A computer-implemented method performed by a consensus node of a blockchain network , comprising: receiving , from a first account: a digitally signed copy of the following: a commitment value of a transaction amount associated with a balance transfer from the first account to a second account generated based on a first random number, in addition to the commitment value, a second random number encrypted using a public key of the first account, a third random number encrypted using a public key of the second account, one or more range proofs, and a set of values generated based on one or more selected random numbers; verifying a digital signature corresponding to the digitally signed copy using a public key of the first account corresponding to a private key used to generate the digital signature; determining that the one or more range proofs prove that the transaction amount is greater than zero and less than, or equal to, a balance of the first account; determining whether the first random number, the second random number, and the third random number are the same based on the set of values; and in response to determining that the first random number, the second random number, and the third random number are the same, updating the balance of the first account and a balance of the second account based on the amount of the balance transfer; wherein the second random number and the third random number are encrypted based on a deterministic homomorphic encryption, HE, scheme that has linear properties of HE(a + b) = HE(a) ∗ HE(b) and HE(ab) = HE(b) a , where a and b are plaintext used for HE. a commitment value of a transaction amount associated with a balance transfer from the first account to a second account generated based on a first random number, in addition to the commitment value, a second random number encrypted using a public key of the first account, a third random number encrypted using a public key of the second account, one or more range proofs, and a set of values generated based on one or more selected random numbers; a third random number encrypted using a public key of the second account, one or more range proofs, and a set of values generated based on one or more selected random numbers; verifying a digital signature corresponding to the digitally signed copy using a public key of the first account corresponding to a private key used to generate the digital signature; determining that the one or more range proofs prove that the transaction amount is greater than zero and less than, or equal to, a balance of the first account; determining whether the first random number, the second random number, and the third random number are the same based on the set of values; and in response to determining that the first random number, the second random number, and the third random number are the same, updating the balance of the first account and a balance of the second account based on the amount of the balance transfer; wherein the second random number and the third random number are encrypted based on a deterministic homomorphic encryption, HE, scheme that has linear properties of HE(a + b) = HE(a) ∗ HE(b) and HE(ab) = HE(b) a , where a and b are plaintext used for HE. <EOS>