Geo-Locked NFTs

Geo-Locked NFTs do exactly what they sound like, they are geo-restricted and user can only mint them in specific location, as decided by owner of NFT.

How Is It Possible?

Using FHE i.e Homomorphic Encryption we can send user's encrypted location freely on-chain which was the only barrier previously stopping us from implementing this.

The project "Geo Locked NFT" depicts one of many use cases that FHE unlocks in web3.

Deployed FHE Handler Contract Addresses [All are testnets]

1. Arbritrum: 0x39DAf5111096520efae34054bfD2A2febA271325
2. Base: 0xaa87F6Ff58D587b286a8EE98629D4b5CB2c506A7
3. Polygon-zkevm: 0x4097aF75b84D600c2851ea551D5FD7c8D5e07A70
4. Fantom: 0x4097aF75b84D600c2851ea551D5FD7c8D5e07A70
5. Linea: 0x9dC4638e22936Da7723B4923e0Bfe249d4A7fa62

FHE Key generation

1. Define the bit length of the modulus n, or keyLength in bits.
2. Choose two large prime numbers p and q randomly and independently of each other such that gcd( p·q, (p-1)(q-1) )=1 and n=p·q has a key length of keyLength. For instance:
   1. Generate a random prime p with a bit length of keyLength/2 + 1.
   2. Generate a random prime q with a bit length of keyLength/2.
   3. Repeat until the bitlength of n=p·q is keyLength.
3. Compute parameters λ, g and μ. Among other ways, it can be done as follows:
   1. Standard approach:
      1. Compute λ = lcm(p-1, q-1) with lcm(a, b) = a·b / gcd(a, b).
      2. Generate randoms α and β in Z* of n, and select generator g in Z* of n**2 as g = ( α·n + 1 ) β**n mod n**2.
      3. Compute μ = ( L( g^λ mod n**2 ) )**(-1) mod n where L(x)=(x-1)/n.
   2. If using p,q of equivalent length, a simpler variant would be:
      1. λ = (p-1, q-1)
      2. g = n+1
      3. μ = λ**(-1) mod n

The public (encryption) key is (n, g).

The private (decryption) key is (λ, μ).

FHE Encryption

Let m in [0, n) be the clear-text message,

1. Select random integer r in Z* of n.

2. Compute ciphertext as: c = g**m · r**n mod n**2

FHE Decryption

Let c be the ciphertext to decrypt, where c in (0, n**2).

1. Compute the plaintext message as: m = L( c**λ mod n**2 ) · μ mod n