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Entropy

Entropy is a measure of randomness. The more entropy, the more secure. A bit is the smallest unit of data in a computer. It can be either 0 or 1.

We use the crypto.getRandomValues() function to generate random bits. This function is available in modern browsers and Node.js. Learn more on MDN

TOTAL 128 BITS

Entropy to Mnemonic

A mnemonic is a group of easy to remember words generated from the entropy. The valid number of words for a mnemonic is 12, 15, 18, 21, or 24. Different numbers of words require different lengths of entropy.

1abandon

2abandon

3abandon

4abandon

5abandon

6abandon

7abandon

8abandon

9abandon

10abandon

11abandon

12about

It takes 2 steps to convert an entropy to a mnemonic:

Checksum

By adding a checksum to the entropy, we can make the mnemonic self-verifiable. This is useful fot detecting errors when fat fingering the words.

The checksum is the first 4 bits of the SHA256 hash of the entropy.

For different lengths of entropy, the checksum will be different. A 128 bits entropy will have a 4 bits checksum.

Entropy

SHA-256

Checksum

Entropy (bits)	Checksum (bits)	Entropy + checksum (bits)	Mnemonic length (words)
128	4	132	12
160	5	165	15
192	6	198	18
224	7	231	21
256	8	264	24

TOTAL 132 BITS

Map to Words

The entropy itself is 128 bits, plus 4 bits for the checksum, for a total of 132 bits.

All 132 bits can be divided into 12 groups of 11 bits each.

The 11-bit binary number can convert to a decimal value between 0 and 2047.

We can use this value as an index to get a word from the BIP-39 wordlist.

The BIP-39 wordlist contains 2048 words. Supports multiple languages. The mostly used language is English.

The 2048 English words are choosen in a way that the first 4 letters of each word are unique. This way, the first 4 letters are enough to identify a word.

0 0 0 0 0 0 0 0 0 0 0	#0	1abandon
0 0 0 0 0 0 0 0 0 0 0	#0	2abandon
0 0 0 0 0 0 0 0 0 0 0	#0	3abandon
0 0 0 0 0 0 0 0 0 0 0	#0	4abandon
0 0 0 0 0 0 0 0 0 0 0	#0	5abandon
0 0 0 0 0 0 0 0 0 0 0	#0	6abandon
0 0 0 0 0 0 0 0 0 0 0	#0	7abandon
0 0 0 0 0 0 0 0 0 0 0	#0	8abandon
0 0 0 0 0 0 0 0 0 0 0	#0	9abandon
0 0 0 0 0 0 0 0 0 0 0	#0	10abandon
0 0 0 0 0 0 0 0 0 0 0	#0	11abandon
0 0 0 0 0 0 0 0 0 1 1	#3	12about

Mnemonic to Seed

A seed is a 512-bit (64-byte) value generated from mnemonic . Will be used to derive the master extended key. We will cover this in the next section.

You may have noticed that the length of a mnemonic is not fixed, but the seed requires exactly 512 bits. To achieve this, the mnemonic needs to be processed through a function called PBKDF2 (Password Based Key Derivation Function 2).

Mnemonic

Passphrase

PBKDF2

Seed

PBKDF2

PBKDF2 is a key derivation function with a sliding computational cost. It is used to protect against brute-force attacks by increasing the cost of key derivation. Briefly, it will hash the data for 2048 rounds using HMAC-SHA512.

PBKDF2 is designed to be slow by hashing the data for 2048 rounds. Make it more difficult for anyone to brute-force other people's mnemonic sentences.

Last generation took 0ms on your device.

PBKDF2 accepts a "Passphrase" as a salt. Different Passphrase produce completely different seeds from the same mnemonic

Most wallets use an empty string as a Passphrase. If you use a Passphrase, make sure you remember it. Losing it will result in the loss of all funds.

PBKDF2

PBKDF2 cost 0 ms

This seed will be used to derive a HD wallet.