Post-Quantum Link-based Ring Signature Model and Artificial Bee Colony (ABC) Algorithm for Effective Data Management in IoT-based Smart Cities

3.1 Data details and preprocessing

The Pune Smart City Dataset is part of the data collected by the Pune Smart City Development Corporation Limited (PSCDCL) and IISC, Bangalore, for smart city projects. It can be used to estimate the Air Quality Index (AQI) and predict AQI in various places, like bus stops and IT centres, based on local data such as the railway station. Analysing AQI with factors like temperature, sound, light, and weather can help improve living conditions in Pune. Data preprocessing is done by addressing missing values using the KNN technique, where the missing values ( $x_i$ ) are filled in based on nearby data points. The distance between $d(x_i,x_k)$ instances and the imputed $\widehat{x_{\mathit{ij}}}$ values is calculated using specific Equations (1) and (2).

$x_{\mathit{il}}$ and $x_{\mathit{kl}}$ denote the values of certain features I for different instances $x_i$ and $x_k$ , respectively, and $x_{\mathit{kj}}$ missing values are filled in by using similar instances $x_k$ , based on their k-nearest neighbours $j$ features $N\left(i\right).$ Min-max normalisation is a technique for adjusting dataset values to fit within a specific range, typically between 0 and 1. $x^{\prime }$ denotes the normalised data in Equation (3), and “min” and “max” refer to the respective minimum and maximum values of the feature.

3.2 Post-quantum linkable ring signature scheme

PQLRS schemes utilising hash functions improve performance, storage, and bandwidth for privacy-centric blockchain applications, particularly in high-frequency transaction contexts. A post-quantum pluggable ring signature scheme based on hash functions.

3.2.1 Initialisation phase

The initialisation phase includes two key steps: key generation and ring generation. The security parameter λ and the establishment of two hash functions.

Definition of knowledge signatures: ${\mathit{SOK}}_m\left(1^{\lambda }\right)⟶{\mathit{pp}}_s$

The pair generation where users create their own key pairs $({\mathit{pk}}_i,{\mathit{sk}}_i)$ using the XMSS post-quantum security scheme. Here, the public keys are denoted as $({\mathit{pk}}_i$ ), and the private keys are denoted as ( ${\mathit{sk}}_i$ ), which are stored in the users' devices. The network includes N participants. Were a user initiates a transaction that selects a ring signature group, which is denoted as S = $\{{\mathit{pk}}_1,{\mathit{pk}}_2,\dots ,{\mathit{pk}}_N\}$ , that includes their own ( $p_k$ ) and other users maintain the public keys of $N-1$ . Followed by that a ring signature is generated mainly to enhance security against forgery. In the ring signature, the corresponding public keys are properly validated to avoid such malfunctions among the IoT devices. The key generation procedure is detailly in Algorithm 1.

3.2.2 Signature creation phase

In this process, the user selects the signer itself, which helps to create an $R$ ring. Each signer consists of its public key ( ${\mathit{pk}}_i$ ), which constructs a Merkle tree, with a root hash that serves as an entry point for authentication paths $\left(P\right)$ derived from each signer’s index $\left(j\right)$ , and private key. Each signer generates a ring signature for the transaction hash using their private key $\left(R\right)$ , which includes all public keys in the ring while identifying a unique initiator. The complete signature process involves generating the Merkle tree and its authentication path, forming a zero-knowledge signature $\mathit{Sok}{\sigma }_s$ , and combining it with a signature label $T$ , as detailed in Algorithm 2.

3.2.3 Signature verification phase

In a blockchain network, each node validates a signature's authenticity using transaction data and the public key from a signature ring. A hash function ensures the signature is legitimate and that the transaction remains unchanged. The process involves creating a Merkle tree and verifying the signature as a zero-knowledge proof stemming from a verified secret key ${\mathit{sk}}_j$ , which is part of the corresponding public key ring $R$ . Based on specified parameters such as event ID, singular signature, message, and ring public key $R,$ detailed in Algorithm 3, the verification will return 1 for a valid signature or 0 if invalid.

Each transaction creates a unique ring signature that is stored with the transaction data on the blockchain.

3.3 Artificial Bee Colony (ABC) algorithm

The ABC algorithm is an optimisation method that uses swarm intelligence, where agents (represented as bees) work together and with their environment. Each bee aims to find the best food source, symbolising potential solutions. There are three types of bees: scout, employed, and observation bees. Employed bees start by randomly finding a food source and then search for better options nearby. The ABC algorithm is a nature-inspired method based on swarm intelligence mimicking honey bee foraging. It uses food sources as potential solutions, with fitness evaluated by nectar amount. Bees include employed bees adjusting local solutions, onlooker bees exploring based on fitness, and scout bees maintaining diversity. Through neighbor generation and greedy selection, solutions are enhanced. Deb's rules prioritize feasible solutions in constrained optimization. They only move if a new source is better than their current one. Observant bees learn from employed bees and choose new food sources based on their findings. If a food source is rich or of high quality, observation bees are more likely to select it. They will pick one food source before looking for another nearby. The number of iterations is fixed, so the recruited bees for a chosen food source become scout bees to explore new sources if a better one isn't found. Groups of bees engage in both explorative and exploitative activities. Exploratory behaviour involves searching for new food sources to avoid settling for a lesser option, while exploitative behaviour focuses on finding better options near the current source. Q-learning to enhance problem-solving solutions by optimising exploitative behaviour, given that the ABC algorithm has constraints in exploitation while exhibiting robust exploration capabilities. The process starts with the ABC algorithm locating food supplies and generating them randomly in Equation (4), followed by assigning worker bees to these sources, with the Q-table starting at zero.

During the employed bee phase, the focus is on identifying the neighbouring food source ( $v_j^t$ ) relative to the current food ( $x_j^t$ ) source, which is measured using Equation (5). The paragraph does not specify exact lower ( $x_j^{\mathit{min}})$ or upper limits ( $x_j^{\mathit{max}})$ for the optimisation parameter $j^{\mathit{th}}$ .

From Equation (5), the terms, $x_{i,j}^t$ representation $j^{\mathit{th}}$ of optimisation parameters and indices ${\overline{v_i}}^t$ , and k. When a newly discovered food source ${\overline{v_i}}^t$ exhibits a higher fitness value than the current one $x_i^t\mathit{Fit}\left({\overline{v_i}}^t\right)>\left({\overline{x_i}}^t\right)$ , the associated current source is discarded in favour of the new one. A reward-penalty scheme outlined in Equation (5) is employed to adjust the Q-table based on fitness evaluations: rewarding new food sources that outperform the current one while penalising the others. Network updates to the Q-values occur with each recruited bee confirmation, specifically driven by an allowed number of Emp. If a new eligible food source is discovered that exhibits improved outcomes in Equation (6), trends related to the Q-values will similarly adjust.

The $v_{i,j}^t$ optimisation process in the foraging algorithm uses food sources represented by $,\varnothing$ in the range of [-1,1] and $x_{\mathit{RFS},k}^t$ . Observer bees optimise specific dimensions by Equation (6), assigning varying weight values to improve exploitation, while also adjusting Q-values associated with rewards and penalties. If a scout bee does not find a better food source after multiple attempts, it will abandon the current source and begin a random search for another one.

4.1 Signature time calculation

The FHPCC model has a signing time of 0.17 seconds; the ELDSE scheme is faster at 0.06 seconds with limited post-quantum defence. PQBFR requires 2.2 seconds due to its complex post-quantum formulation. The PQRAEI model, signing in 1.7 seconds, improvement over PQBFR while enhancing post-quantum security. It captures a 22.7% reduction in signing time relative to PQBFR in Figure 2.

Figure 2. Signature time calculation.

This figure compares the signature generation time of the proposed PQRAEI model with existing post-quantum and hybrid cryptographic schemes. The comparison highlights the computational cost associated with signing operations under different security models. The red bar represents the FHPCC scheme, the green bar corresponds to ELDSE, the orange bar denotes PQBFR, and the blue bar represents the proposed PQRAEI model. Lower bar heights indicate faster signature generation time, demonstrating the efficiency of the proposed approach.

4.2 Signature verification calculation

The FHPCC scheme moderate verification time of 110 ms, whereas the ELDSE model performs better at 65 ms. The PQBFR model shows a longer verification time of 2500 ms due to its complex post-quantum structure. The PQRAEI model achieves a verification time of 1 ms, showing a 99.96% improvement over PQBFR. This efficiency arises from its optimised verification process that combines a PQLRS scheme with ABC-Q learning, as shown in Figure 3.

Figure 3. Signature verification calculation.

This figure illustrates the signature verification time required by different cryptographic schemes, emphasizing the efficiency of the proposed PQRAEI framework during the verification phase. The red bar corresponds to FHPCC, the green bar denotes ELDSE, the orange bar represents PQBFR, and the blue bar indicates the proposed PQRAEI model. The reduced height of the blue bar reflects the optimized verification process achieved by the post-quantum link-based ring signature mechanism.

4.3 PSNR calculation

PSNR (Peak Signal-to-Noise Ratio) measures image reconstruction quality by comparing compressed images to the original. The FHPCC model achieves a PSNR of 25 dB, while ELDSE improves it to 28 dB, and PQBFR reaches 26 dB. The PQRAEI model has the highest PSNR at 29 dB in Figure 4 with lower prediction errors than the others. The use of Q-learning with the ABC algorithm and a PQLRS-based blockchain framework ensures optimised performance and data integrity.

Figure 4. PSNR calculation.

This figure presents a comparison of the Peak Signal-to-Noise Ratio (PSNR) among different cryptographic models to evaluate data reconstruction quality and integrity in IoT-based smart city environments. The red bar represents FHPCC, the green bar corresponds to ELDSE, the orange bar denotes PQBFR, and the blue bar represents the proposed PQRAEI model. Higher PSNR values indicate improved signal reconstruction quality and enhanced data integrity.

4.4 Latency calculation

Latency is the time between a process's start and finish in systems or devices, showing how quickly data moves between points. The FHPCC model has a greatest latency increase from approximately 1 ms to nearly 20 ms. PQBFR managed latency between 1 ms and 18 ms, while ELDSE had moderate latency fetching between 1 ms and 17 ms due to better processing protocols. The lowest latency, peaking at 16 ms, achieves roughly 20% lower latency than FHPCC and better performance against PQBFR (12% lower) and ELDSE (8% lower) in Figure 5.

Figure 5. Latency calculation.

This figure shows the end-to-end latency comparison of different cryptographic and data-processing models, reflecting system responsiveness within smart city IoT networks. The red curve represents FHPCC, the green curve corresponds to PQBFR, and the blue curve denotes the proposed PQRAEI model. Lower latency values indicate reduced communication delay and processing overhead, highlighting the improved performance of the proposed framework.

4.5 Throughput calculation

Throughput is the data rate over a network or processed by a system in a specific time, typically one second. It is measured in bits, packets, or transactions per second. The analysis identifies that PQRAEI achieves high throughput at 100 units, FHPCC (by 5%), PQBFR (by 25%), and ELDSE (by over 40%). This improvement is attributed to its Q-learning-enhanced ABC optimisation and a PQLRS post-quantum blockchain layer. The FHPCC reached around 95 units, while ELDSE and PQBFR reached only 70 and 80 units in managing air quality data in Figure 6.

Figure 6. Throughput calculation.

This figure compares the throughput performance of different cryptographic models, demonstrating their ability to efficiently process and transmit IoT data under smart city conditions. The blue bar represents FHPCC, the orange bar denotes PQBFR, and the green bar corresponds to the proposed PQRAEI model. Higher throughput values indicate improved data transmission efficiency and scalability of the system.