Implement closest zipcode finder concept.

[a-t-0]

Context

You want to know which shop/zipcode is closest to your own zipcode, without telling the website where you live.

Note

The zipcode is not an appropriate application of FHE because the list of zipcodes is not private data, so instead of running an encrypted computation on the zipcode of the user, one could just send the whole zipcode list to the user, and let the user do the computation client/user-side, e.g. using javascript in the browser. However, this was an interesting case to learn about how the FHE would work in code.

Approach/Idea using Paillier cryptosystem

Create the list of distances to the zipcodes.
pass the encrypted zipcode, encrypted 1, and encrypted 0 into the function.
Compute differences between the incoming zipcodes and the shop zipcodes.
Then subtract 1 from all distances until subtractedDistance equals the encrypted 0.

Doubts

Can one derive the incoming zipcode based on the existing list of zipcodes?
Perhaps the randomness implies the subtractedDistance value of zero is different than the incoming encrypted 0 value.

First draft outline

func main() {
	// Assuming you have the Paillier public key
	n, g, lambda, mu := keygen.GetKeys()

	// Encrypt zipcodes
	zipcodeList := []int{12345, 56789, 98765}
	encryptedZipcodes := encryptZipcodes(zipcodeList, pubKey)

	// Given zipcode X
	X := 54321
	encryptedX := encryptNumber(X, pubKey)

	// Compute encrypted distances
	encryptedDistances := computeEncryptedDistances(encryptedZipcodes, encryptedX, pubKey)

	// Find the minimum distance
	minimumDistance, _ := findMinimumDistance(encryptedDistances, pubKey)

	// Decrypt minimum distance to get plaintext distance
	plaintextDistance, _ := pubKey.Decrypt(minimumDistance)

	// Retrieve closest zipcode
	closestZipcode := decryptClosestZipcode(encryptedDistances, minimumDistance, pubKey)

	fmt.Printf("Closest Zipcode to %d: %d (Distance: %d)\n", X, closestZipcode, plaintextDistance)
}