To address the problem that existing bipartite secret sharing scheme is short of dynamic characteristic, and to solve the problem that each participant can only use secret share once, this paper proposed a bipartite (...To address the problem that existing bipartite secret sharing scheme is short of dynamic characteristic, and to solve the problem that each participant can only use secret share once, this paper proposed a bipartite (n1+n2, m1+m2)-threshold multi-secret sharing scheme which combined cryptography and hypersphere geometry. In this scheme, we introduced a bivariate function and a coordinate function over finite field Zp to calculate the derived points of secret share, which can reconstruct the shared secrets by producing the intersection point of hypernormal plane and normal line on the hypertangent plane. At the initial stage the secret dealer distributes to each participant a secret share that can be kept secret based on the intractability of discrete logarithm problem and need not be changed with updating the shared secrets.Each cooperative participant only needs to submit a derived point calculated from the secret share without exposing this secret share during the process of reconstructing the shared secret. Analyses indicate that the proposed scheme is not only sound and secure because of hypersphere geometric properties and the difficulty of discrete logarithm problem, but also efficient because of its well dynamic behavior and the invariant secret share. Therefore, this bipartite threshold multi-secret sharing scheme is easy to implement and is applicable in practical settings.展开更多
A threshold scheme, which is introduced by Shamir in 1979, is very famous as a secret sharing scheme. We can consider that this scheme is based on Lagrange＇s interpolation formula. A secret sharing scheme has one key...A threshold scheme, which is introduced by Shamir in 1979, is very famous as a secret sharing scheme. We can consider that this scheme is based on Lagrange＇s interpolation formula. A secret sharing scheme has one key. On the other hand, a multi-secret sharing scheme has more than one key, that is, a multi-secret sharing scheme has p （〉_ 2） keys. Dealer distribute shares of keys among n participants. Gathering t （〈 n） participants, keys can be reconstructed. Yang et al. （2004） gave a scheme of a （t, n） multi-secret sharing based on Lagrange＇s interpolation. Zhao et al. （2007） gave a scheme of a （t, n） verifiable multi-secret sharing based on Lagrange＇s interpolation. Recently, Adachi and Okazaki give a scheme of a （t, n） multi-secret sharing based on Hermite interpolation, in the case ofp 〈 t. In this paper, we give a scheme ofa （t, n） verifiable multi-secret sharing based on Hermite interpolation.展开更多
Verifiable secret sharing mainly solves the cheating behavior between malicious participants and the ground control center in the satellite network.The verification stage can verify the effectiveness of secret shares ...Verifiable secret sharing mainly solves the cheating behavior between malicious participants and the ground control center in the satellite network.The verification stage can verify the effectiveness of secret shares issued by the ground control center to each participant and verify the effectiveness of secret shares shown by participants.We use a lot of difficult assumptions based on mathematical problems in the verification stage,such as solving the difficult problem of the discrete logarithm,large integer prime factorization,and so on.Compared with other verifiable secret sharing schemes designed for difficult problems under the same security,the verifiable secret sharing scheme based on the Elliptic Curve Cryptography(ECC)system has the advantages of less computational overhead and shorter key.At present,the binary polynomial is a single secret scheme and cannot provide effective verification.Therefore,based on a Protected Verifiable Synchronous Multi Secret Sharing(PVS-MSS)scheme,this paper is designed based on bivariate asymmetric polynomials.The advanced verifiable attribute is introduced into the Protected Secret Sharing(PSS)scheme.This paper extends the protected synchronous multi-secret sharing scheme based on bivariate polynomial design.The ECC system constructs the security channel between the ground control center and participants and constructs the verification algorithm.Through the verification algorithm,any participant can verify the consistency and effectiveness of the secret shadow and secret share received from other participants or presented by the secret distribution center.Therefore,no additional key agreement protocol is required;participants do not need to negotiate the session key for encryption;the secret share polynomial can generate the session key between participants and speed up the secret reconstruction process.The verification stage has lower computational complexity than the verifiable scheme constructed by Rivest Shamir Adleman (RSA) and other encryption methods. Chinese Remainder Theorem (CRT)is used to update the secret shadow. The secret shadow does not need to beupdated with the change of the scheme shared secret, and the public valueupdate efficiency is higher. Reduce the complexity of sharing secret updatesin a synchronous multi-secret sharing scheme.展开更多
文摘To address the problem that existing bipartite secret sharing scheme is short of dynamic characteristic, and to solve the problem that each participant can only use secret share once, this paper proposed a bipartite (n1+n2, m1+m2)-threshold multi-secret sharing scheme which combined cryptography and hypersphere geometry. In this scheme, we introduced a bivariate function and a coordinate function over finite field Zp to calculate the derived points of secret share, which can reconstruct the shared secrets by producing the intersection point of hypernormal plane and normal line on the hypertangent plane. At the initial stage the secret dealer distributes to each participant a secret share that can be kept secret based on the intractability of discrete logarithm problem and need not be changed with updating the shared secrets.Each cooperative participant only needs to submit a derived point calculated from the secret share without exposing this secret share during the process of reconstructing the shared secret. Analyses indicate that the proposed scheme is not only sound and secure because of hypersphere geometric properties and the difficulty of discrete logarithm problem, but also efficient because of its well dynamic behavior and the invariant secret share. Therefore, this bipartite threshold multi-secret sharing scheme is easy to implement and is applicable in practical settings.
文摘A threshold scheme, which is introduced by Shamir in 1979, is very famous as a secret sharing scheme. We can consider that this scheme is based on Lagrange＇s interpolation formula. A secret sharing scheme has one key. On the other hand, a multi-secret sharing scheme has more than one key, that is, a multi-secret sharing scheme has p （〉_ 2） keys. Dealer distribute shares of keys among n participants. Gathering t （〈 n） participants, keys can be reconstructed. Yang et al. （2004） gave a scheme of a （t, n） multi-secret sharing based on Lagrange＇s interpolation. Zhao et al. （2007） gave a scheme of a （t, n） verifiable multi-secret sharing based on Lagrange＇s interpolation. Recently, Adachi and Okazaki give a scheme of a （t, n） multi-secret sharing based on Hermite interpolation, in the case ofp 〈 t. In this paper, we give a scheme ofa （t, n） verifiable multi-secret sharing based on Hermite interpolation.
基金This work is supported by The State Key Laboratory of Integrated Services Networks,Xidian University(ISN22-13).
文摘Verifiable secret sharing mainly solves the cheating behavior between malicious participants and the ground control center in the satellite network.The verification stage can verify the effectiveness of secret shares issued by the ground control center to each participant and verify the effectiveness of secret shares shown by participants.We use a lot of difficult assumptions based on mathematical problems in the verification stage,such as solving the difficult problem of the discrete logarithm,large integer prime factorization,and so on.Compared with other verifiable secret sharing schemes designed for difficult problems under the same security,the verifiable secret sharing scheme based on the Elliptic Curve Cryptography(ECC)system has the advantages of less computational overhead and shorter key.At present,the binary polynomial is a single secret scheme and cannot provide effective verification.Therefore,based on a Protected Verifiable Synchronous Multi Secret Sharing(PVS-MSS)scheme,this paper is designed based on bivariate asymmetric polynomials.The advanced verifiable attribute is introduced into the Protected Secret Sharing(PSS)scheme.This paper extends the protected synchronous multi-secret sharing scheme based on bivariate polynomial design.The ECC system constructs the security channel between the ground control center and participants and constructs the verification algorithm.Through the verification algorithm,any participant can verify the consistency and effectiveness of the secret shadow and secret share received from other participants or presented by the secret distribution center.Therefore,no additional key agreement protocol is required;participants do not need to negotiate the session key for encryption;the secret share polynomial can generate the session key between participants and speed up the secret reconstruction process.The verification stage has lower computational complexity than the verifiable scheme constructed by Rivest Shamir Adleman (RSA) and other encryption methods. Chinese Remainder Theorem (CRT)is used to update the secret shadow. The secret shadow does not need to beupdated with the change of the scheme shared secret, and the public valueupdate efficiency is higher. Reduce the complexity of sharing secret updatesin a synchronous multi-secret sharing scheme.
