The Biggest Challenge in Bitcoin Management: The Role of Private Keys and BIP39

The intrinsic value of Bitcoin is centered around how properly you manage your private keys. If you lose this key, you also lose access to your Bitcoin. The well-known saying “No key, no coin” symbolizes Bitcoin’s self-sovereignty.

Where Does Bitcoin Exist?

One of the concepts that can be difficult for non-technical people to understand is where Bitcoin actually exists. Generally, wallets are thought of as boxes that store money. However, in reality, a wallet does not hold Bitcoin itself. It only holds the private key.

The actual nature of Bitcoin is just data entries on the blockchain hosted by all network participants. Using Bitcoin is essentially proposing to update data recorded on the blockchain. The private key is a tool that proves only its owner can approve these data updates.

The Nature of Private Keys: Very Large Numbers

A private key is ultimately a very large number composed of 256 randomly generated 1s and 0s. In binary form, it looks like this:

1110001011011001011110111100000101000000100010011110101110110101110111001111111111111010101110100101110100111010011100101001 101111010001100001111101011110011010010111100110111010000011011011011100011010001100011110100011000111101101001001111011010101010110011011010

This overwhelming randomness is the core of wallet security. The number of possible combinations for a Bitcoin private key is roughly equal to the number of atoms in the observable universe. Therefore, if generated through a truly random process, private keys are fundamentally secure.

Multiple Representations of Private Keys

The same private key can be expressed in different encoding schemes.

In hexadecimal: E2D97BC144089EBB5773FFABA5D3A729BD187D79A5E6E836DC68C7A24F6AB36A

In Wallet Import Format (WIF): 5KYC9aMMSDWGJciYRtwY3mNpeTn91BLagdjzJ4k4RQmdhQvE98G

WIF was the standard format for exchanging private keys during Bitcoin’s early days. Back then, users generated a single private key and derived the public key from it.

How Public Keys Are Generated

Creating a public key from a private key is essentially a very large number multiplication. Bitcoin uses elliptic curve cryptography Secp256k1, which involves a special point called the “generator point.” This point is fundamental to key generation and signing processes.

The generator point G is as follows: G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798

Multiplying the private key by this generator point establishes a new point on the curve, which is mathematically related to your private key and becomes your public key.

Uncompressed public key: 04C0E410A572C880D1A2106AFE1C6EA2F67830ABCC8BBDF24729F7BF3AFEA06158F0C04D7335D051A92442330A50B8C37CE0EC5AFC4FFEAB41732DA5108261FFED

For data efficiency, public keys are often “compressed,” which only retains one byte indicating the sign of the y-coordinate along with the x-coordinate.

How Transaction Signatures Work

Signing a transaction with a private key also involves multiplication operations. Wallets generate a nonce (a random number), then use the private key and transaction hash to perform calculations, producing a signature (two values, r and S).

This signature allows anyone to verify that it was signed with the legitimate key without revealing the private key. Establishing ownership of Bitcoin fundamentally boils down to a mathematical operation involving large number multiplication.

BIP39: A User-Friendly Solution

The above content can be overwhelming for those unfamiliar with cryptocurrency technology. Binary numbers, hexadecimal, elliptic curve coordinates—all demand understanding at once. A particularly practical challenge is how to securely back up private keys, which is a serious concern for many users.

To address this, a more intuitive and secure method was developed: the seed phrase (mnemonic seed).

What is a BIP39 Mnemonic Seed Phrase

The problem behind mnemonic seeds is the difficulty of copying and transcribing 256 bits of 1s and 0s. Even a single error can invalidate the entire backup:

1110001011011001011110111100000101000000100010011110101110110101110111001111111111111010101110100101110100111010011100101001 101111010001100001111101011110011010010111100110111010000011011011011100011010001100011110100011000111101101001001111011010101010110011011010

Instead of such complex strings of numbers, a human-friendly representation was needed.

Example mnemonic seed: “Track Update Anger Donkey Memory Laptop Reform Details Split Sorrow Fat”

Just 12 words. Handling becomes dramatically easier. So how are these meaningful words generated from a random collection of 1s and 0s?

How BIP39 Encoding Works

Similar to binary and hexadecimal, an encoding scheme is used. Each word in the mnemonic seed corresponds to a specific string of 1s and 0s mapped through an encoding method.

BIP39 introduces a standardized encoding scheme. Each word in a specially created dictionary is mapped to a binary number from 00000000001 to 11111111111 in alphabetical order.

Mapping examples for demo seeds:

• Track: 11101001001
• Update: 10110110001
• Anger: 01011110011
• Donkey: 01000001001
• Memory: 10110101110
• Laptop: 01111101000
• Reform: 10110100010
• Details: 00111100010
• Split: 11010010001
• Sorrow: 01100110100
• Fat: 00010011110
• Why: 01010011011

In binary form: 11101001001 10110110001 01011110011 01000001001 10110101110 01111101000 10110100010 00111100010 11010010001 01100110100 00010011110 01010011011

2048 Words and 11-Bit System

BIP39 uses 2048 words, each mapped to an 11-bit sequence of 1s and 0s. This makes it easier for people to handle private keys.

When a wallet generates a random number from a private key, it divides that number into 11-bit chunks and maps each chunk to a word in the BIP39 mnemonic dictionary. The same large number can then be represented as a sequence of recognizable words. The human brain is far better at processing word sequences than long strings of bits. This significantly reduces the risk of losing Bitcoin due to transcription errors.

Checksum Mechanism

Looking at the binary encoding above, you’ll notice that the last “word” actually only uses 8 bits. This is a checksum to verify the validity of the seed phrase.

When generating a private key, the necessary bits to exactly map to 12 (or 24) words are not always available. The wallet hashes the existing number and appends the first few bits of the hash to the end of the private key. This ensures the final word has the correct number of bits to map properly.

This checksum word allows for mathematical verification of the seed copy’s correctness. If you input a mnemonic seed incorrectly, the checksum will not match. Each seed (12 or 24 words) has multiple valid checksum words, but if the final word does not match the seed’s checksum, the wallet will warn that it is invalid.

Unlike the hassle of copying raw binary data, this approach is intuitive yet mathematically secure.

Word Selection Strategy

The 2048 words in the BIP39 list are carefully chosen so that the first four characters of each word are not the same. This reduces the risk of confusing similar words during transcription, which could corrupt the backup of the private key.

From Mnemonic Seed to Multiple Key Pairs

The process of deriving multiple private and public keys from a mnemonic seed is surprisingly simple.

The mnemonic seed is hashed using SHA512, producing a 512-bit hash of 1s and 0s. The first half of this output functions as the actual private key, while the second half, combined with an index number and existing private or public key, is used as input to SHA512 to generate new key pairs. Repeating this operation allows the derivation of countless new private and public keys from a single mnemonic phrase.

Innovations BIP39 Brought

These mechanisms enable the management of private keys as simply and securely as possible, while minimizing the risk of asset loss due to errors. All of this is achieved through mathematics.

The reason Bitcoin is called “money protected by mathematics” becomes clearer now. BIP39 is a crucial invention in the Bitcoin ecosystem, implementing its mathematical robustness in a user-friendly way.

Source: Bitcoin Magazine