end{itemize} +\end{itemize} + +For each instance, constraints ensure that: +\begin{itemize} + \item at each row: + \begin{itemize} + \item \texttt{is\_full\_input\_block} and \texttt{is\_final\_input\_len} columns are all binary. + \item Only one column in \texttt{is\_full\_input\_block} and \texttt{is\_final\_input\_len} is set to 1. + \item \texttt{xored\_rate\_u32s} is \texttt{original\_rate\_u32s} XOR \texttt{block\_bytes}. + \item The CTL with Keccak ensures that (\texttt{updated\_digest\_state\_bytes columns}, \texttt{partial\_updated\_state\_u32s}) is the Keccak permutation output of (\texttt{xored\_rate\_u32s}, \texttt{original\_capacity\_u32s}). + \end{itemize} + \item at the first row: + \begin{itemize} + \item \texttt{original\_rate\_u32s} is all 0. + \item \texttt{already\_absorbed\_bytes} is 0. + \end{itemize} + \item at each full input row (i.e. \texttt{is\_full\_input\_block} is 1, all \texttt{is\_final\_input\_len} columns are 0): + \begin{itemize} + \item \texttt{context}, \texttt{segment}, \texttt{virt} and \texttt{timestamp} are unchanged in the next row. + \item Next \texttt{already\_absorbed\_bytes} is current \texttt{already\_absorbed\_bytes} + \texttt{KECCAK\_RATE\_BYTES}. + \item Next (\texttt{original\_rate\_u32s}, \texttt{original\_capacity\_u32s}) is current (\texttt{updated\_digest\_state\_bytes columns}, \texttt{partial\_updated\_state\_u32s}). + \item The CTL with Memory ensures that \texttt{block\_bytes} is filled with contiguous memory elements [$a$ + \texttt{already\_absorbed\_bytes}, $a$ + \texttt{already\_absorbed\_bytes} + \texttt{KECCAK\_RATE\_BYTES} - 1] + \end{itemize} + \item at the final row (i.e. \texttt{is\_full\_input\_block} is 0, \texttt{is\_final\_input\_len}'s $i$-th column is 1 for a certain $i$, the rest are 0): + \begin{itemize} + \item The CTL with Memory ensures that \texttt{block\_bytes} is filled with contiguous memory elements [$a$ + \texttt{already\_absorbed\_bytes}, $a$ + \texttt{already\_absorbed\_bytes} + $i$ - 1]. The rest are padding bytes. + \item The CTL with CPU ensures that \texttt{context}, \texttt{segment}, \texttt{virt} and \texttt{timestamp} match the \texttt{KECCAK\_GENERAL} call. + \item The CTL with CPU ensures that $l$ = \texttt{already\_absorbed\_bytes} + $i$. + \item The CTL with CPU ensures that \texttt{updated\_digest\_state\_bytes} is the output of the \texttt{KECCAK\_GENERAL} call. + \end{itemize} +\end{itemize} + +The trace is padded to the next power of two with dummy rows, whose \texttt{is\_full\_input\_block} and \texttt{is\_final\_input\_len} columns are all 0. diff --git a/evm/spec/zkevm.pdf b/evm/spec/zkevm.pdf index 5d1949aee0341b7dbad0c77b8741c70947c67117..150acd307398685af6b9fd79d3ac4c9c8be927e4 100644 GIT binary patch delta 89209 zcmce-W00p$vnJfOZQHhO+vc>*U)#2=Y1^8%ZTGZoOmpY|Z0zniah?zFz7c0X+;>z| zWkp<(S#?!rRc726>_!?KfLuvTf}WXy9fo{vX?P8WjfjcJ!NdlJj}L}X&CAi8h*3+? 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