Journal of Optical Communications and Networking
Vol. 16,
Issue 7,
pp. 735-749
(2024)
•https://doi.org/10.1364/JOCN.511999

Multi-protocol updating for seamless key negotiation in quantum metropolitan networks

Jiali Zhu, Yuan Cao, Mingxuan Guo, Xingyu Zhou, Chunhui Zhang, Jian Li, Xiaosong Yu, Yongli Zhao, Jie Zhang, and Qin Wang

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Jiali Zhu, Yuan Cao, Mingxuan Guo, Xingyu Zhou, Chunhui Zhang, Jian Li, Xiaosong Yu, Yongli Zhao, Jie Zhang, and Qin Wang, "Multi-protocol updating for seamless key negotiation in quantum metropolitan networks," J. Opt. Commun. Netw. 16, 735-749 (2024)
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Abstract

Quantum key distribution (QKD) can provide long-term security for numerous users. Currently, quantum networks are still in the early stages of small-scale deployment, most of which can only support a single QKD protocol (QKDP). However, with the advancement of various QKDPs, a single-protocol quantum network is no longer sufficient to meet the demands of multiple users, prompting the emergence of multi-protocol quantum networks. Nevertheless, the transition from a single-protocol to a multi-protocol quantum network still faces many challenging issues, such as key negotiation interruptions due to device initialization and channel calibration during protocol updating. To address the quantum key negotiation interruption problem, we propose a seamless key negotiation oriented multi-protocol updating algorithm in this work, which can fulfill the protocol updating requests of different users in quantum metropolitan networks. Furthermore, to better improve network performance while meeting diverse user demands, we propose four heuristic algorithms for optimal QKDP recommendation, focusing on their applications for multi-protocol updating in different types of typical networks. We perform the simulations with different QKDP recommendation algorithms to analyze the impact of the cache time of the key cache area on the key negotiation interruption probability and the time resource utilization. Simulation results demonstrate that the proposed algorithm can reduce the key negotiation interruption probability by 77.7% while increasing the time resource utilization by 15.3% compared to no key cache area.

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Notations	Definitions
$G (V, E)$	Quantum metropolitan network topology
$V$	Set of QKD nodes
$E$	Set of QKD links
$h (s_{m}, d_{m})$	The $m$ th QKD service between $s_{m}$ and $d_{m}$
$H$	Set of QKD services of the network topology
$f (s_{m}, d_{m})$	Number of QKD nodes of $h (s_{m}, d_{m})$
$r_{(q_{C}, q_{S}, t_{n})}^{(s_{m}, d_{m})}$	QKDP updating request of $h (s_{m}, d_{m})$
$s_{m}$	Source QKD node of $h (s_{m}, d_{m})$
$d_{m}$	Destination QKD node of $h (s_{m}, d_{m})$
$t_{m, n}$	Arrival time of the $n$ th QKDP updating request of $h (s_{m}, d_{m})$
$q_{m, n}^{C}$	Proportion of key rate requirements of the $n$ th QKDP updating request of $h (s_{m}, d_{m})$ (0%–100%)
$q_{m, n}^{S}$	Proportion of security level requirements of the $n$ th QKDP updating request of $h (s_{m}, d_{m})$ (0%–100%)
$q_{m, n}^{T}$	Proportion of cache time requirements of the $n$ th QKDP updating request of $h (s_{m}, d_{m})$ (0%–100%)
$M_{m, k}^{C}$	Score of the key rate demand for the $n$ th QKDP updating request of $h (s_{m}, d_{m})$
$M_{m, k}^{S}$	Score of the security demand for the $n$ th QKDP updating request of $h (s_{m}, d_{m})$
$M_{m, n, k}^{F, C, S}$	Final score of the $k$ th protocol for the $n$ th QKDP updating request of $h (s_{m}, d_{m})$ considering the key rate and security level
$M_{m, n, k}^{T}$	Final score of the cache time of the $k$ th protocol
$M_{m, n, k}^{F, C, S, T}$	Final score of the $k$ th protocol for the $n$ th QKDP updating request of $h (s_{m}, d_{m})$ considering the key rate, security level, and cache time
$R_{m}$	Set of QKDP updating requests of $h (s_{m}, d_{m})$ during a period of time $T_{m}$
$T_{m}$	The total duration of $h (s_{m}, d_{m})$
$T_{k}^{b e g i n}$	Cache start time of the $k$ th protocol
$T_{s}$	Maximum cache time of the key cache area for each protocol
$τ_{u n i t}^{i n i}$	Initialization time unit of a random QKDP
$τ_{m, n}^{i n i}$	Initialization time of the $n$ th QKDP of $h (s_{m}, d_{m})$
$τ_{m, n}^{d u r}$	Duration of the $n$ th QKDP of $h (s_{m}, d_{m})$
$W_{p}$	The weight of the initialization time of the selected protocol $p$
$k_{m, n}$	The ranking of the selected protocol in the applicable protocol after the $n$ th QKDP updating request of $h (s_{m}, d_{m})$
$O_{m, n, k}$	The overall interruption probability of the $k$ th QKDP
$F_{m, j, k}$	Boolean value, is one if the $k$ th protocol is selected in the $j$ th QKDP updating request and the $j$ th QKDP updating request is interrupted
$B_{m, j, k}$	Boolean value, is one if the $k$ th protocol is selected in the $j$ th QKDP updating request and the $(j + 1)$ th QKDP updating request is interrupted
$N_{m, n - 1, k}$	Times the $k$ th protocol is selected in the first ( $n - 1$ ) QKDP updating requests of $h (s_{m}, d_{m})$
$N_{r}$	Total number of QKDP updating requests
$N_{s}$	Total number of QKD services
$D$	Number of elements in the set $P_{sd}$
$P_{sd}$	Set of optional QKDPs for a QKD service
$P_{2}$	Set of two-party protocols
$P_{3}$	Set of three-party protocols

	BB84	COW	GG02	BBM92	MDI	TF
Distance	10.6 km	14.2 km	19.92 km	16.9 km	42 km	511 km
Key rate	2.58 Mbps [26]	1956 bps [11]	10 kbps [30]	9074 bps [10]	38.8 bps [9]	3.37 bps [12]

Notations	Definitions
$G (V, E)$	Quantum metropolitan network topology
$V$	Set of QKD nodes
$E$	Set of QKD links
$h (s_{m}, d_{m})$	The $m$ th QKD service between $s_{m}$ and $d_{m}$
$H$	Set of QKD services of the network topology
$f (s_{m}, d_{m})$	Number of QKD nodes of $h (s_{m}, d_{m})$
$r_{(q_{C}, q_{S}, t_{n})}^{(s_{m}, d_{m})}$	QKDP updating request of $h (s_{m}, d_{m})$
$s_{m}$	Source QKD node of $h (s_{m}, d_{m})$
$d_{m}$	Destination QKD node of $h (s_{m}, d_{m})$
$t_{m, n}$	Arrival time of the $n$ th QKDP updating request of $h (s_{m}, d_{m})$
$q_{m, n}^{C}$	Proportion of key rate requirements of the $n$ th QKDP updating request of $h (s_{m}, d_{m})$ (0%–100%)
$q_{m, n}^{S}$	Proportion of security level requirements of the $n$ th QKDP updating request of $h (s_{m}, d_{m})$ (0%–100%)
$q_{m, n}^{T}$	Proportion of cache time requirements of the $n$ th QKDP updating request of $h (s_{m}, d_{m})$ (0%–100%)
$M_{m, k}^{C}$	Score of the key rate demand for the $n$ th QKDP updating request of $h (s_{m}, d_{m})$
$M_{m, k}^{S}$	Score of the security demand for the $n$ th QKDP updating request of $h (s_{m}, d_{m})$
$M_{m, n, k}^{F, C, S}$	Final score of the $k$ th protocol for the $n$ th QKDP updating request of $h (s_{m}, d_{m})$ considering the key rate and security level
$M_{m, n, k}^{T}$	Final score of the cache time of the $k$ th protocol
$M_{m, n, k}^{F, C, S, T}$	Final score of the $k$ th protocol for the $n$ th QKDP updating request of $h (s_{m}, d_{m})$ considering the key rate, security level, and cache time
$R_{m}$	Set of QKDP updating requests of $h (s_{m}, d_{m})$ during a period of time $T_{m}$
$T_{m}$	The total duration of $h (s_{m}, d_{m})$
$T_{k}^{b e g i n}$	Cache start time of the $k$ th protocol
$T_{s}$	Maximum cache time of the key cache area for each protocol
$τ_{u n i t}^{i n i}$	Initialization time unit of a random QKDP
$τ_{m, n}^{i n i}$	Initialization time of the $n$ th QKDP of $h (s_{m}, d_{m})$
$τ_{m, n}^{d u r}$	Duration of the $n$ th QKDP of $h (s_{m}, d_{m})$
$W_{p}$	The weight of the initialization time of the selected protocol $p$
$k_{m, n}$	The ranking of the selected protocol in the applicable protocol after the $n$ th QKDP updating request of $h (s_{m}, d_{m})$
$O_{m, n, k}$	The overall interruption probability of the $k$ th QKDP
$F_{m, j, k}$	Boolean value, is one if the $k$ th protocol is selected in the $j$ th QKDP updating request and the $j$ th QKDP updating request is interrupted
$B_{m, j, k}$	Boolean value, is one if the $k$ th protocol is selected in the $j$ th QKDP updating request and the $(j + 1)$ th QKDP updating request is interrupted
$N_{m, n - 1, k}$	Times the $k$ th protocol is selected in the first ( $n - 1$ ) QKDP updating requests of $h (s_{m}, d_{m})$
$N_{r}$	Total number of QKDP updating requests
$N_{s}$	Total number of QKD services
$D$	Number of elements in the set $P_{sd}$
$P_{sd}$	Set of optional QKDPs for a QKD service
$P_{2}$	Set of two-party protocols
$P_{3}$	Set of three-party protocols

	BB84	COW	GG02	BBM92	MDI	TF
Distance	10.6 km	14.2 km	19.92 km	16.9 km	42 km	511 km
Key rate	2.58 Mbps [26]	1956 bps [11]	10 kbps [30]	9074 bps [10]	38.8 bps [9]	3.37 bps [12]

Abstract

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Tables (4)

Equations (10)

Journal of Optical Communications and Networking