Secret Reconstruction Research Articles

Publicly Verifiable Secret Sharing Scheme Based on the Chinese Remainder Theorem

Publicly verifiable secret sharing schemes based on Lagrange interpolation utilize public cryptography to encrypt transmitted data and the validity of their shares can be verified by everyone, not only the participants. However, they require O(klog2k) operations during secret reconstruction phase. In order to reduce the computational complexity during the secret reconstruction phase we propose a non-interactive publicly verifiable secret sharing scheme based on the Chinese Remainder Theorem utilizing ElGamal cryptosystem to encrypt data, whonly requires O(k) operations during secret reconstruction phase. Theoretical analysis proves the proposed scheme achieves computation security and is more efficient.

New Efficient and Practical v-Fairness (t, n) Multi-Secret Sharing Schemes

Secret sharing plays an important role in protecting confidential information among all participants. A fairness secret sharing scheme assures that a dishonest participant cannot get any advantages over the honest ones in the process of secret reconstruction. Though there are many secret sharing schemes available in the literature, most of them do not satisfy the requirement of fairness. In this paper, we focus on v-fairness (t, n) multi-secret sharing schemes which are (t, n) threshold multi-secret sharing schemes with the feature of fairness even if there are v<t/2 dishonest participants. We show security weaknesses in an existing v-fairness (t, n) multi-secret sharing scheme, and then present two new v-fairness (t, n) multi-secret sharing schemes. Our new schemes are not only secure, but also remove the need for private channels.

Verifiable quantum (k, n)-threshold secret sharing

In a conventional quantum (k, n) threshold scheme, a trusted party shares a quantum secret with n agents such that any k or more agents can cooperate to recover the original secret, while fewer than k agents obtain no information about the secret. Is the reconstructed quantum secret same with the original one? Or is the dishonest agent willing to provide a true share during the secret reconstruction? In this paper we reexamine the security of quantum (k, n) threshold schemes and show how to construct a verifiable quantum (k, n) threshold scheme by combining a qubit authentication process. The novelty of ours is that it can provide a mechanism for checking whether the reconstructed quantum secret is same with the original one. This mechanism can also attain the goal of checking whether the dishonest agent provides a false quantum share during the secret reconstruction such that the secret quantum state cannot be recovered correctly.

Rational Secret Sharing Scheme Based on Probability Encryption without Trusted Center

Considering the case of players’ deceptions, traditional secret sharing scheme can not resolve the security issues. To address these security issues, the paper proposes a rational secret sharing scheme against cheating based on game theory. Under the conditions of the rational, applying the idea of threshold, the scheme is composed of key generation, share encryption, verification and secret reconstruction. In the process, the scheme firstly utilizes secure multiparty computation function instead of trusted center for key generation and share validation; secondly uses probability encryption which can effectively solve the problem of players keeping silent in the final iteration; thirdly without revealing the secret, employs the commitment to detect the cheat in the scheme; finally, the scheme can reconstruct the secret in the meaningful encryption. In conclusion, the scheme is safe and effective.

Verifiable Quantum (k,n)-threshold Secret Key Sharing

Based on Lagrange interpolation formula and the post-verification mechanism, we show how to construct a verifiable quantum (k,n) threshold secret key sharing scheme. Compared with the previous secret sharing protocols, ours has the merits: (i) it can resist the fraud of the dealer who generates and distributes fake shares among the participants during the secret distribution phase; Most importantly, (ii) It can check the cheating of the dishonest participant who provides a false share during the secret reconstruction phase such that the authorized group cannot recover the correct secret.

REEXAMINING THE SECURITY OF THE RECONSTRUCTION PHASE OF THE HILLERY-BUZĚK-BERTHIAUME QUANTUM SECRET-SHARING PROTOCOL

The participant attack is the most serious threat for quantum secret-sharing protocols. However, it is only during the transmission of quantum information carriers that attention is paid to this kind of attack in the existing quantum secret-sharing protocols. The security considerations of the secret reconstruction phase of quantum secret-sharing protocols against this kind of attack are neglected. We demonstrate our viewpoint by taking the scheme of Hillery, Buzěk, and Berthiaume (HBB) [Phys. Rev. A59 (1999) 18–29] as an example. By telling a lie in the reconstruction phase, a dishonest participant can easily attain the entire secret key instead of eavesdropping during the transmission awkwardly, whereas the honest one cannot judge whether the dishonest one tells the truth and the obtained secret random key is identical to what the secret distributor owns because of lack of verification mechanism in the HBB protocol. It is not difficult to find that almost all the quantum secret-sharing protocols have such disadvantages. Our viewpoint presented may be useful for the design of other similar protocols.

Detection and identification of cheaters in (t, n) secret sharing scheme

In a (t, n) secret sharing scheme, a secret s is divided into n shares and shared among a set of n shareholders by a mutually trusted dealer in such a way that any t or more than t shares will be able to reconstruct this secret; but fewer than t shares cannot know any information about the secret. When shareholders present their shares in the secret reconstruction phase, dishonest shareholder(s) (i.e. cheater(s)) can always exclusively derive the secret by presenting faked share(s) and thus the other honest shareholders get nothing but a faked secret. Cheater detection and identification are very important to achieve fair reconstruction of a secret. In this paper, we consider the situation that there are more than t shareholders participated in the secret reconstruction. Since there are more than t shares (i.e. it only requires t shares) for reconstructing the secret, the redundant shares can be used for cheater detection and identification. Our proposed scheme uses the shares generated by the dealer to reconstruct the secret and, at the same time, to detect and identify cheaters. We have included discussion on three attacks of cheaters and bounds of detectability and identifiability of our proposed scheme under these three attacks. Our proposed scheme is an extension of Shamir's secret sharing scheme.

On Secret Reconstruction in Secret Sharing Schemes

A secret sharing scheme typically requires secure communications in each of two distribution phases: (1) a dealer distributes shares to participants (share distribution phase); and later (2) the participants in some authorised subset send their share information to a combiner (secret reconstruction phase). While problems on storage required for participants, for example, the size of shares, have been well studied, problems regarding the communication complexity of the two distribution phases seem to have been mostly neglected in the literature so far. In this correspondence, we deal with several communication related problems in the secret reconstruction phase. Firstly, we show that there is a tradeoff between the communication costs and the number of participants involved in the secret reconstruction. We introduce the communication rate as the ratio of the secret size and the total number of communication bits transmitted from the participants to the combiner in the secret reconstruction phase. We derive a lower bound on the communication rate and give constructions that meet the bound. Secondly, we show that the point-to-point secure communication channels for participants to send share information to the combiner can be replaced with partial broadcast channels. We formulate partial broadcast channels as set systems and show that they are equivalent to the well-known combinatorial objects of cover-free family. Surprisingly, we find that the number of partial broadcast channels can be significantly reduced from the number of point-to-point secure channels. Precisely, in its optimal form, the number of channels can be reduced from n to O(log n), where is the number of participants in a secret sharing scheme. We also study the communication rates of partial broadcast channels for the secret reconstruction.

Batch verification of validity of bids in homomorphic e-auction

Bid opening in e-auction is efficient when a homomorphic secret sharing function is employed to seal the bids and homomorphic secret reconstruction is employed to open the bids. However, this high efficiency is based on an assumption: the bids are valid (e.g., within a special range). An undetected invalid bid can compromise correctness and fairness of the auction. Unfortunately, validity verification of the bids is ignored in the auction schemes employing homomorphic secret sharing (called homomorphic auction in this paper). In this paper, an attack against the homomorphic auction in the absence of bid validity check is presented and a necessary bid validity check mechanism is proposed. Then a batch cryptographic technique is introduced and applied to improve the efficiency of bid validity check.

A secure and efficient (t, n) multi-secret sharing scheme

Based on Shamir's secret sharing, a (t, n) multi-secret sharing scheme is proposed in this paper.p secrets can be shared amongn participants, andt or more participants can co-operate to reconstruct these secrets at the same time, butt−1 or fewer participants can derive nothing about these secrets. Each participant's secret shadow is as short as each secret. Compared with the existing schemes, the proposed scheme is characterized by the lower complexity of the secret reconstruction and less public information. The security of this scheme is the same as that of Shamir's threshold scheme. Analyses show that this scheme is an efficient, computationally secure scheme.

A new ( t, n) multi-secret sharing scheme based on Shamir’s secret sharing

In 2000, Chien et al. proposed a ( t, n) multi-secret sharing scheme. At least t of the n participants can easily reconstruct p secrets at the same time. But the secret reconstruction needs to solve simultaneous equations, which is a complex process. In order to reduce the complexity of the secret reconstruction, Yang et al. proposed an alternative scheme based on Shamir’s secret sharing in 2004. But there are more public values required in Yang’s scheme than in Chien’s scheme when p < t. Motivated by these concerns, a new ( t, n) multi-secret sharing scheme is proposed in this paper, which is as easy as Yang’s scheme in the secret reconstruction and requires the same number of public values as Chien’s scheme.

A unified approach to secret sharing schemes with low distribution cost

In secret sharing schemes, the secret holder has to distribute secret shares to each participant before distributing the secrets. To distribute or redistribute shares is a very costly process with respect to both time and resources. Unlike previous works, where different approaches are proposed for different scenarios, we propose a unified approach for both threshold‐based schemes and generalized group‐oriented cryptosystems. This unified implementation has the following merits: (1) With a unified approach, the implementation requires much less overhead than its counterparts when various secret sharing problems are simultaneously involved; (2) The Secret Holder (SD) does not need to redistribute new secret shares after the secret reconstruction; (3) The SD can, dynamically and efficiently, determine the capacities (weight) of each user on recovering the secrets, and the threshold values of the secrets; (4) To dynamically adjust the capacities of users, the SD does not need to refresh the shadow of each user and each user just memorizes one secret shadow.

Model calculations to estimate the probability of secret reconstruction in computer environments

Information technologies have ushered in a new era for computer‐related communications. Use of the Internet for commercial applications and resource sharing has accelerated in recent years as well. Owing to such developments, computer security has become a critical issue nowadays. In some applications, a critical message can be divided into pieces and allocated at several different sites over the Internet for security access concern. To access such an important message, one must access the divided pieces from different sites to reconstruct the message. In this paper, we propose model calculations to evaluate the probability of secret reconstruction and a weighted share assignment algorithm for assigning shares on hosts in such a way that the probability to be able to reconstruct the secret becomes the highest. Examples are presented to illustrate the feasibility of the proposed approach.

Shared Secret Reconstruction

In this paper we consider the secret reconstruction problem in a secret sharing scheme. We emphasize that a shared secret should be reconstructed in a fair way, i.e., all involved participants should have the same chance to be able to reconstruct the shared secret. We propose and analyze several methods to achieve such a fair reconstruction of shared secrets.

V-fairness (t, n) secret sharing scheme

All secret sharing schemes proposed to date are not really fair on reconstructing a secret since there exists a probability ɛ, ɛ &gt; 0, such that a dishonest shareholder can obtain the secret while honest ones cannot. The paper proposes a V-fairness (t, n) secret sharing scheme, VFSS scheme, such that all shareholders have an equal probability of obtaining the secret without releasing their shadows simultaneously, even if V, V &lt; t/2, shareholders are dishonest. Furthermore, the cheaters can easily be identified and they have no advantage over other participants during secret reconstruction.

Fair reconstruction of a secret

After gathering sufficient shadows from honest participants and deriving the secret exclusively, a participant, in the process of reconstruction a secret, can turn dishonest and withhold his own shadow (or present a fake shadow) so that others cannot obtain the secret. Previous solutions to overcome this cheating problem require all participants to release their shadows simultaneously; which is difficult to enforce without other supporting protocols. In this paper, we propose a secret reconstruction protocol to solve the cheating problem without the simultaneous release constraint. This protocol is unconditionally secure and can be incorporated with any secret sharing scheme to realize any secret sharing policy.

Cheating detection and cheater identification in secret sharing schemes

A threshold scheme for secret sharing can protect a secret with high reliability and flexibility. These advantages can be achieved only when all the participants are honest, i.e. all the participants willing to pool their shadows shall always present the true ones. Cheating detection is an important issue in the secret sharing scheme. However, cheater identification is more effective than cheating detection in realistic applications. If some dishonest participants exist, the other honest participants will obtain a false secret, while the cheaters may individually obtain the true one. The paper presents a method to enforce the security of any threshold scheme with the ability to detect cheating and identify cheaters. By applying a one-way hashing function along with the use of arithmetic coding, the proposed method can be used to deterministically detect cheating and identify the cheaters, no matter how many cheaters are involved in the secret reconstruction.