Ethereum uses Elliptical Curve Cryptography
Private Key
A number chosen at random acts as the private key
This key is used to create signatures and prove ownership of funds
Ethereum uses the OSes random number generator to generate entropy
Usually a a very large number is generated and passed to a 256-bit hash function
If the result is within the acceptable range it can be used as private key
Public Key
The public key is a point on the elliptical curve (has a x and y co-ordinate)
k = Private Key, G = Generator Point, K = Public Key
Elliptical curve arithmetic does not have division, this operation cannot be reversed
Ethereum uses secp256k1 the same elliptical curve used by Bitcoin
Elliptical Curve Cryptography (ECC)
Ethereum only uses uncompressed public keys (prefixed with 04)
Public Key = 04 + x-coordinate (32 bytes) + y-coordinate (32 bytes)
Ethereum Address
They are derived from the public key using Keccak-256 hash function
The last 20 bytes of the output becomes the address
The addresses will generally be prefixed with 0x (hex)
Inter Exchange Client Address Protocol (ICAP)
Is an encoding scheme that is compatible with IBAN (used by banks)
IBAN is 34 alphanumeric characters (country code, checksum & bank identifier)
ICAP uses (XE, 2 character checksum & 3 possible variables of account identifier)
This format is only supported by a few wallets
Direct
Uses base-36, 30 alphanumeric characters
Represent 155 least significant bits of the Ethereum address
Only works for addresses that start with 0s as (Ethereum address is 160 bits)
The result is 33 characters long
Basic
Similar to Direct encoding but is 31 characters long
Not compatible with IBAN validation
The result is 35 characters long
Indirect
Uses identifier that resolves to Ethereum address through a name registry provider
16 characters long. Consists of asset identifier, name server and 9 character name
The result is 20 characters long
Hex Encoding with Checksum (EIP-55)
In this encoding some of the characters in the hex address are represent in capital
The capital characters act as checksum for the address
The hash of the hex address is calculated
Capitalize the letter if the hex digit in the hash is greater than 8
To verify the hash of the lowercase of the address is calculated and checked