A method for implementing blockchain-based transactions, implementable by a first computing device associated with a remitter and a second computing device associated with a receiver, the method comprising: at said first computing device determining a transaction amount to be remitted from the remitter's blockchain account into a receiver's blockchain account, wherein a commitment of the remitter's balance is recorded with the remitter's blockchain account in a blockchain, a commitment of the receiver's balance is recorded with the receiver's blockchain account in the blockchain, the commitment of the remitter's balance is calculated by using a homomorphic encryption algorithm according to the remitter's balance, and the commitment of the receiver's balance is calculated by using the homomorphic encryption algorithm according to the receiver's balance; obtaining a commitment of the transaction amount by using the homomorphic encryption algorithm according to the transaction amount; and submitting to the blockchain a transaction comprising information of the remitter's blockchain account, information of the receiver's blockchain account, and the commitment of the transaction amount, for the commitment of the transaction amount to be deducted from the commitment of the remitter's balance and the commitment of the transaction amount to be added to the commitment of the receiver's balance after the transaction is implemented by the blockchain, wherein: the commitment of the receiver's balance is calculated by using the homomorphic encryption algorithm according to the receiver's balance and a first random number; and the commitment of the transaction amount is calculated by using the homomorphic encryption algorithm according to the transaction amount and a transaction random number, characterized in that: before submitting the transaction, the method further comprises sending the transaction random number to said second computing device via an off-chain channel, at the second computing device receiving said transaction random number and, in response, determining an updated receiver's balance according to an updated commitment of the receiver's balance and an updated first random number. at said first computing device determining a transaction amount to be remitted from the remitter's blockchain account into a receiver's blockchain account, wherein a commitment of the remitter's balance is recorded with the remitter's blockchain account in a blockchain, a commitment of the receiver's balance is recorded with the receiver's blockchain account in the blockchain, the commitment of the remitter's balance is calculated by using a homomorphic encryption algorithm according to the remitter's balance, and the commitment of the receiver's balance is calculated by using the homomorphic encryption algorithm according to the receiver's balance; obtaining a commitment of the transaction amount by using the homomorphic encryption algorithm according to the transaction amount; and submitting to the blockchain a transaction comprising information of the remitter's blockchain account, information of the receiver's blockchain account, and the commitment of the transaction amount, for the commitment of the transaction amount to be deducted from the commitment of the remitter's balance and the commitment of the transaction amount to be added to the commitment of the receiver's balance after the transaction is implemented by the blockchain, wherein: the commitment of the receiver's balance is calculated by using the homomorphic encryption algorithm according to the receiver's balance and a first random number; and the commitment of the transaction amount is calculated by using the homomorphic encryption algorithm according to the transaction amount and a transaction random number, characterized in that: before submitting the transaction, the method further comprises sending the transaction random number to said second computing device via an off-chain channel, at the second computing device receiving said transaction random number and, in response, determining an updated receiver's balance according to an updated commitment of the receiver's balance and an updated first random number. the commitment of the receiver's balance is calculated by using the homomorphic encryption algorithm according to the receiver's balance and a first random number; and the commitment of the transaction amount is calculated by using the homomorphic encryption algorithm according to the transaction amount and a transaction random number, characterized in that: before submitting the transaction, the method further comprises sending the transaction random number to said second computing device via an off-chain channel, at the second computing device receiving said transaction random number and, in response, determining an updated receiver's balance according to an updated commitment of the receiver's balance and an updated first random number. before submitting the transaction, the method further comprises sending the transaction random number to said second computing device via an off-chain channel, at the second computing device receiving said transaction random number and, in response, determining an updated receiver's balance according to an updated commitment of the receiver's balance and an updated first random number.