# BIP 0038

## Contents

## Proposed encoding for a passphrase-protected private key

**User story:**As a Bitcoin user who uses paper wallets, I would like the ability to add encryption, so that my Bitcoin paper storage can be two factor: something I have plus something I know.**User story:**As a user of physical bitcoins, I would like a third party to be able to create password-protected Bitcoin private keys for me, without them knowing the password, so I can benefit from the physical bitcoin without the issuer having access to the private key, but also for it to be possible to memorize the material needed to unlock the physical bitcoin.

This proposal contemplates existence of a private key that requires a decryption passphrase before it can be used.

This proposal makes use of the following functions and definitions:

**AES256Encrypt, AES256Decrypt**: the simple form of the well-known AES block cipher without consideration for block chaining. Each of these functions takes a 256-bit key and 16 bytes of input, and deterministically yields 16 bytes of output.**SHA256**, a well-known hashing algorithm that takes an arbitrary number of bytes as input and deterministically yields a 32-byte hash.**scrypt**: A well-known key derivation algorithm. It takes the following parameters: (string) password, (string) salt, (int) n, (int) r, (int) p, (int) length, and deterministically yields an array of bytes whose length is equal to the length parameter.**ECMultiply**: Multiplication of an elliptic curve point by a scalar integer with respect to the secp256k1 elliptic curve.**G, N**: Constants defined as part of the secp256k1 elliptic curve. G is an elliptic curve point, and N is a large positive integer.**Base58Check**: a method for encoding arrays of bytes using 58 alphanumeric characters commonly used in the Bitcoin ecosystem.

### Prefix

I propose having the Base58Check-encoded string start with a '6'. The number '6' is intended to represent, from the perspective of the user, "a private key that needs something else to be usable" - an umbrella definition that could include keys participating in multisig transactions. The second character ought to give a hint as to what is needed, and for an AES256-encoded key based on the SHA256 hash of a passphrase, I propose the lowercase letter p.

I propose the string having an optional 14 bits of password typo resistance. That is, a 14-bit checksum of the password may be added so that the vast majority of password typos can be detected and reported to the user, rather than inadvertently accepted as correct, which will simply yield the wrong private key and frustrate the user. This checksum is optional, and a bit flag is defined for the purpose of disabling it.

The choice of a low-bitcount checksum is intended to reduce its usefulness to someone attempting to crack the password.

To encrypt the key requires the AES256Encrypt function, which takes a 16-byte input and a 32-byte key and yields a 16-byte output. The SHA256 hash of the passphrase is used as the 32-bit key given to the AES functions.

Encryption is:

- firsthalf: AES256Encrypt(bitcoinprivkey[0...15], SHA256(passphrase))
- lasthalf: AES256Encrypt(bitcoinprivkey[16...31] xor firsthalf[0...15], SHA256(passphrase))

Decryption is the reverse:

- firsthalf: AES256Decrypt(ciphertext[0...15], SHA256(passphrase))
- lasthalf: AES256Decrypt(ciphertext[16...31], SHA256(passphrase)) xor firsthalf[0...15]

To keep the size of the encrypted key down, no initialization vectors are used.

### Proposed specification

- Object identifier prefix: 0x0142
- How the user sees it: 58 characters always starting with '6P'
- Count of payload bytes (beyond prefix): 37
- 1 byte: compressed flag, EC multiply flag, five unused bits, call this
*bitflags* - 4 bytes: SHA256(SHA256(expected_bitcoin_address))[0...3], used both for typo checking and as salt
- 16 bytes: firsthalf: AES256Encrypt(bitcoinprivkey[0...15], SHA256(passphrase))
- 16 bytes: lasthalf: AES256Encrypt(bitcoinprivkey[16...31] xor firsthalf, SHA256(passphrase))

- 1 byte: compressed flag, EC multiply flag, five unused bits, call this
- Range in base58check encoding:
- Minimum value: 6PBFqPa2USdAvd91kpeDHpeuYsT9JUYLZDCVLQUpLZi4mJssFEpKogvS6o
- Maximum value: 6PfKzduKZXAFXWMtJ19Vg9cSvbFg4va6U8p2VWzSjtHQCCLk3JSBddFK3S

Of the one byte:

- the most significant bit is always set to preserve the prefix.
- the bit with value 0x40 when set indicates EC multiplication is required to decrypt the key, that it was created by someone not knowing the password.
- the bit with value 0x20 when set indicates the key should be converted to a bitcoin address using the compressed public key format.

#### Encryption when EC multiply flag is not used

Encrypting a private key without the EC multiplication offers the advantage that any known private key can be encrypted.

Encryption steps:

- Compute the Bitcoin address (ASCII), and take the first four bytes of SHA256(SHA256()) of it. Let's call this "salt", as this is one way it will be used.
- Derive a key from the passphrase using scrypt
- Parameters:
*passphrase*is the passphrase itself encoded in UTF-8.*salt*came from the earlier step, n=1048576, r=8, p=16, length=64 - Let's split the resulting 64 bytes in half, and call them
*derivedhalf1*and*derivedhalf2*.

- Parameters:
- Do AES256Encrypt(bitcoinprivkey[0...15] xor derivedhalf1[0...15], derivedhalf2), call the 16-byte result
*encryptedhalf1* - Do AES256Encrypt(bitcoinprivkey[16...31] xor encryptedhalf1, derivedhalf2), call the 16-byte result
*encryptedhalf2*

The encrypted private key is the Base58Check-encoded concatenation of the following:

- 0x0142 + bitflags + salt + encryptedhalf1 + encryptedhalf2

#### Encryption when EC multiply flag is used

Encrypting a private key with EC multiplication offers the ability for someone to generate encrypted keys knowing only an EC point derived from the original passphrase, not the passphrase itself. Only the person who knows the original passphrase can decrypt the private key. This methodology does not offer the ability to encrypt a known private key - this means that the process of creating encrypted keys is also the process of generating new addresses.

Steps performed by the person with the passphrase:

- Generate 16 random bytes, call this
*ownersalt* - Derive a key from the passphrase using scrypt
- Parameters:
*passphrase*is the passphrase itself encoded in UTF-8. salt is*ownersalt*. n=1048576, r=8, p=16, length=32. - Call the resulting 32 bytes
*passfactor*.

- Parameters:
- Compute the elliptic curve point G * passfactor, and convert the result to compressed notation (33 bytes). Call this
*passpoint*. - Convey
*ownersalt*and*passpoint*to the party generating the keys, along with a checksum to ensure integrity.

Encryption steps:

- Generate 16 random bytes, call this
*seedb*. Take SHA256(SHA256(*seedb*)) to yield 32 bytes, call this*factorb*. - Multiply
*passpoint*by*factorb*. Use the resulting EC point as a public key and hash it into a Bitcoin address. This is the generated Bitcoin address, call it*generatedaddress*. - Take the first four bytes of SHA256(SHA256(
*generatedaddress*)) and call it*addresshash*. - Now we will encrypt
*seedb*. Derive a second key from the passphrase using scrypt- Parameters:
*passphrase*is*passpoint*provided from the first party (expressed in binary as 33 bytes).*salt*is*addresshash*, n=1048576, r=8, p=16, length=64 - Split the result into two 16-byte halves and call them
*derivedhalf1*and*derivedhalf2*.

- Parameters:
- Do AES256Encrypt(ownersalt xor derivedhalf1[0...15], derivedhalf2), call the 16-byte result
*encryptedownersalt* - Do AES256Encrypt(seedb xor derivedhalf1[16...31], derivedhalf2), call the 16-byte result
*encryptedseedb*

The encrypted private key is the Base58Check-encoded concatenation of the following:

- 0x0142 + bitflags + addresshash + encryptedownersalt + encryptedseedb

Decryption steps:

- Collect passphrase from user
- Recompute
*passfactor*and*passpoint*using same steps done pre-encryption - Derive decryption key for
*factorb*by passing*passpoint*and*salt*into scrypt function. (*salt*is stored in the base58-encoded encrypted private key) - Decrypt
*encryptedhalf1*and*encryptedhalf2*to yield*factorb*using AES256Decrypt and derived decryption key. - Multiply
*passfactor*by*factorb*mod N to yield the private key associated with*generatedaddress*.