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How does Axie infinity maintain variable information, such as breed count, to an axie that was already sold as an NFT?

From my understanding of the ethereum blockchain and NFTs in general, once an NFT is minted into the blockchain, its metadata freezes, making it immutable. An interesting question that entered my mind is how a game like Axie Infinity could store variable data, such as breed count, into the same axie NFT which was already minted. Take this 3 mystic Axie, for example.

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Source(Ask order expires on 11/02/2022): https://marketplace.axieinfinity.com/axie/3224/

In order for this axie to be listed in the marketplace in the first place, it must have been minted into an NFT. Now, I don’t know if the breed count variable remained constant once the axie became an NFT, but the point I want to make is that none of the purchased axies should be modifiable(i.e. have its stats leveled up or breed count incremented) since the ethereum blockchain would not allow that. Cryptography wise, it also seems impossible that an NFT can be modified, since it would then output a different SHA256 hash value(used in IPFS for content identifying purposes), which the original CID for the original NFT would not be able to locate. So how is all of this possible in Axie infinity? I can personally think of 2 possibilities:

  1. Any user interaction that modifies the initial state of each axie nft(i.e. breeding, levelling up) removes the original nft, so when owners of the axie resell the axie, they technically remint a new token.

  2. Any modifications to an axie nft are managed in a centralized server, so that it does not affect the original axie nft. The ethereum blockchain only recongizes the original, unmodified axie nft, as the correct token that belongs to the buyer of the nft. When an axie owner decides to sell his or her axie after modifying it, axie infinity uses a custom protocol that removes the ownership from the original token(I don’t know the exact details; maybe transfer ownership to a null address?, and remints a new nft(that includes modifications on the original nft) that can be sold again. I believe this is an important question relevant not just to Axie Infinity but also to P2E gaming in terms of security and ownership.

What are your thoughts?

How do we sign a hash value?

In RSA, signing the hash of a message is doing the operation $h^{d} mod N$ where d is the private key. Given that the size of $d$ is usually 2048 bits and $h$ is a quite big number, the exponentiation will take too much time. For example in python raising a number of 9 digits::Listen

In RSA, signing the hash of a message is doing the operation $h^{d} mod N$ where d is the private key.

Given that the size of $d$ is usually 2048 bits and $h$ is a quite big number, the exponentiation will take too much time.

For example in python raising a number of 9 digits to the power of a number of 8 digits took 600s on my laptop. And the execution time multiplies by about 40 everytime I add a digit to the exponent.

And I don’t think we can make use of Euler’s theorem here because $Φ(N)=(p-1)times(q-1)$ may still leave us with a large exponent.

What do I miss here ? How do we sign the hash value ?

How does Axie infinity maintain variable information, such as breed count, to an axie that was already sold as an NFT?

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