Research On Key Technology Of Quantum Threshold Secret Sharing

Quantum Threshold Secret Sharing(QTSS)is a kind of quantum cryptography that splits and reconstructs the secret message.It is an important means of information security and data privacy in quantum communication environment,and it mainly solves the problem that some participants are absent or dishonest,or some shares are under attack.In order to make up for the deficiencies in the current research on quantum secret sharing at home and abroad,this thesis takes quantum threshold technology as the center and undertakes the theory study on four key issues of expanding quantum space dimension,constructing quantum state reconstruction algorithm,improving computational efficiency and enhancing security.To address these issues,five QTSS schemes are put forward,where the first two schemes are high-dimensional QTSS schemes,and the last three ones are verifiable QTSS schemes.The main research contents and innovation points of this thesis are as follows:(1)In order to solve the problem of high computational cost and communication cost in the existing high-dimensional QTSS schemes,a high dimensional QTSS based on GHZ(Greenberger-Horne-Zeilinger)state(HDQTSS-BGHZ)scheme is proposed.To reduce computational cost,the scheme embeds the classical share of the authorized participant into the particle of GHZ entangled state by using a d dimensional Pauli operator,and performs one inverse quantum Fourier transform on the measurement output of the first particle of GHZ state to reconstruct the classical secret.To reduce communication cost,the scheme uses the exchangeability of the phases of d-dimensional multiparticle entangled state to aggregate all participants' shares into the phase of the reconstructors' particle directly and are not transmitted in the channel.Security analysis shows that HDQTSS-BGHZ not only reduces the risk of interception attack but also resists the collusion attack of t-1 participants.Compared with other schemes such as threshold quantum secret sharing of secure direct communication(TQSSSDC)and secret sharing based on quantum Fourier transform(SSBQFT),HDQTSS-BGHZ has higher computational efficiency and lower communication cost.(2)For the existing high-dimensional QTSS schemes,resource consumption on particle measurement are expensive and the schemes are difficult to resist Trojan horse attack,a high dimensional QTSS based on teleportation(HDQTSS-BT)scheme is proposed.To reduce the resource consumption of particle measurement,the schemeperforms joint projection measurement on the particle of Cat state and the particle of Bell state.To resist multiple quantum attacks,by means of one d dimensional entanglement swapping,the shadows of the shares of t participants in the authorized subset are teleported to reconstructor's particle,so that the classical secret is restored.Security analysis shows that HDQTSS-BT can resist Trojan horse attack in addition to the attacks that HDQTSS-BGHZ can resist.Compared with other schemes such as secret sharing based on quantum Fourier transform(SSBQFT)and threshold quantum secret sharing based on single qubit(TQSSBSQ),HDQTSS-BGHZ has lower resource consumption of particle measurement and higher computational efficiency.(3)In order to solve the problems of the existing verifiable quantum state QTSS schemes,such as high resource consumption on particle preparation and low efficiency of verification,a verifiable quantum state threshold secret sharing based on Lagrange unitary operator(VQSTTSS-BLUO)scheme is proposed.To reduce resource consumption of multiple particles preparation,the scheme first prepares a secret particle,then performs the Lagrangian unitary operator on it,which is shared among authorized participants.To improve verification efficiency,the scheme performs the mixed rotation unitary operator on the message particle after the unitary transformation,which not only verifies the validity of the message particle but also reconstructs the original secret particle.Compared with the two schemes(MQSSSBPSO and TQSSUPSO)based on rotation unitary operator,VQSTTSS-BLUO provides stronger verification security.Compared with the two schemes(SMQCSHM-VQSS and VQSTTSS)based on verification function,VQSTTSS-BLUO has lower resource consumption of particle preparation and higher verification efficiency.(4)Aiming at the problem that verifiable quantum state QTSS schemes are difficult to resist the denial attacks of distributor and participants,a verifiable quantum state threshold secret sharing against denial attack(VQSTTSS-ADA)is proposed.Based on the designed quantum state signature(QSTDS)algorithm,to resist the distributor's denial attack,the scheme sends the quantum secret sequence encoded by the distributor into the quantum message sequences and the quantum signature sequence to the trusted participants.To resist the participants' denial attack,the previous participant in the authorized subset first verifies the validity of the received quantum signature sequence,and then encodes the received quantum message sequence into two new quantum information sequence and a new quantum signature sequence,and further transmitsthem to the next participant.Compared with the three typical schemes(including VQSTTSS-BLUO),in addition to the attacks they can resist,VQSTTSS-ADA can also resist denial attacks by distributor and participants as well as external man-in-the-middle attack by external attacker.(5)Aiming at the problem that the original verifiable QTSS(VQTSS)scheme has a single form of sharing secret and is difficult to resist the chosen plaintext attack of external attacker,an improved verifiable QTSS against chosen plaintext attack(VQTSS-ACPA)is proposed.The improved measures are as follows: firstly,the quantum one-way function is used to transform the participant's identity and private share into a quantum fingerprint,which ensures the integrity of share.Secondly,the quantum fingerprint is signed by both the distributor and the designated participant,and private shares and the quantum double signatures are encrypted and sent to the reconstructor via the quantum channel.The dual quantum signatures track the forgery and denial deception of the distributor and the participant,and the quantum ciphertext prevents the malicious attack of external attacker.Finally,the reconstructor restores the classical or quantum state secret,which increases the diversity of the forms of shared secret.Security analysis and comparison demonstrate that the improved VQTSS-ACPA makes up for the security vulnerability of the original VQTSS and resists the denial attacks by distributor and participant as well as the chosen plaintext attack by external attacker.With the topics of high-dimensional QTSS and verifiable QTSS,five schemes are proposed in this thesis.The correctness and feasibility of the five schemes are demonstrated from security analysis and performance comparison.The research of this thesis has established theoretical base for further improving the theoretical research of QSS and broadening the application scenarios of QTSS.