Confidential Transaction Balance Verification by the Net Using Non-Interactive Zero-Knowledge Proofs
Volume 35, Issue 3 (2024), pp. 601–616
Pub. online: 19 August 2024
Type: Research Article
Open Access
Open Access
Received
1 March 2024
1 March 2024
Accepted
1 June 2024
1 June 2024
Published
19 August 2024
19 August 2024
Abstract
One of the main trends for the monitoring and control of business processes is to implement these processes via private blockchain systems. These systems must ensure data privacy and verifiability for the entire network here denoted by ‘Net’. In addition, every business activity should be declared to a trusted third party (TTP), such as an Audit Authority (AA), for tax declaration and collection purposes.
We present a solution for a confidential and verifiable realization of transactions based on the Unspent Transaction Output (UTxO) paradigm. This means that the total sum of transaction inputs (incomes) $In$ must be equal to the total sum of transaction outputs (expenses) $Ex$, satisfying the balance equation $In=Ex$. Privacy in a private blockchain must be achieved through the encryption of actual transaction values. However, it is crucial that all participants in the network be able to verify the validity of the transaction balance equation. This poses a challenge with probabilistically encrypted data. Moreover, the inputs and outputs are encrypted with different public keys. With the introduction of the AA, the number of different public keys for encryption can be reduced to two. Incomes are encrypted with the Receiver’s public key and expenses with the AA’s public key.
The novelty of our realization lies in taking additively-multiplicative, homomorphic ElGamal encryption and integrating it with a proposed paradigm of modified Schnorr identification providing a non-interactive zero-knowledge proof (NIZKP) using a cryptographically secure h-function. Introducing the AA as a structural element in a blockchain system based on the UTxO enables effective verification of encrypted transaction data for the Net. This is possible because the proposed NIZKP is able to prove the equivalency of two ciphertexts encrypted with two different public keys and different actors.
This integration allows all users on the Net to check the UTxO-based transaction balance equation on encrypted data. The security considerations of the proposed solution are presented.
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Biographies
Kilčiauskas Aušrys
A. Kilčiauskas is a PhD student of natural sciences’ informatics at the Department of Applied Mathematics. His research area is anonymity, confidentiality, and verifiability functionalities implementation in private blockchain transactions.
Bendoraitis Antanas
A. Bendoraitis is a PhD student at the Faculty of Informatics. He has finished a three-semester competence course in cryptography and blockchain systems at the Department of Applied Mathematics.
Sakalauskas Eligijus
E. Sakalauskas is a professor at the Department of Applied Mathematics, Kaunas University of Technology. He is the head of the Cryptography and Blockchain Systems research group. The scope of his scientific interests is the creation of new cryptographic methods including post-quantum methods and their security analysis. Other area of activity is cryptographic method application to private blockchain technologies, additional functionality and trustworthiness.
