Post-processing is indispensable in quantum key distribution （QKD）, which is aimed at sharing secret keys between two distant parties. It mainly consists of key reconciliation and privacy amplification, which is use...Post-processing is indispensable in quantum key distribution （QKD）, which is aimed at sharing secret keys between two distant parties. It mainly consists of key reconciliation and privacy amplification, which is used for sharing the same keys and for distilling unconditional secret keys. In this paper, we focus on speeding up the privacy amplification process by choosing a simple multiplicative universal class of hash functions. By constructing an optimal multiplication algorithm based on four basic multiplication algorithms, we give a fast software implementation of length-adaptive privacy amplification. ＂Length-adaptive＂ indicates that the implementation of privacy amplification automatically adapts to different lengths of input blocks. When the lengths of the input blocks are 1 Mbit and 10 Mbit, the speed of privacy amplification can be as fast as 14.86 Mbps and 10.88 Mbps, respectively. Thus, it is practical for GHz or even higher repetition frequency QKD systems.展开更多
We present a scheme for quantum privacy amplification （QPA） for a sequence of single qubits. The QPA procedure uses a unitary operation with two controlled-not gates and a Hadamard gate. Every two qubits are perform...We present a scheme for quantum privacy amplification （QPA） for a sequence of single qubits. The QPA procedure uses a unitary operation with two controlled-not gates and a Hadamard gate. Every two qubits are performed with the unitary gate operation, and a measurement is made on one photon and the other one is retained. The retained qubit carries the state information of the discarded one. In this way, the information leakage is reduced. The procedure can be performed repeatedly so that the information leakage is reduced to any arbitrarily low level. With this QPA scheme, the quantum secure direct communication with single qubits can be implemented with arbitrarily high security. We also exploit this scheme to do privacy amplification on the single qubits in quantum information sharing for long-distance communication with quantum repeaters.展开更多
In this paper,we design the differentially private variants of the classical Frank-Wolfe algorithm with shuffle model in the optimization of machine learning.Under weak assumptions and the generalized linear loss(GLL)...In this paper,we design the differentially private variants of the classical Frank-Wolfe algorithm with shuffle model in the optimization of machine learning.Under weak assumptions and the generalized linear loss(GLL)structure,we propose a noisy Frank-Wolfe with shuffle model algorithm(NoisyFWS)and a noisy variance-reduced Frank-Wolfe with the shuffle model algorithm(NoisyVRFWS)by adding calibrated laplace noise under shuffling scheme in thel_(p)(p∈[1,2])-case,and study their privacy as well as utility guarantees for the H?lder smoothness GLL.In particular,the privacy guarantees are mainly achieved by using advanced composition and privacy amplification by shuffling.The utility bounds of the Noisy FWS and NoisyVRFWS are analyzed and obtained the optimal excess population risksO(n-(1+α/4α+log(d)√log(1/δ)/n∈and O(n-1+α/4α+log(d)√log1(+δ)/n^(2)∈with gradient complexity O(n(1+α)^(2)/4α^(2)forα∈[1/√3,1].It turns out that the risk rates under shuffling scheme are a nearly-dimension independent rate,which is consistent with the previous work in some cases.In addition,there is a vital tradeoff between(α,L)-Holder smoothness GLL and the gradient complexity.The linear gradient complexity O(n)is showed by the parameterα=1.展开更多
基金supported by the National Basic Research Program of China(Grant Nos.2011CBA00200 and 2011CB921200)the National Natural Science Foundation of China(Grant Nos.60921091 and 61101137)
文摘Post-processing is indispensable in quantum key distribution （QKD）, which is aimed at sharing secret keys between two distant parties. It mainly consists of key reconciliation and privacy amplification, which is used for sharing the same keys and for distilling unconditional secret keys. In this paper, we focus on speeding up the privacy amplification process by choosing a simple multiplicative universal class of hash functions. By constructing an optimal multiplication algorithm based on four basic multiplication algorithms, we give a fast software implementation of length-adaptive privacy amplification. ＂Length-adaptive＂ indicates that the implementation of privacy amplification automatically adapts to different lengths of input blocks. When the lengths of the input blocks are 1 Mbit and 10 Mbit, the speed of privacy amplification can be as fast as 14.86 Mbps and 10.88 Mbps, respectively. Thus, it is practical for GHz or even higher repetition frequency QKD systems.
基金The project supported by the National Fundamental Research Program of China under Grant No. 001CB309308, National Natural Science Foundation of China under Grant Nos. 60433050, 10325521, and 10447106, and the SRFDP Program of Ministry of Education of China
文摘We present a scheme for quantum privacy amplification （QPA） for a sequence of single qubits. The QPA procedure uses a unitary operation with two controlled-not gates and a Hadamard gate. Every two qubits are performed with the unitary gate operation, and a measurement is made on one photon and the other one is retained. The retained qubit carries the state information of the discarded one. In this way, the information leakage is reduced. The procedure can be performed repeatedly so that the information leakage is reduced to any arbitrarily low level. With this QPA scheme, the quantum secure direct communication with single qubits can be implemented with arbitrarily high security. We also exploit this scheme to do privacy amplification on the single qubits in quantum information sharing for long-distance communication with quantum repeaters.
基金supported by the National Natural Science Foundation of China(No.U1811461,12326615)。
文摘In this paper,we design the differentially private variants of the classical Frank-Wolfe algorithm with shuffle model in the optimization of machine learning.Under weak assumptions and the generalized linear loss(GLL)structure,we propose a noisy Frank-Wolfe with shuffle model algorithm(NoisyFWS)and a noisy variance-reduced Frank-Wolfe with the shuffle model algorithm(NoisyVRFWS)by adding calibrated laplace noise under shuffling scheme in thel_(p)(p∈[1,2])-case,and study their privacy as well as utility guarantees for the H?lder smoothness GLL.In particular,the privacy guarantees are mainly achieved by using advanced composition and privacy amplification by shuffling.The utility bounds of the Noisy FWS and NoisyVRFWS are analyzed and obtained the optimal excess population risksO(n-(1+α/4α+log(d)√log(1/δ)/n∈and O(n-1+α/4α+log(d)√log1(+δ)/n^(2)∈with gradient complexity O(n(1+α)^(2)/4α^(2)forα∈[1/√3,1].It turns out that the risk rates under shuffling scheme are a nearly-dimension independent rate,which is consistent with the previous work in some cases.In addition,there is a vital tradeoff between(α,L)-Holder smoothness GLL and the gradient complexity.The linear gradient complexity O(n)is showed by the parameterα=1.
