Selection of unitary operations in quantum secret sharing without entanglement

Abstract

We propose a substitute-Bell-state attack strategy for quantum secret sharing schemes without entanglement, as well as a definition of the minimum failure probability of such attack strategy. A quantitative analysis of security degrees corresponding to different unitary operations is also provided, when the secret sharing schemes without entanglement are stricken by substitute-Bell-state attack. As a result, the relation between the selection of unitary operations and the effect of substitute-Bell-state attack is shown, which can serve as an important guidance for the selection of unitary operations in designing and implementing quantum secret sharing schemes. Keywords quantum secret sharing, substitute-Bell-state attack, unitary operation, minimum failure probability Citation Xu J, Chen H W, Liu W J, et al. Selection of unitary operations in quantum secret sharing without entanglement.

Same Initial States Attack in Yang et al.’s Quantum Private Comparison Protocol and the Improvement

“…The principles of quantum mechanics, such as no-cloning theorem, uncertainty principle, and entanglement characteristics, provide some interesting ways for cryptography communication and secure computation. During the past thirty years, quantum communication has developed in a variety of directions, including quantum key distribution (QKD) [1,2], quantum secret sharing (QSS) [3,4], quantum direct communication (QDC) [5][6][7], quantum teleportation (QT) [8,9], etc. On the other hand, secure multi-party computation (SMC) has also been discussed in the quantum mechanism.…”

“…The main goal of QPC is to compare the equality of secret inputs between two participants without disclosing any information about each other's secret content. The pioneering QPC protocol was proposed by Yang et al [10] in 2009, and then in 2010, they revised the protocol by removing the step (4) which is in fact unnecessary [26]. Enlightened by Yang et al's work, more QPC protocols are proposed subsequently [11][12][13][14][15][16][17][18].…”

Quantitative security analysis of three-level unitary operations in quantum secret sharing without entanglement

“…The quantitative security analysis of such protocols can be transformed into a quantitative calculation of unitary operation security. The feasibility of this idea has been proven by our pioneering work [23]. In [23], we proposed the substitute-Bell-state attack and the definition of minimum failure probability for the attack.…”

Quantum private comparison based on quantum dense coding

“…The first important application is the quantum key distribution (QKD) protocol [5][6][7][8] with unconditional security. This great scheme has initiated various kinds of cryptographic protocols such as secure transmission of quantum state [9][10][11][12], quantum secret sharing [13][14][15][16][17][18][19], quantum direction communication [20][21][22][23][24][25][26], and quantum steganography protocols [27][28][29]; these schemes have been explored for various security systems.…”