## 4 Applicability on Performance-Constrained Platforms
### Blockchain Technology  
For establishing trust in blockchain technology, it is essential to ensure three pillars: security, authenticity, and integrity. It is crucial that blockchains maintain these attributes even in the post-quantum era, with asymmetric cryptography being the foundational method to secure these properties. The authors of [71] pointed out the shortcomings of Sphincs+ and proposed the use of Dilithium in blockchain technology, not necessarily as a standalone algorithm but also as an enhancement to existing algorithms--essentially, as a hybrid solution. The use of hybrid algorithms was also suggested in [72]. According to [27], Falcon has the most compact key and signature lengths among the lattice-based cryptographic algorithms studied. While alternatives like Dilithium offer rapid performance, they come at the cost of significantly larger keys and signatures. Given this, there is growing consensus that Falcon's integration into blockchain technology could be promising for future advancements. For key generation in blockchain applications, threshold signatures can also be employed [73]. This method replaces the traditional KeyGen and Sign algorithms of digital signatures with an interactive multi-party protocol. The KeyGen protocol involves multiple participants who interactively generate a key. The Sign algorithm is then replaced with an interactive protocol for generating signatures. A unique feature of this protocol is that a sufficient number of participants must agree to sign a message before a signature can be generated. The verification of the signature is performed in the standard way. This ensures that an attacker cannot generate a signature on any message that has not been signed by an \"honest\" party. According to [73], Sphincs+ algorithms are hindered by the need to compute a large number of hash function queries on secret data. Post-quantum digital signature-based blockchain was also proposed as an appropriate method for securing the mobile internet of things (MIoT) ecosystem, increasingly becoming important with the wider availability and increasing speeds of mobile internet (5G and 6G) [74]. In a paper [75], four quantum-resistant algorithms--Sphincs+ + Sha256s, Sphincs+ + Shake256s, Dilithium, and Falcon--were evaluated for their efficiency and practicality. While Dilithium emerged as the most computationally efficient algorithm, it suffered from the disadvantage of having the largest public key size, posing significant challenges for its application in blockchain systems where each transaction embeds the public key. However, after incorporation of the interplanetary file system (IPFS), Dilithium maintained its efficiency and experienced a significant reduction in both signature and public key sizes to just 32 bytes each. Notably, Sphincs+ also benefits from IPFS, with a remarkable 99% reduction in signature size. A paper [71] illustrated that Dilithium can be effectively configured to provide varying levels of quantum security in blockchain systems without significantly inflating the block size. Specifically, an 80 bit quantum security level yields a block size of less than 1 MB, closely aligning with the current 1 MB block size in Bitcoin. For moderate and high security levels, the block sizes range from 1.5 to 2.0 MB and approach 3.0 MB, respectively. These are still within acceptable limits for practical blockchain deployment. Moreover, the performance gains are optimized further by efficient AVX2 implementations, which are consistent with the efficiency trends observed in Skylake architectures. This flexibility makes Crystals-Dilithium a versatile choice for enhancing quantum security in blockchain, accommodating both current needs and future upgradations without burdening the system with large block sizes. A paper [76] evaluated the viability of using the Falcon signature algorithm in the context of blockchain, specifically within the Ethereum mainnet. The analysis revealed a prohibitive cost for Falcon signature verification, consuming an average of 500 million gas units.