Let's go through the summary of the content of this chapter.

Since Shor’s algorithm will break every classical public-key crypto scheme, blockchain applications are vulnerable to quantum computers since any blockchain relies on signatures. However, there are countermeasures available in the form of post-quantum cryptography approaches that are resistant to Shor’s attack, and hence ensure the security of blockchain applications in the post-quantum era. Compared to conventional public-key schemes, the postquantum approaches are already competitive with respect to the signing and verification time.

However, the key and signature sizes are still large. This should be overcome to save storage space in blockchain systems. However, post-quantum approaches are already built into some blockchains, e.g., QRL or IOTA. This shows that the post-quantum procedures are well on track to replace traditional public-key schemes in the future. In particular, hash-based signature systems seem to be currently on the rise.

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