A blockchain account is just a private key, from which public keys (addresses) are derived.

Suppose we are the owner of an account, and a NFT is owned by one public address of this account. Then we are the owner of this NFT.

As we say, not your key, not your coins. So we better not forgot our private key. Else, we’ll loose everything we own !

This is why mnemonic seeds are useful.

Mnemonic seed

A mnemonic seed is a way of representing a large, randomly generated number as a sequence of words.

This sequence is usually 12, 15, 18, 21 or 24 words long. The words are chosen from a predefined list, and the specific word chosen at each position in the sequence is determined by the value of the private key at that position.

To compute the mnemonic seed

• The private key is first converted into a binary representation
• The binary representation is then divided into groups of 11 bits
• Each group is used to index into the list of 2048 words to select a specific word
• The selected words are then concatenated to form the mnemonic seed.

See BIP-39 for more infos about mnemonic standard.

Here is the official english word list https://github.com/bitcoin/bips/blob/master/bip-0039/english.txt

Concrete example

Say the private key is 0x4B6150645367566B5970337336763979

The binary representation of this private key is

01001011011 00001010100 00011001000 10100110110 01110101011
00110101101 01100101110 00000110011 01110011001 10110011101
10001110010 1111001

The list contains 2048 words. Each word is encoded on 11 bits. The private key is encoded on 128 bits. 128/11 is not even, so we can’t represent the private key like this into words.

We need to add 4 more bits, because 132/11 is even (12). These 4 bits are the 4 leftmost bits of the SHA 256 checksum of the private key.

SHA256(4B6150645367566B5970337336763979) = 81339e3d40865082004a0eccf5aba7d15a05d5d99a74547be4718b78f6da1617

1 digit in hexa is 4 digits in binary. The leftmost hexa char is 8, which is 1000 in binary

The 132 bits are

01001011011 00001010100 00011001000 10100110110 01110101011
00110101101 01100101110 00000110011 01110011001 10110011101
10001110010 11110011000

In decimal it’s

603, 84, 200, 1334, 939, 429, 814, 51, 921, 1437, 1138, 1944

The indexes for the 2048 words are 0 to 2047. So 603 means we look for the 604th word in the list, which is enter.

Repeat for each, and we get the mnemonic seed !

enter appear boil plug install cup grape all industry recipe mixture vessel

Conclusion

Private keys are long strings of random characters that are difficult to remember, read, and write for humans. It’s easy to make a mistake by copying the private key, and therefore, loose access the your account.

Mnemonic seeds are a way to represent a private key in a form that is easier for humans to remember, because it’s made up of words.

With a deterministic wallet, the original seed is enough to recover all private and public keys. A few words sequence is the only thing to remember.