Dynamic Sharding and Monte Carlo for Post-Quantum Blockchain Resilience

Abstract

Scalability and security restrictions are posing new challenges for blockchain networks, especially in the face of Distributed Denial-of-Service (DDoS) attacks and upcoming quantum threats. Previous research also found that post-quantum blockchains, despite their improved cryptographic algorithms, are still vulnerable to DDoS attacks, emphasizing the need for more resilient architectural solutions. This research studies the use of dynamic sharding, an innovative approach for post-quantum blockchains that allows for adaptive division of the network into shards based on workload and network conditions. Unlike static sharding, dynamic sharding optimizes resource allocation in real time, increasing transaction throughput and minimizing DDoS-induced disruptions. We provide a detailed study using Monte Carlo simulations to examine transaction success rates, resource consumption, and fault tolerance for both dynamic sharding-based and non-sharded post-quantum blockchains under simulated DDoS attack scenarios. The findings show that dynamic sharding leads to higher transaction success rates and more efficient resource use than non-sharded infrastructures, even in high-intensity attack scenarios. Furthermore, the combination of dynamic sharding and the Falcon post-quantum signature technique creates a layered strategy that combines cryptographic robustness, scalability, and resilience. This paper provides light on the potential of adaptive blockchain designs to address major scalability and security issues, opening the path for quantum-resilient systems.

1. Introduction

Blockchain [1] technology has emerged as an indispensable instrument for facilitating safe, decentralized transactions in industries such as cryptocurrency, supply chain management, and the Internet of Things (IoTs). Blockchain’s capacity to provide immutability, transparency, and security in unsecured contexts has established it as an essential technology for modern digital systems. As the number of applications increases, the necessity for secure, scalable, and resilient blockchain platforms becomes more obvious. The fast growth of quantum computing has presented substantial difficulties to traditional cryptography systems, compromising the integrity of fundamental security protocols widely utilized in blockchain technology. Shor’s approach enables efficient factorization of big integers, destroying widely adopted schemes like RSA and ECDSA [1,2]. Post-quantum cryptography, such as Falcon, offers strong resistance to quantum attacks [3,4], making it a crucial answer to combat this danger.

DDoS attacks continue to pose a substantial threat to blockchain ecosystems, attempting to overwhelm network resources and interrupt availability [5,6]. These attacks can cause increased latency, decreased transaction throughput, and even total network failure [7,8]. Sharding, a technology that divides a blockchain into smaller, independent units known as shards, is a promising approach for improving scalability and mitigating the impact of such attacks [9,10]. This method improves network resilience and efficiency by dividing computational and storage workloads across several shards.

According to studies, post-quantum blockchains, despite their quantum-resistant cryptographic characteristics, are still vulnerable to DDoS attacks [11]. A previous study has demonstrated that these vulnerabilities can have a considerable impact on transaction success rates and network stability under conditions of attack [11]. Building on these findings, this paper looks into the use of dynamic sharding as a possible approach to mitigate these vulnerabilities and improve the performance of post-quantum blockchains. Dynamic sharding tries to reduce the impact of DDoS attacks by allowing for adaptive resource allocation and optimized transaction throughput.

While post-quantum cryptography and blockchain sharding have advanced significantly on their own, their combined application for mitigating network-based threats, such as DDoS, is still mostly unexplored. This study combines Falcon, a post-quantum cryptography system, with dynamic sharding technologies to give strong scalability and tolerance to such attacks.

The remaining sections of this work are organized as follows: Section 2 summarizes relevant work on sharding and post-quantum cryptography. Section 3 describes the suggested framework and Monte Carlo simulation methodology. Section 4 details the experimental setup and results, which compare the performance of sharded and non-sharded blockchains during DDoS attacks. Finally, Section 5 summarizes this article and suggests areas for future investigation.

2. Related Work

Blockchain technology has been widely adopted in areas such as banking, supply chain management, and healthcare, offering safe, decentralized solutions for a variety of applications. However, as blockchain networks expand, scalability, performance, and security issues become increasingly prevalent. Latency, transaction throughput, and attack resilience, notably Distributed Denial-of-Service (DDoS) attacks, are key challenges that must be addressed [12]. Among the offered alternatives, sharding has emerged as a highly promising method for scaling blockchain systems by enabling parallel transaction processing and greatly increasing system throughput [13]. At the same time, the emergence of quantum computing has created significant threats to traditional cryptographic systems, particularly those based on the Elliptic Curve Digital Signature Algorithm (ECDSA), forcing research into post-quantum cryptography solutions [14].

Blockchain networks are particularly vulnerable to Distributed Denial-of-Service (DDoS) attacks, which try to interrupt transaction processing, overload network resources, and reduce system availability [15]. Unlike traditional centralized systems, where firewalls and intrusion detection systems can minimize these dangers, blockchain networks must protect against DDoS attacks while maintaining decentralization [16].

Several forms of DDoS attacks may affect blockchain networks. Volumetric attacks flood the network with transactions, draining the transaction queue and increasing validation delays [17]. Protocol-based attacks, such as Eclipse attacks, aim to exploit vulnerabilities in the consensus system by isolating a node from the main network and forcing it to engage only with compromised peers. Resource depletion attacks take use of computational limitations, exhausting CPU, memory, and storage resources, making it harder for authorized users to communicate with the blockchain [18]. Finally, Sybil-based DDoS attacks use several fake identities to alter voting-based consensus mechanisms, which poses a serious risk to Proof-of-Stake (PoS) blockchains [19].

Figure 1 illustrates the many forms of Distributed Denial-of-Service (DDoS) attacks that target blockchain systems.

This includes the following:

• Volumetric assaults overburden transaction queues, increasing network slowness;
• Protocol-based attacks, such as Sybil and Eclipse attacks, threaten consensus integrity;
• Consumption of resources attacks, which target CPUs, memory, or disks.

These vectors each represent distinct levels of the blockchain infrastructure, demonstrating the need for adaptive architecture solutions like dynamic sharding to maintain performance and robustness in post-quantum scenarios.

DDoS attacks have a serious impact on blockchain performance, causing greater transaction latency, higher fees, network congestion, and decreased availability [20]. Addressing these vulnerabilities needs a combination of cryptographic, protocol-level, and architectural solutions. While authentication-based protections are widely employed in standard networks to prevent Denial-of-Service attacks, they do not provide adequate protection in blockchain systems. Public blockchains are intended to be open and permissionless, allowing any member to publish transactions without previous verification. Unlike centralized networks, where access control lists and firewall rules can limit traffic, blockchain transactions must be authenticated using consensus processes rather than identity verification [5,21].

Furthermore, Sybil attacks render authentication-based systems unreliable. To avoid authentication constraints, an attacker can construct several fake identities, flooding the network with malicious transactions that appear to be from normal users [22]. Furthermore, economic strategies such as imposing transaction costs to discourage spam may not eliminate DDoS concerns, as attackers with sufficient financial resources can still congest the network, particularly in high-fee systems like Ethereum [23].

Given these restrictions, authentication alone cannot successfully protect against large-scale DDoS attacks in decentralized systems. To fight attacks, blockchain networks must employ adaptive architectural solutions that dynamically allocate resources and optimize transaction throughput.

Sharding, inspired by distributed database ideas [24], divides blockchain networks into smaller, independent sub-networks, or shards, each capable of performing transactions concurrently. This minimizes the computational strain on each node while improving overall performance. While static sharding techniques, such as those used in Ethereum 2.0, enable scalability by dividing network transactions into preset shards, they are not adaptable to changing workloads or security risks. A significant disadvantage of static sharding is its susceptibility to targeted DDoS attacks, in which adversaries can concentrate their efforts on overloading specific shards, resulting in localized failures and decreased system efficiency [25].

Figure 2 shows the traditional sharding structure, in which a central Beacon Chain controls the allocation and synchronization of shards, each with independent validators and transaction pools. While this technique improves scalability, it is less adaptable to changing workloads and evolving security threats.

To address these concerns, hybrid sharding techniques have been developed, in which shards can be partially reconfigured depending on workload conditions. Hybrid models provide flexibility over purely static techniques, but they still suffer from synchronization delays and unequal resource allocation [26].

Dynamic sharding, on the other hand, offers real-time adaptability by dynamically redistributing transaction processing and validator assignments in response to network conditions and potential security concerns [25]. Unlike static sharding, dynamic models prevent adversaries from guessing which shard will validate a transaction, reducing targeted attacks while enhancing resource allocation and load balancing.

Early contributions, such as the OmniLedger suggested by Kokoris-Kogias et al. [27], have shown that sharded ledgers may scale successfully while remaining decentralized. Similarly, Ethereum 2.0 uses sharding to address scalability difficulties on the Ethereum blockchain [9]. Further improvements, such as the adaptive sharding algorithms developed by Zhang et al. [28], improve blockchain performance in dynamic network settings. These improvements illustrate the scalability benefits of sharding; nonetheless, its impact on security, particularly in adversarial environments like DDoS attacks, warrants additional examination.

Recent research has examined the inherent benefits of sharding in minimizing DDoS attacks. By dividing network traffic across several shards, sharding decreases the chance of a single point of failure, improving network resilience. Shi et al. [29] showed that sharding’s parallel processing architecture reduces the impact of volumetric DDoS attacks because a compromised shard does not interrupt the entire system. Similarly, Li et al. [30] demonstrated how sharding might separate destructive activities, decreasing potential impact. Han et al. [31] further explored these ideas by developing hybrid sharded blockchain systems, which combine sharding with advanced load-balancing algorithms to increase resistance to network-layer attacks. Building on this, Sousa et al. [22] proposed hierarchical sharding structures, which provide additional levels of resistance against DDoS attacks in large-scale blockchains.

Parallel to these advancements, the emergence of quantum computing has raised questions about the long-term viability of standard cryptography methods. Quantum algorithms like Shor’s algorithm [32] and Grover’s algorithm [33] have the potential to break RSA and ECDSA, the fundamental cryptographic systems that support most blockchain networks. To address these concerns, post-quantum cryptographic (PQC) approaches, such as lattice-based encryption, have been developed to protect blockchain networks against quantum-enabled adversaries [34]. Among these, the Falcon signature scheme is notable for its efficiency and lightweight architecture, making it ideal for resource-constrained contexts such as blockchains [35]. Bernstein et al. [36] and Buchmann et al. [37] conducted studies that improved the development of PQC algorithms, including Falcon and CRYSTALS-DILITHIUM, which are now candidates in the NIST post-quantum cryptography standardization effort [38].

While post-quantum cryptography deals with cryptographic weaknesses, incorporating these techniques into blockchain systems poses additional obstacles. Falcon, for example, provides reduced key sizes and faster verification times, making it a popular choice for blockchain applications [39]. However, its effectiveness in decentralized network environments and its interplay with architectural developments such as sharding remain unexplored. Chen et al. [40] studied Falcon’s integration with blockchain infrastructures, providing the framework for future research on post-quantum safe blockchain systems.

The selection of performance measures is an important part of evaluating blockchain resilience under different settings. The success of sharding-based security methods cannot be evaluated without establishing measurable metrics of both network stability and transaction efficiency.

This study uses the following critical performance metrics:

• Transaction success rate: this indicator measures the percentage of legitimate transactions that are successfully handled. A high transaction success rate implies resilience to congestion and DDoS attacks, whereas a low success rate reflects system inefficiencies and weaknesses [41];
• Transaction latency: this metric measures the time it takes for a transaction to be confirmed and is a direct indicator of blockchain scalability. Increased delay during attacks reveals inefficiencies in resource management and network congestion [42];
• Resource consumption (CPU, memory, and disk usage): these characteristics define the computational cost associated with various blockchain topologies. High CPU and memory consumption represent processing inefficiencies, but efficient resource allocation demonstrates the effectiveness of dynamic sharding in reducing attack-induced bottlenecks [43].

These measures together provide a comprehensive picture of blockchain resilience, demonstrating how well sharded and non-sharded post-quantum blockchains perform in simulated DDoS assault situations. This study guarantees a thorough examination of blockchain security and scalability by combining these metrics with Monte Carlo-based probabilistic modeling.

Monte Carlo simulations are increasingly being used by researchers to investigate the stochastic nature of blockchain activities. These methods have been shown to be successful in predicting network dynamics such as transaction delays, node failures, and attack patterns. Recent research [44] has shown that Monte Carlo techniques are useful for analyzing blockchain performance under a variety of situations, including variable transaction volumes and consensus procedures.

This work combines sharding and post-quantum cryptography to increase our understanding of blockchain robustness. This study provides useful insights into the architecture of next-generation blockchain systems by simulating realistic attack scenarios and measuring key performance parameters such as transaction success rates, resource consumption, and fault tolerance. These findings are likely to shape future research and the design of scalable and secure blockchain networks that can withstand both traditional and emergent threats.

Table 1. Research coverage matrix across key blockchain topics.

References	DDoS	Sharding	Post-Quantum Cryptography	Falcon	Quantum Threats	Monte Carlo Simulations	Scalability	Resilience
Ref. [12]	X							X
Ref. [13]		X					X
Ref. [14]			X		X
Ref. [24]		X
Ref. [27]		X					X
Ref. [9]		X					X
Ref. [28]		X					X
Ref. [29]	X	X						X
Ref. [30]	X	X						X
Ref. [31]	X	X						X
Ref. [32]	X	X						X
Ref. [33]		X						X
Ref. [34]			X		X
Ref. [35]					X
Ref. [36]			X	X
Ref. [37]			X	X
Ref. [38]			X
Ref. [39]			X
Ref. [40]			X
Ref. [41]			X
Ref. [42]			X	X
Ref. [44]			X	X		X

demonstrates that while the existing literature covers elements like DDoS, sharding, post-quantum cryptography, and resilience independently, there is an absence of holistic studies that integrate:

• Dynamic sharding allows for agility and effective resource utilization;
• Post-quantum cryptography (Falcon): to combat quantum threats;
• Monte Carlo simulations: used for stochastic simulation of attack scenarios.

This research gap supports the current work, which seeks to completely assess the combined impact of these technologies on blockchain performance and security under DDoS attacks. By bridging this gap, our research adds a new framework for furthering the design of next-generation blockchain systems that can address both traditional and emergent risks.

3. Methodology

3.1. Introduction

The growing usage of post-quantum cryptographic blockchains raises serious concerns regarding their resilience to classical security threats. While post-quantum encryption is specifically built for resistance to quantum-based attacks, current research suggests that these blockchains may still be vulnerable to classical attacks like Distributed Denial-of-Service (DDoS) attacks. This emphasizes the necessity to evaluate their performance under such conditions and investigate viable solutions like sharding to boost their resilience. This study examines the behavior of post-quantum blockchain topologies under DDoS attack scenarios. The designs being evaluated are a non-sharded blockchain, which processes all transactions through a single validation pool, and a sharded blockchain, which divides transactions among separate shards to minimize congestion and enhance scalability. Both architectures use the Falcon post-quantum cryptographic algorithm, which generates digital signatures that resist quantum decryption methods. The methodology is based around two essential features, and each includes a full integration of resource use analysis:

• The DDoS attack simulation and resource monitoring phase comprises simulating high-traffic DDoS attacks on both blockchain systems. The attacks are intended to stress the network by flooding it with transactions, and the system’s response is measured using metrics such transaction success rates, latency, and resource utilization (CPU, memory, and disk usage). This phase allows for a direct comparison of the performance of sharded and non-sharded systems under comparable situations;
• Monte Carlo simulations and resource monitoring model randomized attack severity and traffic patterns. Each iteration provides heterogeneity in congestion levels, transaction failures, and resource contention, allowing a probabilistic assessment of the durability of blockchain designs. Similarly, resource utilization measurements are collected during this phase to assess the efficiency of shard-based distribution in dealing with dynamic conditions.

This study’s goal is to determine if sharding reduces the vulnerabilities found in post-quantum blockchains when subjected to classical attack vectors. This study aims to contribute to a better understanding of the scalability and security concerns associated with post-quantum blockchains by comparing the performance of sharded and non-sharded systems.

3.2. Experimental Blockchain Architectures

Blockchain infrastructures are divided into two types depending on transaction processing methods: non-sharded and sharded architectures.

• The non-sharded blockchain processes all transactions collectively by a single validation pool, making it very vulnerable to network congestion and delays, especially during attacks;
• In contrast, the sharded blockchain design distributes transactions across several independent shards. Each shard maintains a subset of transactions, which reduces overall system congestion and increases scalability. This design ensures that the failure of a single shard does not compromise the overall integrity of the blockchain.

To improve the robustness of the sharded blockchain, an adaptive sharding technique is used. Unlike static sharding, which uses fixed divisions, adaptive sharding dynamically modifies shard allocations in response to transaction volumes and system congestion. The Algorithm 1 below describes the decision-making process for dynamically altering shard sizes in response to network circumstances.

Algorithm 1 Dynamic Shard Allocation Strategy based on Transaction Load and Network Congestion

Input: transaction_load, shard_threshold, max_shards, congestion_level Output: Updated shard allocations 1. Initialize shard_count ← Initial number of shards 2. Monitor real-time transaction_load and congestion_level 3. While system is running do:   4. If transaction_load > shard_threshold AND shard_count < max_shards then:     5. Increase shard_count by 1 (create new shard)     6. Redistribute active transactions among all shards   7. If congestion_level < predefined_safe_limit AND shard_count > 1 then:     8. Merge least active shards to optimize resource utilization   9. Update shard allocations and broadcast changes to nodes 10. Repeat process periodically

3.3. Comparative Analysis of Sharding Strategies

While sharding improves blockchain performance, sharding solutions range in efficiency, adaptability, and security. The

Table 2. Comparison of static, hybrid, and dynamic sharding.

Criteria	Static Sharding	Hybrid Sharding	Dynamic Sharding
Scalability	High	Moderate High	Very High
DDoS Resilience	Low	Moderate	High
Resource Allocation	Fixed	Partially Adaptive	Fully Adaptive
Synchronization Overhead	Low	Moderate	High
Implementation Complexity	Low	Moderate	High

examines three main techniques to sharding: static, hybrid, and dynamic.

• Static sharding (e.g., Ethereum 2.0) pre-allocates transactions to fixed shards, which improves scalability but exposing individual shards to targeted DDoS attacks;
• Hybrid sharding introduces limited adaptability, which reduces the risk of targeted attacks but still results in synchronization delays;
• Dynamic sharding constantly redistributes transactions and validator assignments, preventing adversaries from forecasting shard allocations. While dynamic sharding improves security and performance, it requires more computational resources.

This study focuses on dynamic sharding because it can reduce DDoS attacks while improving scalability and load balancing. The approach used for evaluating the durability of dynamic sharding vs. a non-sharded blockchain architecture under adversarial situations is described in the sections that follow.

3.4. DDoS Attack Simulation

To assess the durability of the previously described non-sharded and sharded blockchain architectures, Distributed Denial-of-Service (DDoS) attacks were used to simulate real-world stress circumstances. The primary purpose of this simulation is to analyze how high transaction volumes affect the scalability, resilience, and resource efficiency of these designs. The simulation method is organized as follows:

• Objective:

  ○

  Evaluate the transaction success rate, latency, and resource utilization (CPU, memory, disk usage) under stress. Also, compare the ability of the sharded blockchain to handle network congestion against the non-sharded blockchain;

• Configurations:

  ○

  Transaction volume: high-frequency transaction submissions to overwhelm the network;

  ○

  Attack duration: sustained over a specific time frame to evaluate long-term resilience;

  ○

  Distribution: transactions randomly assigned to nodes to replicate adversarial scenarios.

To evaluate the impact of large-scale adversarial stress on blockchain designs, a Distributed Denial-of-Service (DDoS) simulation was used. The Algorithm 2 describes the main process, in which large transaction loads are created and processed in a methodical manner under various setups.

Algorithm 2 Simulation of Transaction Performance and Resource Utilization During Attack

Input: attack_duration, transaction_rate, blockchain_mode Output: transaction success/failure rate, resource utilization 1. Initialize transaction_success ← 0 2. Initialize transaction_failure ← 0 3. Start attack_timer ← 0 4. While attack_timer < attack_duration do   5. Generate incoming_transactions ← transaction_rate per second   6. If blockchain_mode = “Sharded” then:     7. Distribute transactions across shards     8. Process transactions in parallel   Else:     9. Process all transactions in a single validation pool   10. For each transaction in incoming_transactions:     11. If network congestion or node overload then:       12.transaction_failure← transaction_failure + 1      Else:       13.transaction_success← transaction_success + 1       14. Record CPU, memory, and disk usage at this timestep       15. Increment attack_time       16. Compute success_rate ← transaction_success/(transaction_success+transaction_failure)    17. Return success_rate, resource_metrics

• Monitoring:

  ○

  Resource consumption metrics (CPU, memory, and disk usage) are recorded in real-time using ressource.py;

  ○

  These metrics are analyzed post-simulation to identify performance bottlenecks and compare the efficiency of the architectures;

• Rationale:

  ○

  While post-quantum cryptographic schemes like Falcon secure blockchains against quantum-based attacks, they remain vulnerable to traditional attack vectors such as DDoS;

  ○

  This simulation examines whether the sharding mechanism can mitigate these vulnerabilities and improve the scalability of post-quantum blockchains.

3.5. Monte Carlo Simulation

Following the DDoS simulation, which focused on high-stress, single-scenario testing, the Monte Carlo simulation gives a more comprehensive assessment of blockchain resistance by simulating a wide range of randomized attack scenarios. This probabilistic method incorporates the variety and uncertainty inherent in real-world network situations, providing greater insight into the behavior of both non-sharded and sharded blockchain architectures.

3.5.1. Key Objectives

• To evaluate how varying levels of network congestion, transaction volumes, and failure probabilities impact blockchain performance;
• To statistically analyze resource consumption patterns (CPU, memory, disk usage) under diverse adversarial conditions;
• To assess whether the sharded blockchain consistently outperforms the non-sharded architecture across multiple scenarios.

3.5.2. Simulation Design

• Randomized inputs: we have two scripts, one for a sharded architecture and another one for a non-sharded architecture. They generate thousands of iterations with different attack conditions. These include varying transaction frequencies, congestion levels, and shard-specific corruption probabilities;
• Metrics recorded: each iteration captures transaction success rates, latency, and resource consumption (CPU, memory, disk usage) to build a robust dataset for comparison;
• Iteration count: thousands of iterations are performed to ensure statistical reliability and identify consistent performance trends.

To correctly estimate blockchain performance under different network circumstances, we used a Monte Carlo simulation framework. The Algorithm 3 below describes the basic simulation process, in which transactions are dynamically handled under various congestion levels and hostile conditions.

Algorithm 3 Iterative Simulation of Transaction Success and Failure Rates under Variable Load

Input: total_iterations = 10000 Output: success rate and failure rate of transactions 1. Initialize transaction_success ← 0 2. Initialize transaction_failure ← 0 3. For i from 1 to total_iterations do:   4. Generate transaction_load ∈ [low_load, high_load]   5. If system_mode = “Sharded” then:     6. Assign transactions to shards dynamically     7. Execute transactions in parallel    Else:     8. Process all transactions in a single validation pool   9. For each transaction:     10. If network congestion or shard overload:      11. transaction_failure ←transaction_failure + 1     Else:      12. transaction_success← transaction_success + 1 13. Compute success_rate ← transaction_success/total_iterations 14. Compute failure_rate ← transaction_failure/total_iterations 15. Return success_rate, failure_rate

3.5.3. Monte Carlo Simulation Parameters

To assess the resilience and scalability of dynamic sharding in post-quantum blockchain systems under Distributed Denial-of-Service (DDoS) attacks, we employ Monte Carlo simulations to model various attack scenarios and system responses. To improve the analysis, we provide an in-depth examination of the Monte Carlo simulation parameters, providing reproducibility and clarity in the modeling of blockchain resilience. The simulation system uses a variety of probability distributions to precisely simulate real-world blockchain processes under various attack scenarios.

• Number of iterations:

The Monte Carlo simulation runs 10,000 iterations to reach statistical significance. This threshold was set using empirical convergence analysis, which ensures that more iterations have no substantial impact on the projected results.

b.

Input parameter distributions:

To effectively represent real-world blockchain dynamics, we employed the following probability distributions for important parameters:

• Transaction interarrival time: in blockchain systems, transaction arrivals follow an exponential distribution with a rate parameter of λ = 0.05 transactions per millisecond, reflecting the bursty character of transaction flows. This distribution is used to accurately model both normal operating conditions and periods of congestion caused by DDoS attacks;
• Attack intensity (DDoS load): represented by a Poisson distribution with requests per second mean values μ = {50, 100, 500}, simulating different attack magnitudes;
• Shard workload distribution: assumed to follow a normal distribution (μ = 500 transactions; σ = 100), dynamically adjusted through load-balancing mechanisms;
• Transaction size: modeled with a log-normal distribution (μ = 250 bytes; σ = 50), reflecting variations in transaction complexity;
• Validator processing time: defined using a gamma distribution (k = 2; θ = 30 ms), based on empirical benchmarks from blockchain validation processes.

c.

Experimental Conditions:

The simulation evaluates blockchain performance under multiple DDoS attack intensities and sharding configurations:

• Baseline scenario: normal transaction volume, no attack;
• Moderate attack: 100 malicious transactions per second targeting random shards;
• Severe attack: 500 malicious transactions per second directed at a specific shard;
• Adaptive sharding response: dynamic sharding activated with real-time workload redistribution.

Each scenario is analyzed based on transaction success rates, network latency, and resource utilization.

d.

Probabilistic Modeling:

A Markov Chain model is used to simulate state transitions between different network conditions:

• S₀ (normal operation): shards operate optimally with balanced workloads;
• S₁ (mild congestion): transaction queues increase due to sudden transaction surges;
• S₂ (severe congestion): validation delays grow significantly, affecting throughput;
• S₃ (shard overload): one or more shards become unresponsive due to excessive load.

Transition probabilities between these states are computed based on historical blockchain stress-test data, ensuring that the model reflects real-world system behavior.

e.

Transaction Failure Handling:

The simulation accounts for failed transactions due to the following:

• Network congestion: queue overflow probability p = 0.15 under attack conditions;
• Shard overload: probability p = 0.10 in worst-case scenarios where the shard exceeds its maximum capacity;
• Timeout failures: transactions exceeding 5 × the normal processing time are considered lost.

Failed transactions are either retried (if failure is transient) or discarded if congestion remains high.

f.

Validation and Real-World Comparison:

To ensure the accuracy and relevance of the simulation results, they are compared with the following:

• Empirical data from Ethereum 2.0 testnets, particularly sharding proposals;
• Historical DDoS attack logs on blockchain networks, providing real-world insights into attack patterns and mitigations;
• Theoretical models of blockchain scalability, validating the consistency of the Monte Carlo results with prior research.

The Monte Carlo simulation supplements DDoS testing by expanding the scope of this study to include dynamic and probabilistic scenarios. Together, these techniques provide a comprehensive understanding of how sharding affects the performance, scalability, and resilience of post-quantum blockchains in real-world scenarios.

3.6. Simulation Framework and Methodological Flow

To provide a comprehensive overview of the methods used in this study, the simulation framework is illustrated step by step in Figure 3. This framework outlines the interconnected stages needed in building blockchain infrastructures, simulating network conditions, and measuring performance indicators. Each level adds to an overall assessment of the scalability and robustness of sharded and non-sharded post-quantum blockchain designs.

By combining these algorithms and methodologies, we have set up a comprehensive experimental environment to evaluate the performance of both sharded and non-sharded blockchain systems under DDoS Attacks.

4. Results and Analysis

This section describes the results of a comparative study of sharded and non-sharded post-quantum blockchain designs. This study examines their performance in two experimental scenarios: simulated Distributed Denial-of-Service (DDoS) attacks and Monte Carlo simulations. Crucial performance indicators such as transaction latency, success rates, and resource utilization (CPU, memory, and disk usage) are used to evaluate the resilience, scalability, and overall efficiency of the two blockchain topologies.

4.1. DDoS Simulation Results

The evaluation of post-quantum blockchain infrastructures under Distributed Denial-of-Service (DDoS) attacks reveals important details about their performance and durability. This section compares the performance of sharded and non-sharded blockchain designs in terms of latency, transaction success rates, and resource utilization, based on simulated high-traffic scenarios.

(a)

Transaction Latency:

Figure 4 illustrates the comparison of transaction latency between the sharded and non-sharded blockchain architectures.

The average latency for the non-sharded blockchain was 2.115 s, but the sharded blockchain had a lower latency of 2.090 s, indicating better responsiveness in high-traffic conditions. The sharded infrastructure’s lower latency is due to dynamic transaction distribution over numerous shards, which effectively mitigates bottlenecks and balances demand during traffic surges. This parallel processing capability significantly improves the system’s efficiency when compared to the non-sharded architecture, in which all transactions are processed sequentially through a single validation pool, resulting in congestion under heavy loads.

Although the absolute reduction in latency (0.025 s) may look little, the cumulative impact on large-scale blockchain networks is significant. In high-frequency transaction situations, even minor savings in processing time per transaction can result in significant increases in total throughput and system scalability. This latency improvement is especially important for real-world blockchain applications like financial transactions or high-volume decentralized apps, where delays have a direct influence on usability and adoption.

Furthermore, both systems use Falcon post-quantum cryptography, which is a lattice-based cryptographic approach intended for quantum resistance. While Falcon provides security benefits, its computing overhead may affect processing time. The sharded architecture’s ability to distribute cryptographic verification over numerous shards emphasizes its scalability benefit, guaranteeing that security advancements do not degrade speed.

(b)

Transaction Success Rates:

Figure 5 illustrates the impact of Distributed Denial-of-Service (DDoS) attacks on transaction success rates for sharded and non-sharded post-quantum blockchain architectures.

The non-sharded blockchain showed a significant decrease in transaction success rates, with a large proportion of rejected transactions caused by network congestion during high-usage periods. This performance reduction is mostly due to the centralized processing design, which handles all transactions through a single validation pool, resulting in bottlenecks during hostile scenarios.

In comparison, the sharded blockchain continually had greater transaction success rates, even under the identical DDoS attack scenario. The sharded architecture’s ability to split transaction processing across numerous shards was successful in reducing congestion and guaranteeing steady performance. This highlights its inherent scalability and resiliency, especially when dealing with large transaction volumes.

Furthermore, the use of Falcon post-quantum cryptography adds computational complexity to transaction validation. However, the sharded design effectively controls this cryptographic strain by using parallel processing across shards, minimizing severe performance deterioration. The non-sharded blockchain, on the other hand, fails to deal with the combined impact of rising transaction loads and post-quantum cryptographic processes, resulting in a substantial decrease in successful transactions.

(c)

CPU Utilization:

Figure 6 presents the CPU utilization patterns for the sharded and non-sharded post-quantum blockchain architectures under Distributed Denial-of-Service (DDoS) attacks.

The non-sharded blockchain demonstrated frequent CPU spikes, with utilization levels approaching maximum capacity. These spikes indicate the strain created by running all transactions through a single centralized validation pool. The lack of dispersal in transaction handling causes severe computational delays during high-traffic scenarios, reducing the system’s capacity to manage resources efficiently in adversarial environments.

In contrast, the sharded blockchain showed a more stable and constant CPU consumption pattern, with utilization levels much lower than those seen in the non-sharded system. This stability reflects the sharded architecture’s computational efficiency, as transaction demands are distributed across numerous independent shards. The sharded design reduces the burden on individual nodes and avoids CPU saturation during periods of high transaction traffic by allowing for parallel processing.

In addition, the usage of Falcon post-quantum cryptography has a computational expense due to the complexity of its lattice-based operations. Despite this, the sharded blockchain effectively handles the cryptographic effort by exploiting the parallelism built into its architecture. Each shard processes a subset of transactions independently, ensuring that the computational needs of cryptographic verification do not overwhelm a single validation pool.

(d)

Memory Usage:

Figure 7 presents memory utilization patterns under Distributed Denial-of-Service (DDoS) attacks.

Figure 7 shows that memory use trends during Distributed Denial-of-Service (DDoS) attacks differ significantly between sharded and non-sharded post-quantum blockchain designs. The non-sharded blockchain displayed rapid and uneven memory use, frequently approaching saturation. These saturation occurrences caused transaction failures and increased delays as the centralized architecture struggled to allocate enough memory resources to handle the high transaction load induced by the attack. The inability to disperse memory demands over different nodes resulted in bottlenecks, which exacerbated performance loss.

In comparison, the sharded blockchain showed a more consistent and balanced memory use pattern, successfully managing memory resources across numerous shards. The sharded architecture protected individual nodes from experiencing memory overflow by distributing the transaction effort among separate shards. This architecture not only provided easy operations, but it also minimized the possibility of memory saturation, even under high-traffic conditions.

In addition, the incorporation of Falcon post-quantum cryptography, which requires resource-intensive cryptographic procedures, created new memory management difficulties. While the non-sharded blockchain struggled to meet these cryptographic demands, the sharded blockchain’s distributed architecture solved the problem by allowing shards to handle cryptographic operations independently. Parallelization improved memory use and increased the system’s overall efficiency.

(e)

Disk Usage:

Figure 8 illustrates the disk usage patterns observed during the Distributed Denial-of-Service (DDoS) attacks for both the sharded and non-sharded post-quantum blockchain architectures.

The results show that the sharded blockchain has consistently greater disk consumption than the non-sharded blockchain. This is an anticipated result since the sharded design necessitates more storage to support numerous independent shards, each with its own transaction history and validation data. While this raises total disk space needs, it does not create performance bottlenecks since disk write operations are uniformly divided among shards.

In contrast, the non-sharded blockchain, while demonstrating reduced total disk utilization, suffers from storage inefficiencies due to its centralized validation mechanism. The single validation pool struggles to handle heavy transaction loads, which might cause delays in writing data to disks during peak congestion periods.

This trade-off underlines the fundamental difference between the two architectures: while sharding adds storage expense, it also assures more effective resource allocation and prevents performance deterioration during peak traffic periods. The advantages of this technique are especially clear when considering the demanding cryptographic requirements of Falcon post-quantum encryption, which necessitate increased computing and storage resources. The sharded blockchain efficiently spreads these cryptographic activities over numerous shards, reducing localized demand on disk operations.

4.2. Monte Carlo Simulation Results

This section compares the performance of sharded and non-sharded post-quantum blockchain architectures under simulated Monte Carlo conditions. Thousands of randomized iterations were used to simulate different transaction volumes and network congestion levels. The research focuses on overall transaction success, resource consumption (CPU, memory, and disk usage), and latency trends.

(a)

Cumulative Transaction Success

Figure 9 and Figure 10 compare the cumulative successful transactions for non-sharded and sharded architectures over 10,000 iterations:

While Figure 5 displays system behavior under intense adversarial stress, Figure 9 takes a broader view, measuring blockchain transaction performance in the absence of direct attack using Monte Carlo simulations over 10,000 iterations. This simulation considers probabilistic fluctuations in network congestion, transaction arrival rates, and resource availability, providing insights into the blockchain’s long-term stability under various operational scenarios. Unlike the DDoS stress test in Figure 5, in which the non-sharded blockchain saw huge transaction failures, Figure 9 demonstrates that transactions continue to succeed over time when no external assault is occurring. However, some important observations emerge:

• The cumulative number of successful transactions remains below 750 after 10,000 iterations, indicating that even without direct attacks, the non-sharded architecture struggles with scalability;
• The linear growth pattern of successful transactions confirms that the non-sharded blockchain is highly constrained by its centralized validation process, making it less efficient in handling transaction load;
• Compared to the expected performance of the sharded blockchain, the non-sharded system exhibits a significantly lower transaction success rate, reinforcing its susceptibility to congestion over time.

Thus, the results from Figure 9 do not contradict Figure 5 but rather complement them:

• Figure 5 highlights the extreme vulnerability of the non-sharded blockchain to attacks, where transaction failures dominate;
• Figure 9 reveals that, even under normal conditions, the non-sharded blockchain remains inefficient, struggling to maintain high throughput due to its centralized structure.

These findings emphasize the fundamental scalability limitations of non-sharded blockchains and reinforce the necessity of dynamic sharding to enhance transaction success rates and network resilience.

In comparison, the second graph represents the total number of successful transactions on the sharded blockchain. Here, the lines are almost identical, demonstrating consistent performance throughout all simulation runs. The steep and consistent slope indicates the sharded blockchain’s ability to maintain a high transaction success rate despite fluctuations in traffic and network circumstances. This is due to the distributed nature of the sharded architecture, in which transactions are handled simultaneously across numerous shards. The reduced variability in simulation results underscores the sharded approach’s stability and efficiency in addressing high-throughput demands.

(b)

Advanced Cumulative Success Analysis:

The basic Cumulative Transaction Success measure reflects the overall ratio of successfully completed transactions, but it does not account for changes in network behavior over time. In contrast, the Advanced Cumulative Success Analysis provides a more detailed and dynamic evaluation by documenting how success rates change in response to shifting network loads and congestion situations. This statistic measures not just the ultimate result, but also the system’s stability and consistency during the simulation.

Several variables might explain the observed decrease in success rates, notably for the non-sharded architecture. These include temporary resource saturation, queue overflows, and longer transaction times owing to processing delays. Because the non-sharded approach routes all transactions through a single validation pool, it is more prone to performance deterioration as network demands increase. On the other side, the sharded design benefits from distributed processing, allowing it to sustain high throughput and constant success rates even under pressure. This comparative research underscores the necessity for scalable, adaptive infrastructures, such as dynamic sharding, to ensure long-term blockchain stability.

Figure 11 above illustrates the results of an advanced Monte Carlo simulation conducted under varied scenarios for both sharded and non-sharded blockchain architectures.

The total number of successful transactions is plotted against the number of iterations, giving a complete picture of each system’s ability to execute transactions under changing network conditions. The sharded blockchain, shown by the green line, shows a steady linear increase in successful transactions throughout all iterations. This steep and consistent trend demonstrates the scalability and efficiency of the sharded architecture, which effectively distributes workloads over several shards. Even under varying conditions, the sharded blockchain performs well, resulting in a much larger number of successful transactions at the end of the simulation.

The non-sharded blockchain, represented by the blue line, has a significantly flatter trajectory. This suggests a limited transaction processing capability and a high vulnerability to growing network demands. The slower rate of growth in completed transactions indicates that the non-sharded blockchain’s centralized design causes delays, limiting its ability to handle high traffic volumes and dynamic conditions.

(c)

Resource Utilization:

Figure 12 highlights the resource utilization patterns during the Monte Carlo simulation, comparing CPU, memory, and disk usage between the two architectures:

CPU Usage:

• The non-sharded blockchain exhibited frequent spikes, often nearing full capacity, signaling strain due to centralized transaction processing;
• The sharded blockchain maintained lower and more stable CPU utilization, reducing the risk of overloading the system.

Memory Usage:

• The non-sharded architecture experienced rapid and uneven memory consumption, frequently reaching saturation. This led to performance degradation during high transaction volumes;
• Sharded systems managed memory resources efficiently across shards, maintaining a balanced and predictable utilization.

Disk Usage:

• The non-sharded blockchain encountered bottlenecks due to its centralized data writing operations, resulting in inconsistent disk usage patterns;
• The sharded blockchain demonstrated consistent and steady disk utilization, leveraging distributed storage demands to prevent overload.

4.3. Statistical Significance Tests

To confirm the validity of our experimental findings, we used statistical significance tests to determine whether the observed differences between sharded and non-sharded blockchain designs were statistically significant. This section describes the methods utilized for hypothesis testing, the findings, and the implications for this study.

4.3.1. Methodology for Statistical Testing

To determine if the reported improvements in the sharded blockchain are statistically significant, we conducted the following tests:

• The Shapiro–Wilk test for normality: was performed to examine if the performance parameters (transaction success rate, latency, and resource usage) have a normal distribution;
• Student’s t-test: once the normality assumption was granted, we used an independent two-sample t-test to compare the means of sharded and non-sharded blockchain designs;
• Mann-Whitney U test: in situations where normality was not proven, we used this non-parametric test to determine whether one distribution consistently produces greater results than another;
• Binomial exact test: given the enormous imbalance of successful transactions between the two topologies, we used an exact binomial test to see if the difference was statistically significant.

4.3.2. Results of Statistical Tests

The outcomes of our statistical significance tests are summarized below:

• Transaction success rate: the binomial exact test showed a p-value < 0.00001, indicating a substantial increase in transaction success rates in the sharded architecture compared to the non-sharded version;
• CPU usage: the Shapiro–Wilk test showed that CPU utilization data are not regularly distributed (p < 0.0001). The sharded blockchain significantly reduced CPU utilization, as validated by the Mann–Whitney U test (p < 0.0001);
• Memory usage: similarly, the Mann–Whitney U test showed that memory consumption is significantly lower in the sharded blockchain (p < 0.0001), suggesting more efficient resource allocation;
• Disk usage: the Shapiro–Wilk normality test confirmed that disk usage values in both sharded and non-sharded architectures consist of constant values (p = 1.000 for both distributions), indicating no variance in the dataset. Given this, neither the t-test nor the Mann–Whitney U test could be meaningfully applied. While no statistical tests could be conducted due to the dataset’s lack of variation, the findings demonstrate that sharded architectures require additional disk space to allow scalability and decentralized processing.

4.3.3. Interpretation and Implications

The statistical research demonstrates that the sharded blockchain design performs much better than the non-sharded architecture in terms of transaction success rates, CPU efficiency, and memory consumption. These findings confirm the idea that dynamic sharding improves blockchain scalability and resilience in hostile environments, notably against DDoS attacks.

However, disk utilization had a greater absolute value in the sharded design, but no significant statistical tests could be performed due to the dataset’s lack of variation. This is a predicted outcome of sharding, as each shard retains a piece of the blockchain state independently, increasing total storage needs. While this increases storage overhead, it has no negative effect on performance because disk access is still efficient across shards.

These statistical insights provide credibility to our experimental findings, demonstrating that the observed advantages in scalability and security are not the result of random fluctuations, but rather are inherent in the dynamic sharding method.

4.4. Discussion

This paper conducts an in-depth review of post-quantum blockchain architectures, focusing on the benefits of sharding. Beginning with transaction latency, the findings show that sharded systems have much lower delays than non-sharded designs. This improvement is especially important for post-quantum blockchains, because computing costs from cryptographic methods may cause delays during high-usage periods. By efficiently dispersing the workload over several shards, these systems address one of the major issues of sustaining responsiveness in dispersed networks.

Building on this observation, the analysis of transaction success rates demonstrates the scalability of sharded architectures. Under simulated DDoS situations, the sharded blockchain consistently outperformed the non-sharded version, achieving greater success rates. This demonstrates its ability to handle massive transaction volumes without falling to network congestion, an important characteristic for post-quantum systems that require secure and dependable operations.

In addition to these performance measurements, resource use patterns reveal additional information about the efficiency of these structures. Sharded systems displayed balanced use of computing resources, with stable CPU, memory, and disk consumption even under stress. In contrast, non-sharded designs experienced regular resource bottlenecks, indicating an inability to meet the intensive demands of post-quantum cryptography. These findings highlight the relevance of distributed resource management in improving the operational efficiency of blockchain systems.

Expanding on the performance metrics, the Monte Carlo simulations highlighted the scalability potential of sharded systems under various scenarios. The exponential development in cumulative successful transactions for sharded systems demonstrates their adaptability in high-demand environments. In contrast, the limited scalability demonstrated in non-sharded designs emphasizes their limitations in meeting the increasing demands of post-quantum blockchain applications.

These findings all point to one essential conclusion: while post-quantum cryptographic algorithms solve quantum-era security risks, classic challenges like scalability and resilience remain significant. Sharding emerges as a possible approach, allowing post-quantum blockchains to retain performance and scalability in the face of a variety of problems. However, further effort is required to enhance shard synchronization and inter-shard communication in order to realize the full potential of this technique.

5. Conclusions

This paper presents a comprehensive analysis of the performance of post-quantum blockchain architectures under demanding settings, with a focus on comparing sharded and non-sharded configurations. By implementing the Falcon post-quantum cryptography algorithm, this study discusses the fundamental requirement for quantum-resistant blockchain systems while simultaneously demonstrating their operational vulnerabilities in classical attack scenarios such as Distributed Denial-of-Service (DDoS) attacks.

The findings show that sharded designs consistently beat non-sharded systems on key performance criteria such as transaction latency, success rates, and resource consumption. Sharding demonstrates an effective approach to reducing the processing cost and resource constraints inherent with post-quantum blockchains. By dividing the workload across numerous shards, the architecture improves not only the scalability but also the resilience to high traffic and aggressive environments.

Monte Carlo simulations confirmed the scalability of sharded blockchains, demonstrating their ability to manage varying transaction loads with minimum performance degradation. These findings highlight the potential of sharded post-quantum blockchains to satisfy the expectations of future blockchain ecosystems, which prioritize both security and performance.

While the report emphasizes the benefits of sharding in post-quantum blockchains, it also identifies areas for future investigation. Inter-shard communication issues, synchronization costs, and the consequences of shard mismanagement all deserve further examination. Furthermore, as the environment of quantum computing and cryptographic developments shifts, ongoing consideration of post-quantum blockchain systems is important.

Finally, this paper emphasizes the importance of architectural advances such as sharding in realizing the full potential of post-quantum blockchains. These systems are better positioned to ensure secure, efficient, and long-term operations in a quickly changing technological world because they handle scalability and performance issues.