darkfi/script/research/crypsinous

this is an effort to break down the building blocks of crypsinous blockchain

Crypsinous blockchain

Each part $Up$ stores it's own local view of the Blockchain $C{loc}^{Up}$. $C{loc}$ is a sequence of blocks $Bi$ (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 $C{loc}$. $stx{proof}=(cm_{\prime{c}},snc,ep,sl,\rho,h,ptr,\pi)$ 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: $(cm{\prime{c}},r_{\prime{c}})=COMM(pk^{COIN}||\tau||vc||\rho{\prime{c}})$, \emph{$sn_c$} is the coin's serial number revealed to spend the coin. $$snc=PRF{root_{sk}^{COIN}}^{sn}(\rhoc)$$ $$\rho=\eta^{sk{sl}^{COIN}}$$ $\eta$ 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

for $x=(cm_{c2},sn{c1},\eta,sl,\rho,h,ptr,\mu{\rho},\mu{y},root)$, and $w=(path,root{sk^{COIN}},path_{sk^{COIN}},\tau_c,\rhoc,r{c1},v,r{c2})$ for tuple $(x,w) \in L{lead}$ iff:

• $pk^{COIN} = PRF{root{sk^{COIN}}}^{pk}(\tau_c)$.
• $\rho_{c2}=PRF{root{sk{c1}^{COIN}}}^{evl}(\rho{c_1})$.
• $\forall i \in {1,2} : DeComm(cm_{ci},pk^{COIN}||v||\rho{ci},r{c_i})=T$.
• \emph{path} is a valid Merkle tree path to cm_c_1 in the tree with the root \emph{root}.
• \emph{$path_{sk^{COIN}}$} is a valid path to a leaf at position $sl-\tauc$ in a tree with a root $root{sk^{COIN}}$.
• $sn_{c1}= PRF{root{sk}^{COIN}}^{sn}(\rho{c_1})$
• $y = \mu{y}^{root{sk_{c_1}^{COIN}}||\rho_c}$
• $\rho = \mu{\rho}^{root{sk_{c_1}^{COIN}}||\rho_c}$
• $y< ord(G)\phi_f(v)$