Quantum (t, n) threshold signature based on logistic chaotic sequences and mutually unbiased bases

A quantum (t, n) threshold signature (QTS) based on Logistic Chaotic sequences and mutually unbiased bases is proposed, taking advantage of the pseudo-randomness of chaotic sequences and the cyclic characteristics of d-dimensional mutually unbiased bases. In this scheme, only t or more signatories can produce a valid signature on behalf of a signature group consisting of n members. The scheme uses a Logistic Chaotic mapping to generate a chaotic sequence, for which a particle swapping algorithm is used to obtain a position sequence, combined with a generalized Pauli operator to encrypt the message. Also, mutually unbiased bases in d-dimensional Hilbert space are used to verify the threshold value in the scheme. Security analysis proves that the proposed scheme satisfies signature non-repudiation and is resistant to collusive attacks by disloyal signing members. By comparing to existing QTS schemes, the proposed QTS scheme can reduce the resources consumed in the signing phase. The number of particles in the scheme does not increase as the number of signing members increases, except for local operations. That increases the scalability of the signature scheme.