secure trie for storage and state trie

Paper.tex

@@ -186,7 +186,7 @@ \subsection{World State} \label{ch:state}
 \begin{description}
 \item[nonce] A scalar value equal to the number of transactions sent from this address or, in the case of accounts with associated code, the number of contract-creations made by this account. For account of address $a$ in state $\boldsymbol{\sigma}$, this would be formally denoted $\boldsymbol{\sigma}[a]_n$.
 \item[balance] A scalar value equal to the number of Wei owned by this address. Formally denoted $\boldsymbol{\sigma}[a]_b$.
-\item[storageRoot] A 256-bit hash of the root node of a Merkle Patricia tree that encodes the storage contents of the account (a mapping between 256-bit integer values), encoded into the trie as a mapping from the 256-bit integer keys to the RLP-encoded 256-bit integer values. The hash is formally denoted $\boldsymbol{\sigma}[a]_s$.
+\item[storageRoot] A 256-bit hash of the root node of a Merkle Patricia tree that encodes the storage contents of the account (a mapping between 256-bit integer values), encoded into the trie as a mapping from the Keccak 256-bit hash of the  256-bit integer keys to the RLP-encoded 256-bit integer values. The hash is formally denoted $\boldsymbol{\sigma}[a]_s$.
 \item[codeHash] The hash of the EVM code of this account---this is the code that gets executed should this address receive a message call; it is immutable and thus, unlike all other fields, cannot be changed after construction. All such code fragments are contained in the state database under their corresponding hashes for later retrieval. This hash is formally denoted $\boldsymbol{\sigma}[a]_c$, and thus the code may be denoted as $\mathbf{b}$, given that $\texttt{\small KEC}(\mathbf{b}) = \boldsymbol{\sigma}[a]_c$.
 \end{description}
 
@@ -197,7 +197,7 @@ \subsection{World State} \label{ch:state}
 
 The collapse function for the set of key/value pairs in the trie, $L_I^*$, is defined as the element-wise transformation of the base function $L_I$, given as:
 \begin{equation}
-L_I\big( (k, v) \big) \equiv \big(k, \texttt{\small RLP}(v)\big)
+L_I\big( (k, v) \big) \equiv \big(\texttt{\small KEC}(k), \texttt{\small RLP}(v)\big)
 \end{equation}
 
 where:
@@ -215,7 +215,7 @@ \subsection{World State} \label{ch:state}
 \end{equation}
 where
 \begin{equation}
-p(a) \equiv  \big(a, \texttt{\small RLP}\big( (\boldsymbol{\sigma}[a]_n, \boldsymbol{\sigma}[a]_b, \boldsymbol{\sigma}[a]_s, \boldsymbol{\sigma}[a]_c) \big) \big)
+p(a) \equiv  \big(\texttt{\small KEC}(a), \texttt{\small RLP}\big( (\boldsymbol{\sigma}[a]_n, \boldsymbol{\sigma}[a]_b, \boldsymbol{\sigma}[a]_s, \boldsymbol{\sigma}[a]_c) \big) \big)
 \end{equation}
 
 This function, $L_S$, is used alongside the trie function to provide a short identity (hash) of the world state. We assume:
@@ -224,7 +224,8 @@ \subsection{World State} \label{ch:state}
 \end{equation}
 where $v$ is the account validity function:
 \begin{eqnarray}
-\quad v(x) & \equiv & x_n \in \mathbb{P}_{256} \wedge x_b \in \mathbb{P}_{256} \wedge x_s \in \mathbb{B}_{32} \wedge x_c \in \mathbb{B}_{32}
+v(x) \equiv x_n \in \mathbb{P}_{256} \wedge x_b \in \mathbb{P}_{256} \\ \nonumber
+\wedge x_s \in \mathbb{B}_{32} \wedge x_c \in \mathbb{B}_{32}
 \end{eqnarray}
 
 \subsection{The Transaction} \label{ch:transaction}