Verifiable threshold quantum secret sharing with sequential communication

A (t, n) threshold quantum secret sharing (QSS) is proposed based on a single d-level quantum system. It enables the (t, n) threshold structure based on Shamir’s secret sharing and simply requires sequential communication in d-level quantum system to recover secret. Besides, the scheme provides a verification mechanism which employs an additional qudit to detect cheats and eavesdropping during secret reconstruction and allows a participant to use the share repeatedly. Analyses show that the proposed scheme is resistant to typical attacks. Moreover, the scheme is scalable in participant number and easier to realize compared to related schemes. More generally, our scheme also presents a generic method to construct new (t, n) threshold QSS schemes based on d-level quantum system from other classical threshold secret sharing.     

Threshold quantum secret sharing based on single qubit

Based on unitary phase shift operation on single qubit in association with Shamir’s (t, n) secret sharing, a (t, n) threshold quantum secret sharing scheme (or (t, n)-QSS) is proposed to share both classical information and quantum states. The scheme uses decoy photons to prevent eavesdropping and employs the secret in Shamir’s scheme as the private value to guarantee the correctness of secret reconstruction. Analyses show it is resistant to typical intercept-and-resend attack, entangle-and-measure attack and participant attacks such as entanglement swapping attack. Moreover, it is easier to realize in physic and more practical in applications when compared with related ones. By the method in our scheme, new (t, n)-QSS schemes can be easily constructed using other classical (t, n) secret sharing.     

Cryptanalysis of a new circular quantum secret sharing protocol for remote agents

In a recent paper (Lin and Hwang in Quantum Inf Process, 2012. doi:10.1007/s11128-012-0413-8), a new circular quantum secret sharing (QSS) protocol for remote agents was presented. The protocol is designed with entangling a Bell state and several single photons to form a multi-particle GHZ state. For each shared bit among n party, the qubit efficiency has reached 1/2n + 1 which is the best among the current circular QSS protocol. They claim that the protocol is more suitable for a remote agents’ environment as that the newly generated photons are powerful enough to reach to the next receiver. However, we show that the protocol is not secure as the first agent and the last agent in the protocol can illegally obtain all the secret messages without introducing any error.     

New circular quantum secret sharing for remote agents

This study presents a novel circular quantum secret sharing (QSS) protocol based on the controlled-NOT (CNOT) gate for remote agents. A CNOT gate is able to entangle a Bell state and several single photons to form a multi-particle GHZ state. Using this technique, the proposed QSS scheme is designed in purpose to be congenitally free from the Trojan horse attacks. Moreover, for each shared bit among n party, the qubit efficiency has reached ${\frac{1}{2n+1}}$ , which is the best among the current circular QSS??s.     

Quantum secret sharing using orthogonal multiqudit entangled states

In this work, we investigate the distinguishability of orthogonal multiqudit entangled states under restricted local operations and classical communication. According to these properties, we propose a quantum secret sharing scheme to realize three types of access structures, i.e., the (n, n)-threshold, the restricted (3, n)-threshold and restricted (4, n)-threshold schemes (called LOCC-QSS scheme). All cooperating players in the restricted threshold schemes are from two disjoint groups. In the proposed protocol, the participants use the computational basis measurement and classical communication to distinguish between those orthogonal states and reconstruct the original secret. Furthermore, we also analyze the security of our scheme in four primary quantum attacks and give a simple encoding method in order to better prevent the participant conspiracy attack.     

Two secret sharing schemes based on Boolean operations

Traditional secret sharing schemes involve complex computation. A visual secret sharing (VSS) scheme decodes the secret without computation, but each shadow is m times as big as the original. Probabilistic VSS solved the computation complexity and space complexity problems at once. In this paper we propose a probabilistic (2,n) scheme for binary images and a deterministic (n,n) scheme for grayscale images. Both use simple Boolean operations and both have no pixel expansion. The (2,n) scheme provides a better contrast and significantly smaller recognized areas than other methods. The (n,n) scheme gives an exact reconstruction.     

Threshold quantum secret sharing between multiparty and multiparty using Greenberger–Horne–Zeilinger state

We propose a (t, m)?(s, n) threshold quantum secret sharing protocol between multiparty (m members in group 1) and multiparty (n members in group 2) using a sequence of Greenberger–Horne–Zeilinger (GHZ) states, which is useful and efficient when the parties of communication are not all present. In the protocol, Alice prepares a sequence of GHZ states in one of the eight different states and sends the last two particles to the first agent while other members encode their information on the sequence via unitary transformations. Finally the last member in group 2 measures the qubits. It is shown that this scheme is safe.     

An SMVQ-based reversible data hiding technique exploiting side match distortion

Secure online communication is a necessity in today’s digital world. This paper proposes a novel reversible data hiding technique based on side match vector quantization (SMVQ). The proposed scheme classifies SMVQ indices as Case 1 or 2 based on the value of the first state codeword’s side match distortion (SMD) and a predefined threshold t. The proposed scheme uses this classification to switch between compression codes designed for Cases 1 and 2 SMVQ indices. The length of these compression codes is controlled by the parameter ?. Thus, with the selection of appropriate ? and t values, the proposed scheme achieves good compression, creating spaces to embed secret information. The embedding algorithm can embed n secret bits into each SMVQ index, where n = 1, 2, 3, or 4. The experimental results show that the proposed scheme obtains the embedding rates of 1, 2, 3, or 4 bit per index (bpi) at the average bit rates of 0.340, 0.403, 0.465, or 0.528 bit per pixel (bpp) for the codebook size 256. This improves the performance of recent VQ and SMVQ-based data hiding schemes.     

Pseudo-Random Graphs and Bit Probe Schemes with One-Sided Error

We study probabilistic bit-probe schemes for the membership problem. Given a set A of at most n elements from the universe of size m we organize such a structure that queries of type “x∈A??” can be answered very quickly. H. Buhrman, P.B. Miltersen, J. Radhakrishnan, and S. Venkatesh proposed a randomized bit-probe scheme that needs space of O(nlogm) bits. That scheme has a randomized algorithm processing queries; it needs to read only one randomly chosen bit from the memory to answer a query. For every x the answer is correct with high probability (with two-sided errors). In this paper we slightly modify the bit-probe model of Buhrman et al. and consider schemes with a small auxiliary information in “cache” memory. In this model, we show that for the membership problem there exists a bit-probe scheme with one-sided error that needs space of O(nlog² m+poly(logm)) bits, which cannot be achieved in the model without cache. We also obtain a slightly weaker result (space of size n ^1+δ poly(logm) bits and two bit probes for every query) for a scheme that is effectively encodable.     

Strong (n, t, n) verifiable secret sharing scheme

A (t, n) secret sharing divides a secret into n shares in such a way that any t or more than t shares can reconstruct the secret; but fewer than t shares cannot reconstruct the secret. In this paper, we extend the idea of a (t, n) secret sharing scheme and give a formal definition on the (n, t, n) secret sharing scheme based on Pedersen’s (t, n) secret sharing scheme. We will show that the (t, n) verifiable secret sharing (VSS) scheme proposed by Benaloh can only ensure that all shares are t-consistent (i.e. any subset of t shares defines the same secret); but shares may not satisfy the security requirements of a (t, n) secret sharing scheme. Then, we introduce new notions of strong t-consistency and strong VSS. A strong VSS can ensure that (a) all shares are t-consistent, and (b) all shares satisfy the security requirements of a secret sharing scheme. We propose a strong (n, t, n) VSS based on Benaloh’s VSS. We also prove that our proposed (n, t, n) VSS satisfies the definition of a strong VSS.     

Data hiding by an improved exploiting modification direction

This paper represents an improved data hiding scheme, CIE, which uses a codebook to improve the Exploiting Modification Direction (EMD) embedding scheme. In our scheme, one secret (2 ^n?+?x ???1)-ary digit is hidden in a group of pixels in an image as a modified secret digit. Our proposed scheme has an embedding rate $R=\log_2(2^{n+x}-1)/n$ , which is greater than the rate of the EMD scheme, which is R?=?log₂(2n?+?1)/n for n?≥?2 . Embedding rate R is the number of secret bits embedded in each cover pixel. Our experimental results demonstrate that our scheme is able to embed 3 times as many secret bits in an image compared to the original EMD embedding scheme when n?=?2 and x?=?5. Our scheme has low time complexity and achieves this higher embedding performance while retaining reasonable perceptual quality for the image. An experiment verifies these features of our proposed data hiding scheme.     

Restricted (<Emphasis Type="Italic">k</Emphasis>, <Emphasis Type="Italic">n</Emphasis>)-threshold quantum secret sharing scheme based on local distinguishability of orthogonal multiqudit entangled states

In this work, we study a restricted (k, n)-threshold access structure. According to this structure, we construct a group of orthogonal multipartite entangled states in d-dimensional system and investigate the distinguishability of these entangled states under restricted local operations and classical communication. Based on these properties, we propose a restricted (k, n)-threshold quantum secret sharing scheme (called LOCC-QSS scheme). The k cooperating players in the restricted threshold scheme come from all disjoint groups. In the proposed protocol, the participants distinguish these orthogonal states by the computational basis measurement and classical communication to reconstruct the original secret. Furthermore, we also analyze the security of our scheme in three primary quantum attacks and give a simple encoding method in order to better prevent the participant conspiracy attack.     

面向云存储的多维球面门限秘密共享方案

近年来,云存储所提供的“数据存储即服务”为租户实现廉价高效共享资源.由于租户缺乏对云端数据的绝对控制,数据安全,尤其是机密数据的安全存储成为一大问题,这也是近年来云存储安全的研究热点.针对机密数据的云存储问题,提出了一种基于多维球面原理的分布式秘密共享方案.在分发阶段,结合分发者、云存储容器信息,将原始秘密转换为m维球心坐标,进而生成同球面的n个影子秘密坐标,并将这些影子秘密作为机密数据分布式存储在n个云存储容器中.在恢复阶段,通过证明任意k（k=m+1）个线性不相关的坐标可确定唯一球心,完成原始秘密的恢复.算法性能分析和仿真分析表明,该方案具备假数据攻击、共谋攻击防御能力,且密钥不需要额外的管理开销,租户对密钥有绝对控制权,加强了租户对云数据的控制,在运算性能、存储性能方面正确、有效.     

A general (k, n) scalable secret image sharing scheme with the smooth scalability

A novel (k, n) scalable secret image sharing (SSIS) scheme was proposed to encrypt a secret image into n shadow images. One can gradually reconstruct a secret image by stacking k or more shadows, but he/she cannot conjecture any information from fewer than k shadows. The advantage of a (k, n)-SSIS scheme is that it provides the threshold property (i.e., k is a threshold value necessary to start in to reveal the secret) as well as the scalability (i.e., the information amount of a reconstructed secret is proportional to the number of shadows used in decryption). All previous (k, n)-SSIS schemes did not have the smooth scalability so that the information amount can be “smoothly” proportional to the number of shadows. In this paper, we consider the smooth scalability in (k, n)-SSIS scheme.     

A variant of Wiener’s attack on RSA

Wiener’s attack is a well-known polynomial-time attack on a RSA cryptosystem with small secret decryption exponent d, which works if d < n ^0.25, where n = pq is the modulus of the cryptosystem. Namely, in that case, d is the denominator of some convergent p _m /q _m of the continued fraction expansion of e/n, and therefore d can be computed efficiently from the public key (n, e). There are several extensions of Wiener’s attack that allow the RSA cryptosystem to be broken when d is a few bits longer than n ^0.25. They all have the run-time complexity (at least) O(D ²), where d = Dn ^0.25. Here we propose a new variant of Wiener’s attack, which uses results on Diophantine approximations of the form |α ? p/q| <  c/q ², and “meet-in-the-middle” variant for testing the candidates (of the form rq _m+1 +  sq _m ) for the secret exponent. This decreases the run-time complexity of the attack to O(D log D) (with the space complexity O(D)).     

A secure Boolean-based multi-secret image sharing scheme

An (n, n) multi-secret image sharing scheme shares n secret images among n shared images. In this type of schemes, n shared images can be used to recover all n secret images, but the loss of any shared image prevents the recovery of any secret image. Among existing image sharing techniques, Boolean-based secret schemes have good performance because they only require XOR calculation. This study presents a secure Boolean-based secret image sharing scheme that uses a random image generating function to generate a random image from secret images or shared images. The proposed function efficiently increases the sharing capacity on free of sharing the random image. The use of a bit shift subfunction in the random image generating function produces a random image to meet the random requirement. Experimental results show that the proposed scheme requires minimal CPU computation time to share or recover secret images. The time required to share n secret images is nearly the time as that required to recover n secret images. The bit shift subfunction takes more computation load than the XOR subfunction needs.     

A real-time secret image sharing with fairness

When traditional secret image sharing techniques reconstructed the secret, they input the shares over t. While less than t shares can know nothing about the secret, the problem arises when there are more than t shares. The cheater can use this to put their share in the last. Therefore, fairness is a important objective of the secret image sharing. Tian et al. proposed the fairness secret sharing scheme in 2012. However, they generated v polynomials for one secret data and performed v-times to reconstruct the polynomial using Lagrange interpolation. Therefore, their scheme is unsuitableness in the real-time processing. The proposed scheme generates one polynomial for the one secret data based on the fairness concept of Tian et al.’s scheme. For the providing fairness, the proposed scheme hides the verification value at the random coefficient of the polynomial. During the secret image reconstruction procedure, each shadow image brought by a participant is verified for its fairness using XOR operation. Our scheme not only satisfies the fairness, but also is suitable for the real-time process. This helps to detect the participant from intentional provision of a false or cheating. In addition, our scheme uses the steganography technique for increasing the security protection purpose. The proposed scheme as a whole offers a high secure and effective mechanism for the secret image sharing that is not found in existing secret image sharing methods. In the experimental result, PSNR of the proposed scheme is average 44.67 dB. It is higher 4 dB than the previous schemes. The embedding capacity is also similar to the other schemes.     

An ideal multi-secret sharing scheme based on MSP

A multi-secret sharing scheme is a protocol to share m arbitrarily related secrets s₁, … , s_m among a set of n participants. In this paper, we propose an ideal linear multi-secret sharing scheme, based on monotone span programs, where each subset of the set of participants may have the associated secret. Our scheme can be used to meet the security requirement in practical applications, such as secure group communication and privacy preserving data mining etc. We also prove that our proposed scheme satisfies the definition of a perfect multi-secret sharing scheme.     

Efficient and secure multi secret sharing schemes based on boolean XOR and arithmetic modulo

Multi Secret Sharing (MSS) scheme is an efficient method of transmitting more than one secret securely. In (n, n)-MSS scheme n secrets are used to create n shares and for reconstruction, all n shares are required. In state of the art schemes n secrets are used to construct n or n + 1 shares, but one can recover partial secret information from less than n shares. There is a need to develop an efficient and secure (n, n)-MSS scheme so that the threshold property can be satisfied. In this paper, we propose three different (n, n)-MSS schemes. In the first and second schemes, Boolean XOR is used and in the third scheme, we used Modular Arithmetic. For quantitative analysis, Similarity metrics, Structural, and Differential measures are considered. A proposed scheme using Modular Arithmetic performs better compared to Boolean XOR. The proposed (n, n)-MSS schemes outperform the existing techniques in terms of security, time complexity, and randomness of shares.     

Meaningful (2, infinity) secret image sharing scheme based on flipping operations

In this paper, a new method to construct a secret image sharing (SIS) scheme is proposed, where a secret image is shared into several shares by a perfect secure way without any knowledge of cryptography. A basic algorithm implemented by flipping operations with probability for constructing a meaningful (2, 2) SIS scheme is first proposed. Neither codebook tailor-made requirement nor pixel expansion is required in the proposed scheme. Additionally, the meaningful shares by the proposed scheme can be directly generated without any extra data hiding process. During the decrypting procedure, the secret image is visually revealed by performing XOR operations on two meaningful shares. In the following stage, a meaningful (2, infinity) SIS scheme is extended underlying the basic algorithm, where the number of shares can be extended anytime. Further, no matter how large the number of the extended shares is, the visual qualities of both the meaningful share and revealed secret image remain unchanged. Finally, sufficient number of formal proofs are provided to validate the correctness of the proposed schemes, whose superiority is also demonstrated by the experimental results.