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 first amount of a balance transfer from a first account to a second account generated based on a first random number, in addition to the commitment value, the first amount of the balance transfer and the first random number encrypted using a first public key of the first account based on a probabilistic homomorphic encryption algorithm, a second amount of the balance transfer and a second random number, wherein the second amount and the second random number are encrypted using a public key of the second account based on the probabilistic homomorphic encryption algorithm, 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 second 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 amount of the balance transfer is greater than zero and less than or equal to a balance of the first account; determining if the first amount and the second amount are the same and if the first random number and the second random number are the same, based on the encrypted second amount, the encrypted second random number, the commitment value of the first amount of the balance transfer generated based on the first random value, and the set of values; and updating the balance of the first account and a balance of the second account based on the first amount of the balance transfer in response to determining that the first amount and the second amount are the same and the first random number and the second random number are the same. receiving, from a first account: a digitally signed copy of the following: a commitment value of a first amount of a balance transfer from a first account to a second account generated based on a first random number, in addition to the commitment value, the first amount of the balance transfer and the first random number encrypted using a first public key of the first account based on a probabilistic homomorphic encryption algorithm, a second amount of the balance transfer and a second random number, wherein the second amount and the second random number are encrypted using a public key of the second account based on the probabilistic homomorphic encryption algorithm, one or more range proofs, and a set of values generated based on one or more selected random numbers; a digitally signed copy of the following: a commitment value of a first amount of a balance transfer from a first account to a second account generated based on a first random number, in addition to the commitment value, the first amount of the balance transfer and the first random number encrypted using a first public key of the first account based on a probabilistic homomorphic encryption algorithm, a commitment value of a first amount of a balance transfer from a first account to a second account generated based on a first random number, in addition to the commitment value, the first amount of the balance transfer and the first random number encrypted using a first public key of the first account based on a probabilistic homomorphic encryption algorithm, a second amount of the balance transfer and a second random number, wherein the second amount and the second random number are encrypted using a public key of the second account based on the probabilistic homomorphic encryption algorithm, 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 second 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 amount of the balance transfer is greater than zero and less than or equal to a balance of the first account; determining if the first amount and the second amount are the same and if the first random number and the second random number are the same, based on the encrypted second amount, the encrypted second random number, the commitment value of the first amount of the balance transfer generated based on the first random value, and the set of values; and updating the balance of the first account and a balance of the second account based on the first amount of the balance transfer in response to determining that the first amount and the second amount are the same and the first random number and the second random number are the same.