## 5 Conclusions  
Dilithium and Falcon rely on lattice-based cryptography, a domain with substantial theoretical grounding for resistance against quantum attacks. Sphincs+ takes a different approach, opting for hash-based mechanisms that minimize the algorithm's security assumptions, providing a more easily quantifiable security posture. Their computational efficiency was benchmarked across ARM and x86-64 platforms, revealing distinct performance characteristics. Dilithium consistently excelled in computational efficiency across both platforms, which makes it a prime candidate for systems where processing power is limited. Falcon, on the other hand, stood out in signature verification speed, despite requiring more computational resources for key generation. Sphincs+ remains the most computationally demanding algorithm, yet it offers the flexibility to trade off between computational efficiency and security parameters. Energy consumption evaluations further emphasized Dilithium's advantage in low-power scenarios, such as IoT devices. Falcon follows closely, with its energy footprint moderated by its efficiency in signature verification, whereas Sphincs+ is generally less energy-efficient due to its higher computational load. In terms of key and signature sizes, Falcon scored well with its compact design, thereby optimizing bandwidth. Dilithium, while generally efficient, suffers from somewhat larger signature sizes, which affects its bandwidth efficiency. Sphincs+, although secure, presents a significant challenge in bandwidth-constrained applications due to its large signatures. Dilithium appears as a highly versatile and computationally efficient algorithm, particularly appealing for embedded systems and internet of things (IoT) devices, thanks to its low energy consumption and computational requirements across ARM and x86-64 platforms. It also presents adaptability in smart cards and shows potential for strengthening blockchain architectures through hybrid cryptographic solutions. Falcon, despite its more cumbersome key generation, emerges as an ideal fit for high-throughput, low-latency environments due to its excellence in rapid signature verification. This makes it particularly suited for IoT platforms with RAM constraints up to 64 KB and real-time V2V communication systems, though its higher computational costs render it less favorable for smart card deployments. Sphincs+, on the other hand, brings to the table a high degree of security customizability at the expense of computational speed and energy efficiency. While this trade-off positions it as a viable option for certain IoT configurations, its less efficient performance and large signature size significantly limit its utility in smart cards and make it a less-than-optimal choice for multi-party threshold signature-based blockchain systems. Furthermore, the computational burden imposed by hashing operations in these algorithms, especially in Sphincs+, opens avenues for further optimization through hardware-accelerated hashing solutions. These insights underscore the necessity of context-specific evaluations for algorithm selection, given the trade-offs between computational efficiency, energy consumption, and security. Overall, our study offers insights for the implementation and integration of post-quantum cryptographic algorithms into existing systems and highlights the importance of interdisciplinary expertise in quantum computing, cybersecurity, and algorithmic theory. Conclusively, a comparative evaluation across key metrics revealed the following features:  
* Security level: we compared public key and signature sizes, showing that Sphincs+ offers the smallest public key size, beneficial for storage-limited devices. * Performance speed: Dilithium leads in key generation and signing speed, while Falcon is optimal for fast signature verification. * Computational efficiency: this paper outlines the potential for hardware-accelerated optimizations and the significant computational demands of Sphincs+ in comparison to the other two algorithms.