A Scalable Cross-Chain Access Control and Identity Authentication Scheme

. 2023 Feb 10;23(4):2000. doi: 10.3390/s23042000

Symbol	Explanation
$S C$	Superchain
$A C$	the set of application chains
$A C_{i}$	the application chain i
$C h a i n I D_{i}$	the chain ID of $A C_{i}$
$C h a i n I D_{s}$	the chain ID of $S C$
$C H A I N S$	the set of chains in the cross-chain system
$u_{i}$	normal users in application chain i
$A G_{i}$	the set of auto agents of application chain i
$A G_{i}^{j}$	the j-th auto agent of application chain i
$A G R o b o t_{i}$	the program independent of blockchain client of $A G_{i}$
$A G S C a d d r_{i}^{j}$	the address of the j-th auto agent of $A C_{i}$ in $S C$
$A G A C a d d r_{i}^{j}$	the address of the j-th auto agent of $A C_{i}$ in $A C_{i}$
$O p t i o n s_{i}^{j}$	the set of cross-chain options from $A C_{i}$ to $A C_{j}$
$C r o s s C o n_{i}$	$A C_{i}$ ’s cross-chain contract
$t x_{i}$	transaction in $A C_{i}$ format
$< P K_{u_{s}}, S K_{u_{s}} >$	the public key and private key of $u_{s}$
$< P K_{u_{i}}, S K_{u_{i}} >$	the public key and private key of $u_{i}$
$< P K_{A G_{i}}, S K_{A G_{i}} >$	the public key and private key of $A G_{i}$
$S i g_{u}$	the signature of u’s options
$S i g_{A G_{i}}$	the signature of $A G_{i}$ ’s cross-chain options
$A C I A C$	the smart contract of access control and identity authentication
$λ$	the security parameter
$G^{s y b i l}$	the Sybil-resistance game
$A$	the stateful PPT adversary in the cross-chain system
$t x_{F}$	the forged transaction
$t x_{T}$	the tampered transaction