Dynamic-threshold-based pre-relaying for enhanced key allocation in quantum-secured networks

Catalina Stan; Dominique Verchere; Juan José Vegas Olmos; Idelfonso Tafur Monroy; Simon Rommel

doi:10.1364/JOCN.544857

Journal of Optical Communications and Networking
Vol. 17,
Issue 3,
pp. 233-248
(2025)
•https://doi.org/10.1364/JOCN.544857

Dynamic-threshold-based pre-relaying for enhanced key allocation in quantum-secured networks

Catalina Stan, Dominique Verchere, Juan José Vegas Olmos, Idelfonso Tafur Monroy, and Simon Rommel

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Catalina Stan, Dominique Verchere, Juan José Vegas Olmos, Idelfonso Tafur Monroy, and Simon Rommel, "Dynamic-threshold-based pre-relaying for enhanced key allocation in quantum-secured networks," J. Opt. Commun. Netw. 17, 233-248 (2025)

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Abstract

Quantum key distribution (QKD) is experiencing a rapid increase of interest due to its security advantages in the face of quantum computers. However, typical QKD deployments are point-to-point and limited in terms of distance, which significantly restricts their utilization for end-user applications. To overcome these restrictions, trusted relays are adopted as intermediate nodes to allow the transition to QKD networks (QKDNs), where one of the hallmarks is the key management system. In this work, we investigate different key allocation strategies as a method to enhance the performance of key management systems in QKDN from the perspective of key allocation success rate and key delivery delay. We first describe an upgrade model from classical to QKDN at three distinct network layers—quantum, key management, and service. Then, we propose a novel, to our knowledge, key allocation strategy leveraging the benefits of key storage and relaying as a solution to improve the QKDN performance. To achieve this, our method makes use of end-to-end virtual quantum key pools (VQKPs) implemented between non-adjacent nodes requesting key material. We introduce static and dynamic upper and lower threshold limits at the VQKP level, with the dynamic thresholds adapted according to application demand, to control the key distribution in the network and fill the pools ahead of end-user requests. We demonstrate through simulations that the introduction of thresholds achieves performance enhancement and explain the trade-off between the key allocation success rate and key delivery delay evaluation metrics in comparison with different on-demand key allocation strategies.

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Idelfonso Tafur Monroy	https://orcid.org/0000-0002-2935-7682
Simon Rommel	https://orcid.org/0000-0001-8279-8180

Priority	Encryption	Key Size [bit]	Key Update
1	OTP	$\geq$ Plaintext	Per plaintext
2	AES	256	Data threshold
3	AES	256	Time threshold

Notation	Description
$k_{s, d}^{i, t} / r_{s, d}^{i, t}$	Application/relay request size with index $i$ between nodes $s$ and $d$ at time $t$
$a$	Authentication tag size
$n, n + 1$	Index of node pair $n$ and $n + 1$
$l^{c}$	(Static) classical link length
$T R N$	(Static) number of trusted relay nodes
${S K R}^{w}$	(Static) secret key rate
KBGD	(Static) key block generation duration
${Q K P}^{w, t}$	(Dynamic) residual quantum key pool
$L K C [S / R]^{w, t}$	(Dynamic) link key consumption size/rate
$N K C [S / R]^{w, t}$	(Dynamic) node key consumption size/rate
${K D D}_{k_{s, d}^{i, t}}$	Key delivery delay for request $k_{s, d}^{i, t}$
$R_{k_{s, d}^{i, t}}$	Relay delay for request $k_{s, d}^{i, t}$
$LT$ / $UT$	VQKP lower/upper threshold limit
$R$	VQKP residual key level
$prk$	Pre-relay key size
$s_{l}$ / $s_{u}$	Lower/upper threshold % in ST-VQKP
$\bar{P_{s, d}^{t}}$	Average predicted application key consumption between nodes $s$ and $d$ at time $t$
$w$	Prediction weight in DT-VQKP
$f$	Threshold mapping factor in DT-VQKP

	$D_{drop}$	Number of TRNs			Span [km]			SKR [kbit/s]			KBGD [s]			KBGS [Mbit]
QKD Protocol	[km]	Avg.	Min.	Max.	Avg.	Min.	Max.	Avg.	Min.	Max.	Avg.	Min.	Max.	Avg.	Min.	Max.
BB84 decoy 1550 nm	119	7.8	1	20	106.1	75	116.7	4.3	1.4	25.8	229.5	60	287	0.8	0.4	1.5
COW 1550 nm	110	8.2	1	21	103.2	75	109.1	5.7	2.7	34.3	252.7	60	293	1.1	0.8	2.1
BB84 decoy 1310 nm	99	9.5	1	24	89.5	75	97.5	3.8	1.3	10.2	204.3	60	285	0.5	0.4	0.7
COW 1310 nm	91	10.2	1	26	84.4	75	90.0	6.0	3.0	12.7	200.0	60	285	1.0	0.8	1.1

Dataset (DS)	Total	$P = 1$ [%]	$P = 2$ [%]	$P = 3$ [%]
DS1	36,839	10.3	61.0	28.7
DS2	36,173	9.8	60.1	30.1
DS3	36,427	9.8	60.4	29.8

Parameter Name	Value
Minimum KBGD $d_{min}$	60 s
Maximum KBGD $d_{max}$	300 s
Application queueing delay $q$	0.3 ms
Maximum QKP storage capacity ${Q K P}_{max}$	10 Gb
Maximum VQKP storage capacity ${V Q K P}_{max}$	1 Gb
TRN delay $T_{d}$	20 ms
QKD node delay $C_{d}$	40 ms
Key request-response delay $c_{1}$	100 ms
Key notification delay $c_{2}$	10 ms
Fiber refractive index $n_{f}$	1.45
Speed of light $c$	$3 \cdot 10^{8}$ m/s

Dynamic-threshold-based pre-relaying for enhanced key allocation in quantum-secured networks

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Journal of Optical Communications and Networking