Publicly Verifiable Secret Sharing Research Articles

Cryptanalysis and improvement of Q. Peng et al.’s PVSS scheme

A publicly verifiable secret sharing (PVSS) scheme based on the m-multilinear Diffie-Hellman hard assumption was proposed by Q. Peng et al., where the public values published by a dealer are verifiable before reconstructing a secret. In addition, the scheme has the advantages that the shares’ cheating/modification by some dishonest participants and dealer’s malicious behavior in shares’ generation and/or distribution can be detected. In this work, we cryptanalyze the scheme and find that a well-known attack called man-in-the-middle (MITM) is possible if the users’ secret shares are modified because they remain undetected and, as a result, a modified common secret is reconstructed by a group of any 1 < t ≤ n participants. We address this issue and propose some modifications of the PVSS scheme with multilinear operations and two additional public values such that the MITM attack is infeasible and the scheme becomes secure. In addition, the proposed improvement is made adeptly without hampering performance, i.e., the computation cost has been marginally increased in our proposed improvement.

A blockchain-enabled trust aware energy trading framework using games theory and multi-agent system in smat grid

Recently, multi-agent systems (MASs) have received attention due to the consideration of distributed optimization and control in blockchain (BC) based energy trading applications. However, due to the dynamic behavior of uncertain and random variables, the coordination and control of MAS are still challenging to attain resilience and dynamicity. Traditional trust systems, which rely on access control and cryptography, cannot deal with dynamic behavior of agents. Furthermore, they are inefficient in addressing the computational overhead of cryptographic primitives. To overcome these limitations, this work proposes a BC-based trusted suite (TS) for MAS to handle privacy and anonymity issues during energy trading in a smart grid (SG). In this work, three objectives are simultaneously achieved: trust, cooperation, and confidentiality. Firstly, the proposed trust system is employed to perform trust credibility of agents based on trust deformation, coherence, and stability. The credibility evaluation is used to determine the dynamic behavior of agents and to detect dishonest agents in the system. Secondly, a tri-tit-for-tat (TTFT) repeated game approach is used to improve the cooperation among agents. The proposed strategy is more forgiving than the existing Di-TFT (DTFT) and TFT techniques. It motivates scammers and deceptive agents to regain their trust by cooperating in three consecutive rounds of a game. Furthermore a proof-of-cooperation (PoC) consensus mechanism is introduced to facilitate agent cooperation in block creation and validation. Thirdly, the publicly verifiable secret sharing (PVSS) technique is introduced to preserve the privacy of the agents. Unlike VSS, PVSS provides the immunity against different types of security threats. Where, the dealer agent maintained the trust, while the verification of the dealer and combiner is maintained within agent-to-agent cooperation. Simulation results show that the devised BTS model is superior to the existing benchmark model such as fuzzy logic trust (FLT) in terms of detecting the cheating and deceptive behavior of agents in the system. Besides, the devised TTFT allows cheating agents to effectively regain the trust if they cooperate thrice in a row as compared to the existing DTFT and TFT strategies. Furthermore, This study analyzes two trust-related attacks: bad-mouthing and on-off. Analysis shows that the proposed system is protected from trust related attacks.

1-Round Distributed Key Generation With Efficient Reconstruction Using Decentralized CP-ABE

Distributed key generation (DKG) is widely used in multi-party computation and decentralized applications. DKG has two phases, namely sharing and reconstruction. Most of the prior DKG protocols need at least 2 rounds for the sharing phase, in case some party raises a dispute. The existing 1-round DKG protocol [Fouque <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , PKC’01], built based on a publicly verifiable secret sharing (PVSS) scheme, assumes a static adversary model and its reconstruction phase requires <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n^{2})$ </tex-math></inline-formula> communication complexity. Motivated by the observation that a ciphertext-policy attribute-based encryption (CP-ABE) scheme hides secret sharing (SS) in ciphertext, we utilize decentralized CP-ABE to achieve the first adaptively secure 1-round DKG protocol. Firstly, a CP-ABE scheme enables the ciphertexts in DKG to be externally decrypted, making our protocol superior to the PVSS-based DKG protocol in reconstruction. The communication and computation complexities are both lowered to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n)$ </tex-math></inline-formula> thanks to the constant-sized decryption key and the proposed batch decryption. The use of CP-ABE also makes our DKG protocol storage-friendly, i.e., the parties store no ciphertext after the sharing phase. Secondly, we add non-interactive zero-knowledge (NIZK) proofs to make the CP-ABE ciphertext publicly verifiable by leveraging the sigma protocol and the Fiat-Shamir heuristic. Thirdly, we demonstrate our protocol’s feasibility by presenting a proof-of-concept implementation over Ethereum, which is used as a public channel and a trustworthy computation platform. The implementation is a non-trivial task due to Ethereum’s incompatibility with the bilinear mapping group.

Baguena: A Practical Proof of Stake Protocol with a Robust Delegation Mechanism

Proof of stake (PoS), aiming at replacing Proof of work (PoW) in blockchain consensus, has drawn great attention from academia and industry. We present Baguena, a novel PoS protocol for public blockchain with high practicality and security. It uses a special designed algorithm with properties of uniqueness and anonymity for leader selection, and uses the longest chain rule for chain selection. Besides, entropy is introduced to prevent manipulation of leader selection process by simulating a random beacon based on Publicly verifiable secret sharing (PVSS) and threshold signature with only a linear number of exponentiations. We analyze the protocol's security by a threat model and design a robust delegation mechanism based on triple Elliptic curve digital signature algorithm (ECDSA) proxy signature. We implement Baguena and evaluate its performance on 100 Amazon EC2 virtual machines simulating 50k users, which shows that Baguena confirms transactions in 2 minutes, achieves 2.16x of Algorand's throughput and 6.95x of Ouroboros' throughput.

A Publicly Verifiable Multi-Secret Sharing Scheme With Outsourcing Secret Reconstruction

A publicly verifiable secret sharing (PVSS) scheme enjoys the public verification and the lower cost of communication than VSS scheme. However, the existing PVSS schemes cannot be applied in the scenarios of the devices with low computation ability and do not share the multiple secrets among all participants efficiently. In this paper, an efficient publicly verifiable multi-secret sharing scheme with outsourcing secret reconstruction is proposed. Each participant only spends a small amount of computational cost to recover multiple secrets because of the expensive burden of computation and verifiability is outsourced to the cloud service provider (CSP). Moreover, the CSP knows no information of the secrets, and the participants have the abilities to verify the returned result. We also prove that our scheme is secure under the hardness assumption of the discrete logarithm problem and the modified generalized bilinear inversion problem.

Paillier-based publicly verifiable (non-interactive) secret sharing

A verifiable secret sharing is a secret sharing scheme with an untrusted dealer that allows participants to verify validity of their own shares. A publicly verifiable secret sharing (PVSS) scheme i...

A New PVSS Scheme with a Simple Encryption Function

A Publicly Verifiable Secret Sharing (PVSS) scheme allows anyone to verify the validity of the shares computed and distributed by a dealer. The idea of PVSS was introduced by Stadler in [18] where he presented a PVSS scheme based on Discrete Logarithm. Later, several PVSS schemes were proposed. In [2], Behnad and Eghlidos present an interesting PVSS scheme with explicit membership and disputation processes. In this paper, we present a new PVSS having the advantage of being simpler while offering the same features.

Critical survey of existing publicly verifiable secret sharing schemes

The existing publicly verifiable secret sharing (PVSS) schemes are surveyed in a critical way in this study. The authors show that they are not so reliable and efficient as they claim or appear. They are limited by assumptions and conditions, vulnerable in important target properties and need more cost in practice. In this study, their actual performance and cost are fairly measured and their drawbacks are pointed out.

Threshold distributed access control with public verification: a practical application of PVSS

To avoid too strong a trust on any single user in sensitive applications, access control can be managed in a distributed way. Namely, an access right is distributed among multiple users such that the access is available if and only if certain subsets of the users cooperate. The most common condition for qualified subsets is the threshold condition, which requires that the number of cooperating users must be over a threshold. Access control based on such a condition is called TDAC (threshold distributed access control). In publicly verifiable applications, TDAC must provide public verification such that it is publicly verifiable that the multiple users share the correct access right and any qualified subset of them can obtain the access. Although the existing PVSS (publicly verifiable secret sharing) techniques can be employed to implement PVTDAC (publicly verifiable TDAC), they are not efficient enough for practical applications. In this paper, new sharing and proof techniques are proposed to design an efficient PVTDAC protocol, which is formally illustrated to be secure and publicly verifiable.

Efficient democratic group signatures with threshold traceability

Democratic group signature (DGS) is a group-oriented primitive with great flexibilities, i.e., no group manager, anonymity, and traceability. In a DGS scheme with (t, n)-threshold traceability, any subset of not less than t members can jointly reveal the identity of the signer while preserving security even in the presence of an active adversary can corrupt up to t − 1 group members. This paper proposes an efficient DGS scheme. We use publicly verifiable secret sharing (PVSS) to distribute the trapdoor via which the real signer is revealed. The computation cost and communication overhead of our DGS signatures are greatly reduced, compared with the existing work. For example, the size of the resulting signature contains only 2n + 1 elements of Z q , except the PVSS output.

A pairing-based publicly verifiable secret sharing scheme

A publicly verifiable secret sharing (PVSS) scheme is a verifiable secret sharing scheme with the special property that anyone is able to verify the shares whether they are correctly distributed by a dealer. PVSS plays an important role in many applications such as electronic voting, payment systems with revocable anonymity, and key escrow. Up to now, all PVSS schemes are based on the traditional public-key systems. Recently, the pairing-based cryptography has received much attention from cryptographic researchers. Many pairing-based schemes and protocols have been proposed. However, no PVSS scheme using bilinear pairings is proposed. This paper presents the first pairing-based PVSS scheme. In the random oracle model and under the bilinear Diffie-Hellman assumption, the authors prove that the proposed scheme is a secure PVSS scheme.

Publicly Verifiable Secret Sharing Member-join Protocol For Threshold Signatures

Publicly verifiable secret sharing (PVSS) allows not only shareholders themselves but also everyone verify the shares of a secret distributed by a dealer. It has a lot of electronic applications. In this paper, we propose a publicly verifiable member-join protocol for threshold signatures. In our proposal, a new member can join a PVSS scheme to share the secret only with the help of old shareholders. What’s more, everyone besides the new member can verify the validity of the new member’s share, while only the new member knows his share. Different from previous protocols, our protocol can tolerate a mobile adversary. This proposal adapts to many electronic applications. Finally, we analyze the security of our scheme.