[script/research/crypsinous] added crypsinous blockchain notes

script/research/crypsinous/README.md

@@ -1,7 +1,21 @@
 this is an effort to break down the building blocks of crypsinous blockchain
 
 # Crypsinous blockchain
-TODO
+Each part $U_p$ stores it's own local view of the Blockchain $C_{loc}^{U_p}$.
+$C_{loc}$ is a sequence of blocks $B_i$ (i>0), where each $B \in C_{loc}$
+$$ B = (tx_{lead},st)$$
+$$tx_{lead} = (LEAD,st\overrightarrow{x}_{ref},stx_{proof})$$
+$st\overrightarrow{x}_{ref}$ it's a vector of $tx_{lead}$ that aren't yet in $C_{loc}$.
+$stx_{proof}=(cm_{\prime{c}},sn_c,ep,sl,\rho,h,ptr,\pi)$
+the Blocks' $\emph{st}$ is the block data, and $\emph{h}$ is the hash of that data.
+the commitment of the newly created coin is:
+$(cm_{\prime{c}},r_{\prime{c}})=COMM(pk^{COIN}||\tau||v_c||\rho_{\prime{c}})$,
+\emph{$sn_c$} is the coin's serial number revealed to spend the coin.
+$$sn_c=PRF_{root_{sk}^{COIN}}^{sn}(\rho_c)$$
+$$\rho=\eta^{sk_{sl}^{COIN}}$$
+$\eta$ is is from random oracle evaluated at $(Nonce||\eta_{ep}||sl)$, $\rho$ is the following epoch's seed. $\emph{ptr}$ is the hash of the previous block, $\pi$ is the NIZK proof of the LEAD statement.
+
+## LEAD statement
 
 # Crypsinous leaderelection
 TODO