# Stealth Address

## Abstract
The `Stealth Address` is the technology which allows us to hide the **recipient** address.

## Details
The blockchain for example `Ethereum`, we generate the private key and the public key based on private key. The hash of the public key is going to be a address which specifies the **recipient**. This address corresponds one private key and public key pair so we can easily identify who is the **recipient** of the transaction. In our blockchain, we generate **recipient** address for each transactions and make it hard to identify the **recipient**.

1. Generates recipient public key pairs
2. Generates recipient `Stealth Address`
3. Prove the ownership of `Stealth Address`

Above sequence used for confidential transfer to keep the **recipient** address anonymous.

## Generates Recipient Public Key Pairs
Every transaction has **recipient** and we hide the **recipient** with stealth address. We assume Alice send transaction to Bod.

First of all, Bod generates the two key pairs (a, A) and (b, B) such that `aG = A` and `bG = B`. `a` and `b` are the private keys and, `A` and `B` are the public keys.

Variable | Explanation | Derivation
:------------ | :------------- | :-------------
a | Bob private key | a ∈ Fp
b | Bob private key | b ∈ Fp
A | Bob public key for `a` | a * G
B | Bob public key for `b` | b * G

## Generates Recipient `Stealth Address`

Secondly, Alice generates the Bob **recipient** address as referred to the `Stealth Address`. Alice selects the random number `r` and calculate the `Stealth Address` with Bob public keys such that following.

$$ P = H(r*A) * G + B $$

No one can link P address with `A` and `B` because it's concealed by elliptic curve arithmetic. Alice publish the `P` and `R` calculated as `R = rG`.

Variable | Explanation | Derivation
:------------ | :------------- | :-------------
r | randomness generated by Alice | r ∈ Fp
H | one-way hash function which takes curve point and maps field element | e: xG -> Fp
R | public value generated by Alice | r * G
P | stealth address of Bob | H(r*A) * G + B

## Prove the ownership of `Stealth Address`
Lastly, Bob needs to prove the ownership of `Stealth Address` to use assets associated with it. Bob knows his private keys `a` and `b`. He can calculate the private key of `P` with `x = H(a * R) + b`. This is the [`Diffie–Hellman key exchange`](https://en.wikipedia.org/wiki/Diffie%E2%80%93Hellman_key_exchange#:~:text=Diffie%E2%80%93Hellman%20key%20exchange%20is,Whitfield%20Diffie%20and%20Martin%20Hellman.&text=Diffie%E2%80%93Hellman%20is%20used%20to%20secure%20a%20variety%20of%20Internet%20services.) algorithm. Only Bob can know the `x`. This is how concealing the **recipient** address. Next section, we explain how we conceal the **amount** of transactions.