EVM vs Cosmos Addresses

Background

Mnemonics

A mnemonic, also known as a seed phrase, is a sequence of 12 or 24 random English words that derives a private key. An example is guard cream sadness conduct invite crumble clock pudding hole grit liar hotel maid produce squeeze return argue turtle know drive eight casino maze host.

A Hierarchical Deterministic (HD) path allows multiple private keys to be generated from a single seed phrase. HD paths are of the form m/purpose'/coin_type'/account'/change/index.

Ethereum uses an HD path of m/44'/60'/0'/0/0.

Cosmos uses an HD path of m/44'/118'/0'/0/0.

That means the same seed phrase will derive different private keys on Bitcoin, Ethereum, and Nibiru Chain.

Private Key -> Public Key

Both Cosmos and Ethereum use elliptic curve cryptography, and specifically they both use the secp256k1 elliptic curve. A private key is simply a point on the curve. Because of the mathematical relationship of the curve, a public key can be derived from the private key, but not the other way around.

Fig 1: secp256k1 curve

For example, the private key FF15BD81CDDF469FD807C069F0542E5287EED9009888B71D7CD6925A456487D0 derives the public key 02FCF004EAE263CB15C045EB5DFD605DA9E14FD8A695F59E5162D0F29331AD1B20.

Public Key -> Address Derivation

An address is not exactly equal to the public key, but is a hash of the public key. Different blockchains use different hashing functions.

Ethereum uses the last 20 bytes of the Keccak-256 hash of the public key as the address. Cosmos uses RIPEMD160(SHA256(pubKey)) as the address. That means that given the same public key, the EVM and Cosmos addresses will be different.

For a public key of 02FCF004EAE263CB15C045EB5DFD605DA9E14FD8A695F59E5162D0F29331AD1B20, the Ethereum address bytes is FAF227DAD0B91C2DEBD41DAE71C959EA4F95F8F8 and the Cosmos address bytes is 177AC608D913F3FE4DAB9C5409D8BFB6CF6DE202.

Address Encoding

Furthermore, the string representation of the address bytes differs between blockchains. Ethereum is simple; it simply uses the hex representation of the address bytes as the string. Cosmos uses Bech32 to encode the address bytes into a string.

For example, the address bytes FAF227DAD0B91C2DEBD41DAE71C959EA4F95F8F8 is represented as 0xFAF227DAD0B91C2DEBD41DAE71C959EA4F95F8F8, which is what you see in wallets like MetaMask. The same address bytes encoded as Bech32 is nibi1ltez0kkshywzm675rkh8rj2eaf8et78cqjqrhc.

Summary

The table below shows all possible outcomes for the seed phrase guard cream sadness conduct invite crumble clock pudding hole grit liar hotel maid produce squeeze return argue turtle know drive eight casino maze host.

HD Path	m/44'/60'/0'/0/0	m/44'/118'/0'/0/0
Private Key	68E80819679ABCCDDFA31064EA84B2FE6870B1EAA0EBE2A1FF40A38533CFAB8B	FF15BD81CDDF469FD807C069F0542E5287EED9009888B71D7CD6925A456487D0
Public Key (Compressed)	026E4A3BEE84DF12A20CB435AAA529B2E2E81F35731E679693CE1AA459CE0980F5	02FCF004EAE263CB15C045EB5DFD605DA9E14FD8A695F59E5162D0F29331AD1B20
Public Key (Uncompressed)	046E4A3BEE84DF12A20CB435AAA529B2E2E81F35731E679693CE1AA459CE0980F53566914E3003EBD626BC1768506FC1CF45A4A9BF5049E28F4EEE508875AEF490	04FCF004EAE263CB15C045EB5DFD605DA9E14FD8A695F59E5162D0F29331AD1B201B39BD254661402973A6D68099AB8910E17F7730EB3FA5E114E0153BB9131D92
Ethereum Address Bytes (Keccak-256)	0xC0F4B45712670CF7865A14816BE9AF9091EDDA1D	0xFAF227DAD0B91C2DEBD41DAE71C959EA4F95F8F8
Ethereum Address Bytes as Bech32	nibi1cr6tg4cjvux00pj6zjqkh6d0jzg7mksaywxyl3	nibi1ltez0kkshywzm675rkh8rj2eaf8et78cqjqrhc
Cosmos Address Bytes RIPEMD160(SHA256())	0xF317E8AC48EFDE20EA094B9F48EF1ECCEA683D5C	0x177AC608D913F3FE4DAB9C5409D8BFB6CF6DE202
Cosmos Address Bytes as Bech32	nibi17vt73tzgal0zp6sffw053mc7en4xs02u4mnvn5	nibi1zaavvzxez0elundtn32qnk9lkm8kmcsz44g7xl

Given one mnemonic, we can end up with four different addresses (eight, if you count the bech32 encodings as distinct) depending on which HD Path we choose and if we use the Ethereum hashing algorithm or the Cosmos hashing algorithm for address derivation.