Pub. online:19 Aug 2024Type:Research ArticleOpen Access
Journal:Informatica
Volume 35, Issue 3 (2024), pp. 601–616
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.
Journal:Informatica
Volume 34, Issue 3 (2023), pp. 603–616
Abstract
The article presents the tax declaration scheme using blockchain confidential transactions based on the modified ElGamal encryption providing additively-homomorphic property. Transactions are based on the unspent transactions output (UTxO) paradigm allowing to effectively represent digital asset of cryptocurrencies in e-wallets and to perform financial operations. The main actors around transaction are specified, include money senders, receivers, transaction creator, Audit Authority (AA) and Net of users. A general transaction model with M inputs and N outputs is created, providing transaction amount confidentiality and verifiability for all actors with different levels of available information.
The transaction model allows Net to verify the validity of a transaction, having access only to encrypted transaction data. Each money receiver is able to decrypt and verify the actual sum that is transferred by the sender. AA is provided with actual transaction values and is able to supervise the tax payments for business actors. Such information allows to verify the honesty of transaction data for each user role.
The security analysis of the scheme is presented, referencing to ElGamal security assumptions. The coalition attack is formulated and prevention of this attack is proposed. It is shown that transaction creation is effective and requires almost the same resources as multiple ElGamal encryption. In addition to ElGamal encryption of all income and expenses, an additional exponentiation operation with small exponents, representing transferred sums, is needed. AA computation resources are slightly larger, since they have to be adequate for search procedures in the small range from 1 to ${2^{32}}-1=4294967295$ for individual money transfers.
Pub. online:7 Dec 2022Type:Research ArticleOpen Access
Journal:Informatica
Volume 33, Issue 4 (2022), pp. 749–769
Abstract
In this paper, we propose a light-weight electronic voting protocol. The approach used by our protocol to conceal the ballots does not imply encryption, and guarantees the privacy of the direction of the vote unless all the contestants (parties) agree to do so. Our method is based on the division of the ballot into different pieces of information, which separately reveal no information at all, and that can be latter aggregated to recover the original vote. We show that, despite its simplicity, this scheme is powerful, it does not sacrifice any of the security properties demanded in a formal electronic voting protocol, and, furthermore, even in post-quantum scenarios, neither the casted votes can be tampered with, nor the identity of any elector can be linked with the direction of her vote.
Pub. online:8 Feb 2021Type:Research ArticleOpen Access
Journal:Informatica
Volume 32, Issue 2 (2021), pp. 321–355
Abstract
Voting systems are as useful as people are willing to use them. Although many electronic election schemes have been proposed through the years, and some real case scenarios have been tested, people still do not trust electronic voting. Voting is not only about technological challenges but also about credibility, therefore, we propose a voting system focused on trust. We introduce political parties as active partners in the elections as a mechanism to encourage more traditional electors to participate. The system we propose here preserves elector’s privacy, it operates publicly through a blockchain and it is auditable by third parties.
Pub. online:17 Jun 2020Type:Research ArticleOpen Access
Journal:Informatica
Volume 31, Issue 3 (2020), pp. 499–522
Abstract
A $(k,n)$-threshold secret image sharing scheme is any method of distributing a secret image amongst n participants in such a way that any k participants are able to use their shares collectively to reconstruct the secret image, while fewer than k shares do not reveal any information about the secret image. In this work, we propose a lossless linear algebraic $(k,n)$-threshold secret image sharing scheme. The scheme associates a vector ${\mathbf{v}_{i}}$ to the ith participant in the vector space ${\mathbb{F}_{{2^{\alpha }}}^{k}}$, where the vectors ${\mathbf{v}_{i}}$ satisfy some admissibility conditions. The ith share is simply a linear combination of the vectors ${\mathbf{v}_{i}}$ with coefficients from the secret image. Simulation results demonstrate the effectiveness and robustness of the proposed scheme compared to standard statistical attacks on secret image sharing schemes. Furthermore, the proposed scheme has a high level of security, error-resilient capability, and the size of each share is $1/k$ the size of the secret image. In comparison with existing work, the scheme is shown to be very competitive.