Wallet Cryptographic Protocols

1. Elliptic Curve Cryptography (ECC)

• Petro Wallet relies on Elliptic Curve Cryptography (ECC) for the generation of public and private keys. Specifically, it uses secp256k1, the elliptic curve standard employed by Ethereum (and Bitcoin).

• secp256k1 is defined by the equation: y2=x3+7y^2 = x^3 + 7y2=x3+7 This curve offers a high level of security while allowing efficient key generation and transaction signing.

• The private key is a 256-bit random number, while the public key is derived from this private key using elliptic curve multiplication. These keys are used for creating and verifying signatures on the blockchain.

2. Keccak-256 Hashing Algorithm (SHA-3 Family)

• Petro Wallet uses the Keccak-256 hashing algorithm for several critical operations, such as generating Ethereum addresses from public keys and transaction signing.

• Ethereum chose Keccak-256 (a member of the SHA-3 family) as its hashing algorithm because of its security and speed. The process looks like this:

  1. A user’s public key is hashed using Keccak-256.

  2. The last 20 bytes of this hash are used to generate the user’s Ethereum address.

Example:

Ethereum Address=Keccak-256(Public Key)[12:]\text{Ethereum Address} = \text{Keccak-256}(\text{Public Key})[12:]Ethereum Address=Keccak-256(Public Key)[12:]

3. ECDSA (Elliptic Curve Digital Signature Algorithm)

Petro Wallet uses ECDSA for transaction signing. ECDSA is a variant of the Digital Signature Algorithm (DSA) that uses elliptic curve cryptography for higher efficiency and security.

• When a transaction is made, MetaMask:

  1. Hashes the transaction data using Keccak-256.

  2. Signs the hashed transaction with the user’s private key using ECDSA.

  3. Sends the signed transaction to the Ethereum network.

ECDSA signing involves generating a random number (k) and using the curve equation to calculate the signature:

r=(kG) x ​ modn(where G is the base point of the curve and n is the order of the curve)

𝑠𝑘 − 1 ( 𝐻 ( 𝑚 ) + 𝑟 ⋅ 𝑑 ) m o d     𝑛 (where 𝐻 ( 𝑚 ) is the hash of the message, and 𝑑 is the private key) s=k −1 (H(m)+r⋅d)modn(where H(m) is the hash of the message, and d is the private key)

This signature is then attached to the transaction and broadcast to the network.

5. Gas Estimation Algorithm

Petro Wallet uses an internal gas estimation algorithm to determine the amount of gas required for a given transaction. Gas is the unit of computation on Ethereum, and the algorithm estimates how much gas is needed based on:

• Transaction complexity (e.g., the number of computational steps required to execute a smart contract).

• Network congestion and current gas prices.

Petro Wallet typically queries nodes (by default through Infura) to get current gas price estimates, and then it provides users with different gas fee options, such as low, medium, and high. Users can also manually adjust gas limits and prices.

6. Web3.js and EIP-1559 for Transaction Handling

Petro Wallet leverages Web3.js, a JavaScript library, for interacting with the Ethereum blockchain. Web3.js enables Petro Wallet to send transactions, interact with smart contracts, and retrieve on-chain data.

• For Ethereum transactions, Petro Wallet also uses EIP-1559 for gas fee handling. EIP-1559 introduced a base fee and a priority fee (or “tip”) to make gas pricing more predictable:

  • Base fee: Automatically determined by the network based on demand.

  • Priority fee: User-defined fee to prioritize the transaction.

7. Encryption Standards

• AES-256: Petro Wallet uses AES-256 encryption to locally encrypt and store the user’s private key on the device. This ensures that the private key is not accessible without decrypting the data with the user’s password.

• PBKDF2 (Password-Based Key Derivation Function 2): Used for deriving a secure encryption key from the user’s password. It applies many rounds of hashing to slow down brute-force attacks.