Threshold quantum cryptography

Threshold quantum cryptograph based on Grover's algorithm

“…The t-outof-n quantum cash threshold protocol proposed by Tokunaga et al [10] is not secure. With the help of the attack schemes proposed in Ref.…”

“…[8,9], the first participant P 1 , called a center in Ref. [10], can completely eavesdrop t − 1 secret inputs kept by t − 1 other participants in a issuing phase one by one, and then reconstructs the copies of quantum cash that can pass the checking phase.…”

“…The sample photons schemes [8,9] can improve the security of the threshold quantum protocol [10]. However the number of qubits of the generated quantum state by the threshold protocol must exceed that of the quantum state generated by the original (nonthreshold) protocol.…”

“…Section II introduces two-qubit operators based on Grovers algorithm [11]. Section III proposes an t-out-of-n quantum cash threshold protocol followed the line sketched in [10] but with some relevant differences. Section IV then shows security of the threshold protocol.…”

Quantum secret sharing between m-party and n-party with six states

“…The basic idea of secret sharing in the simplest case is that a secret of one person, say Alice, is shared between other two persons, say Bob and Charlie, in such a way that it can only be reconstructed if both collaborate. In a more general case, notably for secure key management, a t-out-of-n protocol (or (t, n)-threshold scheme) with 1 ≤ t ≤ n spreads a secret to n participants in a way that any t participants can reconstruct it [12]. Lance et al have reported an experimental demonstration of a (2,3) threshold quantum secret sharing scheme [13].…”