# Bitcoin Keys

Bitcoin Cash transactions are secured through the use of key-pairs generated by all senders and receivers.
The key-pair is comprised of a **private key**, which is generated randomly and stored securely on a user's device, and a **public key**, which is calculated from the private key but can be sent to others without revealing the private key.
The private key can be used to generate signatures, which can then be verified using the public key.

## Private Key Generation

Bitcoin Cash uses elliptic-curve cryptography (ECC); in particular, the secp256k1 curve with 32-byte (256-bit) private keys.

From SEC 2, ver. 2.0, the curve parameters are as follows:

The elliptic curve domain parameters over Fp associated with a Koblitz curve secp256k1 are specified by the sextuple

`T = (p, a, b, G, n, h)`

where the finite field`F<sub>p</sub>`

is defined by:p = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F = 2

^{256}− 2^{32}− 2^{9}− 2^{8}− 2^{7}− 2^{6}− 2^{4}− 1The curve E:

`y<sup>2</sup> = x<sup>3</sup> + ax + b`

over`F<sub>p</sub>`

is defined by:a = 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000

b = 00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000007

The base point G in compressed form is:

G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798

and in uncompressed form is:

G = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8

Finally the order n of G and the cofactor are:

n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141

h = 01

Private keys are then 256-bit values and can be chosen at random from the set `[1, n-1]`

.

It is important that private keys are stored securely and never revealed to untrusted third-parties. Anyone with access to a given private key would be able to control any funds secured with that key.

## Public Key Generation

Public keys are created by performing scalar multiplication of the generator, G, with the private key.

This means that public keys are a point on the elliptic curve, represented as two 256-bit coordinates, `(x, y)`

.
This means that a full public key is 512-bits (64 bytes) in length.
However, since elliptic curves are symmetrical across the x-axis, there are always two y-values that correspond to a given x-value, which can be calculated using the curve function, E.
These are also necessarily negations of each other mod p (i.e. y_{1} = p - y_{2}).
As a result, public keys are often **compressed** into 33 bytes, 32 bytes for the x-value and an additional bit (generally expanded to a full byte) indicating which y-value should be used.

When included in scripts, public keys follow one of two formats:

### Uncompressed Public Key Format

Field | Length | Format | Description |
---|---|---|---|

magic number | 1 byte | byte | Always `0x04` , indicating that this is an uncompressed public key. |

x-value | 32 bytes | bytes | The zero-padded x-value of the public key. |

y-value | 32 bytes | bytes | The zero-padded y-value of the public key. |

### Compressed Public Key Format

Field | Length | Format | Description |
---|---|---|---|

magic number | 1 byte | byte | `0x02` if the (discarded) y-value was even, `0x03` if it was odd. This bytes indicates both that this is a compressed public key and which y-value should be used.NOTE: this works because the y-values are negations of each other (mod p), so it is always that case that one is even and the other odd. |

x-value | 32 bytes | bytes | The zero-padded x-value of the public key. |