# Recovery Phrases

Recovery phrases (also known as mnemonics) provide a way for humans to easily read and write down arbitrary large numbers which would otherwise be very difficult to remember.

They use a predefined dictionary of simple words (available in many different languages) which map uniquely back and forth to a binary code.

## Seeds / Entropy

The recovery phrase is normally used to encode a wallet’s “seed” - a secret random number which is 28 decimal digits long, or more!

A seed is also called just entropy 1 , implying that it is a sequence of bytes which has been generated using high-quality randomness methods.

All keys belonging to a wallet are derived somehow from the wallet seed.

## Encoding

The process for encoding recovery phrases is described in BIP-0039 § Generating the mnemonic. Below is a reformulation of this specification.

The allowed size of entropy is 96-256 bits and must be multiple of 32 bits (4 bytes).

A checksum is appended to the initial entropy by taking the first $$|ent| / 32$$ bits of the SHA-256 hash of it, where $$|ent|$$ designates the entropy size in bits.

Then, the concatenated result is split into groups of 11 bits, each encoding a number from 0 to 2047 serving as an index into a known dictionary (see below).

Sentence LengthEntropy SizeChecksum Size
9 words96 bits (12 bytes)3 bits
12 words128 bits (16 bytes)4 bits
15 words160 bits (20 bytes)5 bits
18 words192 bits (24 bytes)6 bits
21 words224 bits (28 bytes)7 bits
24 words256 bits (32 bytes)8 bits

## Dictionaries

Cardano uses the same dictionaries as defined in BIP-0039.

## Example

This is an English recovery phrase, ordered left-to-right, then top-to-bottom.

write       maid        rib
female      drama       awake
release     inhale      weapon
crush       mule        jump
sound       erupt       stereo

It is 15 words long, so $$15\times11 = 165$$ bits of information, which is split into a 160 bit seed and 5 bit checksum.

Using the dictionary, these words resolve to:

2036        1072        1479
679         529         129
1449         925        1986
424        1162         967
1662         615        1708

Which is:

Seed:
01111100111 11100100110 01111101011
01010100111 01000010001 00010000001
10110101001 01110011101 11111000010
00110101000 10010001010 01111000111
11001111110 01001100111 110101
Checksum:                     01100

Seed (base16):     fe90c2e3aa7422206d4b9df846a2453c7cfc99f5
Checksum (base16): 0c
Footnotes
1.