Orthogonal-state-based and semi-quantum protocols for quantum private comparison in noisy environment

Abstract

Private comparison is a primitive for many cryptographic tasks, and recently several schemes for the quantum private comparison (QPC) have been proposed, where two users can compare the equality of their secrets with the help of a semi-honest third party (TP) without knowing each other's secret and without disclosing the same to the TP. In the exisiting schemes, secrecy is obtained by using conjugate coding, and considering all participants as quantum users who can perform measurement(s) and/or create states in basis other than computational basis. In contrast, here we propose two new protocols for QPC, first of which does not use conjugate coding (uses orthogonal states only) and the second one allows the users other than TP to be classical whose activities are restricted to either reflecting a quantum state or measuring it in computational basis. Further, the performance of the protocols is evaluated under various noise models. made to achieve QPC without TP [22,23], but they have been found to be insecure and/or unfair [24]. Thus, in what follows, we will concentrate on three party protocols of QPC, where a TP helps Alice and Bob to compare the equality of their information. Such protocols for QPC have been proposed using different types of entangled states. For example, in Ref.[5], a scheme for QPC has been proposed using χ-type state, W state was used in Ref. [12], Bell state was used in [6,7,13], GHZ state was used in [11]. Further, in Ref.[25], a group theoretic structure of the protocols of quantum dialogue was proposed using a large number of different types of entangled states (e.g., W, GHZ, cluster, Q 4, Q 5, and Brown states), and it was shown that the quantum dialogue scheme proposed there can be converted to a protocol of the socialist millionaire problem, which is equivalent to QPC. Thus, in [25], several options for realization of protocols for QPC were provided. Further, in the similar line, in [26], a set of new options (e.g., 4-qubit Ω state, 4-qubit cat state, etc.) for realization of QD, and thus, QPC have been proposed.It's already established that the schemes for QPC have useful applications in private bidding and auctions, secret ballot elections, e-commerce, etc. ( [8] and references therein). Due to the fact that a scheme for QPC has applications in many fields, many variants of QPC have been studied in the recent past. For example, Huang et al., have recently proposed a GHZ-state-based QPC scheme for n users [11]. Huang et al.'s scheme considers an almost-dishonest TP and allows him to compare the equality of the secrets of a subset of users, too.In what follows, we plan to propose two protocols for QPC in the line of modified Tseng-Lin-Hwang (TLH) protocol, which was proposed in its original form in 2012 [6]. In the original TLH protocol a scheme for quantum private comparison was proposed using Bell states, but almost immediately after the publication of TLH scheme, Yang et al., [13] had shown that there exist a security flaw in the original TLH scheme and other similar schemes, whic...

Semi-quantum cryptography

“…Protocol: SQPC Protocol [143] 1. Parties A and B, using the fully quantum third-party, first run a mediated SQKD protocol (such as the one in [76]) to establish a shared secret key which only A and B know, but not the third party.…”

“…A security analysis and also the effects of noise, was performed on this protocol in [143]. Other SQPC protocols have been proposed.…”

Lightweight mediated semi-quantum key distribution protocol

“…After the semi-quantum environment was proposed, various kinds of semi-quantum protocols have been proposed for different security issues, some of which are SQKD for different situations [17][18][19][20][21][22][23][24][25][26], semi-quantum communication [27][28][29], semi-quantum secret sharing [30][31][32], semi-quantum private comparison [33,34], and semi-quantum information splitting [35], among others. According to the existing semi-quantum protocols , this study summarizes the semi-quantum environments and the quantum capabilities of the classical participants in Table 1.…”

Semiquantum key distribution with high quantum noise tolerance

“…Beyond key distribution itself, the semi-quantum model has been used for other cryptographic tasks including secret sharing [23,24,25,26], direct communication [27,28,29], and quantum private comparison [30,31,32,33]. There has also been work recently in analyzing SQKD protocols in more practical settings (where it is impossible for B to accurately perform the Measure and Resend operation as he cannot prepare a photon in exactly the same state it was received) [2,34,35].…”

“…1 − S(A|E) (since we are assuming a symmetric attack in both protocols thus A's key bit is unbiased and, so, equally likely to be 0 or 1 yielding S(A) = 1). In this case, it is trivial algebra to show (using Equation 30 and basic definitions of mutual information): Figure 6 shows a comparison of S(A|E) for our protocol and BB84 with CAD in the independent case; Figure 7 shows the same but for the dependent channel case. For the dependent case, Eve's uncertainty is far greater than BB84 [2] in all cases except for MODE-2 when Q > 25%.…”