Abstract: A computer-implemented method, non-transitory, computer-readable medium, and computer-implemented system are provided for implementing privacy protection. In an implementation, a public key pk={N, h} corresponding to a target user is obtained, where h is a generator of a predetermined cyclic group with a size of k in a random number space Z*N, a length of k is i bits, a length of N is n bits, and i<<n. A random number r is selected, so that hr belongs to the predetermined cyclic group. To-be-encrypted data m, corresponding to the target user using the public key pk and the random number r, is processed to generate a homomorphic ciphertext c=(1+N)m·(hN mod N2)r mod N2. The homomorphic ciphertext c is provided to the target user, where the homomorphic ciphertext c can be decrypted using a private key sk to obtain the data m.

Abstract: Implementations are directed to cross-asset trading in blockchain networks, and include a first node providing transaction information based on a first value, a second value, and an exchange rate of a second node, receiving, from the second node, a first evidence set, a first range proof, and a digital signature of the second node, and submitting the transaction for verification based on the first range proof, a second range proof, the first evidence set, a second evidence set, a digital signature of the first node, and the digital signature of the second node, the transaction being executed to decrease a balance of the first node by the first value, increase a first balance of the second node by the first value, decrease a second balance of the second node by the second value, and increase a balance of the third node by the second value.

Abstract: Implementations are directed to cross-asset trading in blockchain networks, and include a first node providing transaction information based on a first value, a second value, and an exchange rate of a second node, receiving, from the second node, a first evidence set, a first range proof, and a digital signature of the second node, and submitting the transaction for verification based on the first range proof, a second range proof, the first evidence set, a second evidence set, a digital signature of the first node, and the digital signature of the second node, the transaction being executed to decrease a balance of the first node by the first value, increase a first balance of the second node by the first value, decrease a second balance of the second node by the second value, and increase a balance of the third node by the second value.

Abstract: Implementations are directed to cross-asset trading in blockchain networks, and include a first node providing transaction information based on a first value, a second value, and an exchange rate of a second node, receiving, from the second node, a first evidence set, a first range proof, and a digital signature of the second node, and submitting the transaction for verification based on the first range proof, a second range proof, the first evidence set, a second evidence set, a digital signature of the first node, and the digital signature of the second node, the transaction being executed to decrease a balance of the first node by the first value, increase a first balance of the second node by the first value, decrease a second balance of the second node by the second value, and increase a balance of the third node by the second value.

Abstract: A computer-implemented method, non-transitory, computer-readable medium, and computer-implemented system are provided for implementing privacy protection. In an implementation, a public key pk={N, h} corresponding to a target user is obtained, where h is a generator of a predetermined cyclic group with a size of k in a random number space Z*N, a length of k is i bits, a length of N is n bits, and i<<n. A random number r is selected, so that hr belongs to the predetermined cyclic group. To-be-encrypted data m, corresponding to the target user using the public key pk and the random number r, is processed to generate a homomorphic ciphertext c=(1+N)m·(hN mod N2)r mod N2. The homomorphic ciphertext c is provided to the target user, where the homomorphic ciphertext c can be decrypted using a private key sk to obtain the data m.

Abstract: A computer-implemented method, non-transitory, computer-readable medium, and computer-implemented system are provided for implementing privacy protection. In an implementation, a public key pk={N, h} corresponding to a target user is obtained, where h is a generator of a predetermined cyclic group with a size of k in a random number space Z*N, a length of k is i bits, a length of N is n bits, and i<<n. A random number r is selected, so that hr belongs to the predetermined cyclic group. To-be-encrypted data m, corresponding to the target user using the public key pk and the random number r, is processed to generate a homomorphic ciphertext c=(1+N)m·(hN mod N2)r mod N2 . The homomorphic ciphertext c is provided to the target user, where the homomorphic ciphertext c can be decrypted using a private key sk to obtain the data m.

Abstract: A computer-implemented method, non-transitory, computer-readable medium, and computer-implemented system are provided for implementing privacy protection. In an implementation, a public key pk={N, h} corresponding to a target user is obtained, where h is a generator of a predetermined cyclic group with a size of k in a random number space Z*N, a length of k is i bits, a length of N is n bits, and i<<n. A random number r is selected, so that hr belongs to the predetermined cyclic group. To-be-encrypted data m, corresponding to the target user using the public key pk and the random number r, is processed to generate a homomorphic ciphertext c=(1+N)m·(hN mod N2)r mod N2. The homomorphic ciphertext c is provided to the target user, where the homomorphic ciphertext c can be decrypted using a private key sk to obtain the data m.

Abstract: Implementations are directed to cross-asset trading in blockchain networks, and include a first node providing transaction information based on a first value, a second value, and an exchange rate of a second node, receiving, from the second node, a first evidence set, a first range proof, and a digital signature of the second node, and submitting the transaction for verification based on the first range proof, a second range proof, the first evidence set, a second evidence set, a digital signature of the first node, and the digital signature of the second node, the transaction being executed to decrease a balance of the first node by the first value, increase a first balance of the second node by the first value, decrease a second balance of the second node by the second value, and increase a balance of the third node by the second value.