SCIENCE CHINA Information Sciences, Volume 64 , Issue 10 : 202301(2021) https://doi.org/10.1007/s11432-019-2858-8

## An incentive-compatible rational secret sharing scheme using blockchain and smart contract

• AcceptedMar 18, 2020
• PublishedFeb 3, 2021
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### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61662009, 61772008), Guizhou Provincial Department of Education Science and Technology Top Talent Support Project (Grant No. 2016060), Science and Technology Major Support Program of Guizhou Province (Grant No. 20183001), Science and Technology Program of Guizhou Province (Grant No. 20175788), Ministry of Education-China Mobile Research Fund Project (Grant No. MCM20170401), Guizhou University Cultivation Project (Grant No. 20175788), Key Program of the National Natural Science Union Foundation of China (Grant No. U1836205), and Science and Technology Program of Guizhou Province (Grant No. 20191098).

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• Figure 1

GameSample.

• Figure 2

Game1.

• Figure 3

Game2.

• Table 1

Table 1The ${p_{ldr}}$'s utility of IVR and NIVR

 Serial $p_{ldr}$ $p_{ldr}$ $p_{flr}$ $p_{flr}$ $u_{\rm~IVR}(p_{ldr})$ $u_{\rm~NIVR}(p_{ldr})$ 1* publish promulgate publish promulgate $b-g$ $b$ 2* publish promulgate publish deceive $b+r-g$ $b$ 3* publish promulgate cheat promulgate $b+r-g$ $d$ 4* publish promulgate cheat deceive $b+r-g$ $d$ 5* publish deceive publish deceive $b-r-g$ $b$ 6* publish deceive cheat promulgate $d-r-g$ $d$ 7* publish deceive cheat deceive $d-r-g$ $d$ 8* cheat promulgate publish deceive $a-r-g$ $a$ 9* cheat promulgate cheat promulgate $c-r-g$ $c$ 10* cheat promulgate cheat deceive $c-r-g$ $c$ 11* cheat deceive publish deceive $a-r-g$ $a$ 12* cheat deceive cheat promulgate $c-r-g$ $c$ 13* cheat deceive cheat deceive $c-r-g$ $c$ 14* publish deceive publish promulgate $b-r-g$ $b$ 15* cheat promulgate publish promulgate $a-r-g$ $a$ 16* cheat deceive publish promulgate $a-r-g$ $a$
• Table 2

Table 2Utility function in Game2

 Node $u(p_1)$ $u(p_2)$ $n_{17}$ $b$ $b$ $n_{18}$ $b+r-g$ $b-r$ $n_{19}$ $b-r$ $b+r-g$ $n_{20}$ $b$ $b$ $n_{21}$ $b+r-g$ $b-r$ $n_{22}$ $b+r-g$ $b-r-g$ $n_{23}$ $d$ $a$ $n_{24}$ $d$ $a$ $n_{25}$ $b-r$ $b+r-g$ $n_{26}$ $a$ $d$ $n_{27}$ $b-r-g$ $b+r-g$ $n_{28}$ $a$ $d$ $n_{29}$ $c$ $c$ $n_{30}$ $c$ $c$ $n_{31}$ $c$ $c$ $n_{32}$ $c$ $c$ Game1 $c$ $c$
• Table 3

Table 3Functions in the smart contract

 Serial Function Description $1$ Sign A player calls this function to sign IC before $T_1$. Auto-transferring each player's deposit $r+g$ to the contract account if the contract takes effect. 2 SendSecretShare A player calls this function to send the commitment of his/her secret share before $T_2$. 3 SendReconstructedSecret A player calls this function to send the commitment of his/her reconstructed secret before $T_3$. 4 IVROrNot A player calls this function to choose whether initiate a verification request or not before $T_4$. 5 Transfer This function can handle disputes in different situations:If (UIVR) contract auto-transfers deposit $r+g$ to $p_{ldr}$, deposit $r+g$ to $p_{flr}$.Else if (IVR) Case1 (Both players are honest): contract auto-transfers deposit $r$ to $p_{ldr}$, deposit $r+g$ to $p_{flr}$ and deposit $g$ to $V$; Case2 ($p_{ldr}$ is honest while $p_{flr}$ is dishonest): contract auto-transfers deposit $2r$ to $p_{ldr}$, deposit $g$ to $p_{flr}$ and deposit $g$ to $V$; Case3 ($p_{ldr}$ is dishonest while $p_{flr}$ is honest): contract auto-transfers deposit $2r+g$ to $p_{flr}$ and deposit $g$ to $V$; Case4 (Both players are dishonest, $p_{flr}~$ either cheats in the PSSP or deceives in the PRSP): contract auto-transfers deposit $g$ to $p_{flr}$ and deposit $2r+g$ to $V$; Case5 (both players are dishonest, $p_{flr}~$ both cheats in the PSSP and deceives in the PRSP): contract auto-transfers deposit $2r+2g$ to $V$. 6 TimeOut $V$ can call this function if it times out: Case1 (Only $p_i$ called the function SendSecretShare before $T_2$): contract auto-transfers deposit $r+g$ to $p_i$, deposit $r+g$ to $V$; Case2 (No player called the function SendSecretShare before $T_2$): contract auto-transfers deposit $2r+2g$ to $V$; Case3 (Only $p_i$ called the function SendReconstructedSecret before $T_3$): contract auto-transfers deposit $r+g$ to $p_i$, deposit $r+g$ to $V$; Case4 (No player called the function SendReconstructedSecret before $T_3$): contract auto-transfers deposit $2r+2g$ to $V$; Case5 (Only $p_i$ called the function IVROrNot before $T_4$): contract auto-transfers deposit $r+g$ to $p_i$, deposit $r+g$ to $V$; Case6 (No player called the function IVROrNot before $T_4$): contract auto-transfers deposit $2r+2g$ to $V$.
• Table 4

Table 4Cost of using the smart contract

 Serial Function Cost in Gas Cost in Dollar $1$ Deploy 1382691 0.26 $2$ Sign 292963 0.056 $3$ SendSecretShare 132224 0.025 $4$ SendReconstructedSecret 132180 0.025 $5$ IVROrNot 95416 0.018 $6$ Transfer 41748 0.008
• Table 5

Table 5Number of calculations

 Player Generate commitment Open commitment Compute hash function $p_1$ 2 3 5 $p_2$ 2 3 5 $V$ 0 0 0 Total 4 6 10

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