Algorithm 3: $Encrypt(M,W_{DO})\to \left\{CT\right\}$

// Params: message M, attribute weights $W_{DO}$ // Returns: ciphertext $CT$ function EncryptMessageWithAttributes(char[] M, int[] $W_{DO}$) →$CT$ 01: // Select a random number $\delta$ from $G_T$ to be used as the symmetric encryption key 02: $\delta$ = selectRandom($G_T$) 03: // Encrypt the message M with $\delta$ using symmetric encryption $E$ 04: $E_{\delta }\left(M\right)$ = symmetricEncrypt($\delta , M$) 05: // Store the encrypted message $E_{\delta }\left(M\right)$ on IPFS and get the storage address 06: Address_$E_{\delta }\left(M\right)$ = IPFS.store($E_{\delta }\left(M\right)$) 07: // Step (i): Compute the sum of weights $W$ and select $W+1$ prime numbers $b_0$ to $b_W$ 08: $W=\mathrm{sum}\left(W_{DO}\right)$ 09: $B=$ selectPrimes($W+1$) 10: // Select a random number $\beta$ from $GF\left(b_0\right)$ 11: $\beta =$ selectRandom($GF\left(b_0\right)$) 12: // Encrypt $\delta$ using the formula given 13: $C=\delta u^{\beta }$ 14: // Step (ii): Set the attribute weight threshold t and compute $\mu$ 15: $Y=$ product($B,1,t$) // Product of the first t primes in $B$ 16: $A=$ selectInteger(0, floor($\left[\frac{Y}{b_0}\right]-1$) 17: $\mu =\beta +A{b}_0$ 18: // Construct the ciphertext $CT$ 19: $CT=\left(A,B,C\right)$ 20: // Store the ciphertext $CT$ on the blockchain using a regulatory node 21: blockchain.store($CT$) 22: // Provide a description of the ciphertext, link it with the attribute category and data storage address 23: blockchain.associate($CT$, “description”, “attribute category”, Address_$E_{\delta }\left(M\right)$) 24: return $CT$ endfunction