Algorithm 5: $Encrypt(M)\to \left\{CT\right\}$

// Params: ciphertext $CT$, attribute permission parameters $R_i$, data storage address Address($E_{\delta }\left(M\right)$) // Returns: plaintext message $M$ function DecryptMessage ($CT,R_i,$ Address_$E_{\delta }\left(M\right)$) →$M$ 01: // Retrieve encrypted data $E_{\delta }\left(M\right)$ using the storage address from IPFS 02: $E_{\delta }\left(M\right)=$ IPFS.retrieve (Address_$E_{\delta }\left(M\right)$) 03: // Step (i): Compute μ using the attribute permission parameters $R_i$ 04: $\mathsf{\mu }=$ computeCRTSolution ($R_i$, $\mathrm{CT}.\mathrm{B}$) 05: // Reverse compute $\beta$ from $\mu$ 06: $\beta =\mu -A{b}_0$ 07: // Step (ii): Decrypt $\delta$ using C from CT and β 08: $u=$ publicParameters.u // u is obtained from the system’s public parameters 09: $g_1=$ publicParameters.$g_1$ // $g_1$ is a generator of $G_1$ 10: $\delta =\frac{C}{u\cdot e{(g_1,g_1)}^{\beta }}$ 11: // Decrypt the message $M$ using symmetric decryption with $\delta$ 12: $M=$ symmetricDecrypt ($E_{\delta }\left(M\right),\delta$) 13: return $M$ endfunction // Helper function to compute $\mu$ using Chinese Remainder Theorem and attribute permission parameters $R_i$ function computeCRTSolution ($R_i,B$,) → int 01: $Y=$ product ($b_1,b_t$) // $Y$ is the product of $b_1,b_2\dots ,b_t$  02: $\mu =0$ 03: // Compute the sum for $\mu$ using the CRT formula 04: for $v=1$ to $R_i$.length do 05:   $y_v$ = modInverse ($\frac{Y}{b_v},b_v$) // Compute the modular inverse 06:   $\mu =\left(\mu +\left(r_v\cdot y_v\cdot \frac{Y}{b_v}\right)\right)\mathrm{mod}Y$ 07: return $\mu$ endfunction