A Scalable Cross-Chain Access Control and Identity Authentication Scheme

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

Algorithm 3 Sybil-resistant game

G^{s y b i l}

(from

A G_{i}

S C

)

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Input:
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$A G_{i}$ : the set of auto agents
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$t x_{i n}$ : the transaction first receives by $A G_{i}$
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$A$ : the adversary
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$λ$ : the security parameter
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Output::
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$t x_{o u t}$ : the transaction first transferred to $S C$ by $A G_{i}$
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Initial:
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$P K_{A G_{i}}, S K_{A G_{i}}, P K_{u_{s}}, S K_{u_{s}} \leftarrow R e g i s t r a t i o n (1^{λ})$
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$A$ $i n i t (A G_{A})$ , where $| A G_{A} | = k$
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - – - - - - - - - - - - - - - - - - - - -
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A.1. Forge the cross-chain transaction:
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$t x_{F}, S i g_{A G_{i}} (t x_{F}) \leftarrow A G_{A} (S K_{A G_{i}})$
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if $V e r i f y (S i g_{A G_{i}} (t x_{F}))$ then
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Broadcast $t x_{F}$ in $S C$
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return $t x_{o u t} = t x_{F}$
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else return nil
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - – - - - - - - - - - - - - - - - - - - -
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A.2. Tamper with the cross-chain transaction:
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$A G_{A}$ receives $t x_{i n}$
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$t x_{T}, S i g_{A G_{i}} (t x_{T}) \leftarrow A G_{A}^{T a m p e r} (S K_{A G_{i}}, t x_{i n})$
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if $V e r i f y (S i g_{A G_{i}} (t x_{T}))$ then
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Broadcast $t x_{T}$ in $S C$
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return $t x_{o u t} = t x_{T}$
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else return nil
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- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - – - - - - - - - - - - - - - - - - - - -
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A.3. Withhold the cross-chain transaction:
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$A G_{A}$ receives $t x_{i n}$
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withhold the transaction
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$A G_{A}$ receives $t x_{i n 2}$ , broadcast
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return $t x_{o u t} = t x_{i n 2}$