Remarkable Math: Bitcoin Private Keys

August 13, 2021 | 

Remarkable Math: Bitcoin Private Keys

A bitcoin wallet’s private key is the only thing standing between a hacker and the cryptocurrency contained in it. This article breaks down the math behind bitcoin wallet private keys to show how and why the deployment of unfathomably large numbers makes bitcoin wallets (when used properly) the most secured vaults in the world.

What is a Private Key?

When it comes to bitcoin, public and private keys are typically one of the first things you interact with. If you think of your bitcoin wallet as a mailbox, the public key is comparable to the public address for your mailbox while the private key is equivalent to the physical key that you would use to unlock and access the contents of your mailbox. Anyone can send you bitcoin by entering your public key in the same way that anyone can send you mail by adding your home address to an envelope.

A bitcoin wallet’s private key is the only thing needed to gain access to your bitcoin wallet. Anyone that may come to learn your private key can take all of your bitcoin for themselves. This fact makes many people uncomfortable with the idea of storing value on bitcoin’s blockchain. Even with a key, you wouldn’t keep all of your money in your mailbox, right? In this article, we break down the match behind bitcoin’s private keys to explain why your private key is absolutely unhackable provided it has been generated and stored securely.

Why Bitcoin’s Private Keys Are the Gold Standard for Security

Remarkable Math: Bitcoin Private Keys

To begin to think about how the bitcoin blockchain approaches security, and the sheer size of the numbers implemented to ensure its security, we will return to the example of the mailbox.

We mentioned before that you’re not likely to feel comfortable leaving your life savings in your mailbox. This analogy suffers mightly when attached to bitcoin as, in this example, anyone could look up your mailbox to see how much money you left in. If it’s a lot, you’ll soon become a target.

To design a system like bitcoin, one must ask how many mailboxes are needed to be safe putting my money in them. For instance, in a world with unlimited space, like the digital world of bitcoin, what if you had 1 billion mailboxes and put your money into one of them. Would that be secure?

This prompts a follow-up question. How long would it take for every hacker on the planet to move through 1 billion mailboxes? Maybe a few hours. So, that’s not secure. We’ll need a larger number. A much larger number.

Now, we introduce the true amount of equivalent mailboxes that are available in bitcoin’s blockchain and compare them to smaller figures to demonstrate just how large it is. Next, we’ll compare the amount to all of the world’s computing power.

The amount used to generate a bitcoin private is a quindecillion or 10^48. Meaning that the odds of correctly guessing a private key for a bitcoin wallet are:

1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Now, imagine you have that many mailboxes. Leaving your money in one of them is starting to look incredibly secure. Let’s look at another figure to get a better perspective on this unfathomably large number.

When we look at having 1 billion mailboxes and 7 billion people to attempt a hack on them once per day for 100 years, that leaves us with a total of attempts near 260*10^21. This number is considered to be in the range of the number of grains of sand on the entire planet. The number of grains of sand represents a total that is more than one quadrillion times smaller than the quindecillion protecting your bitcoin.

To take this one step further, let’s look at the total potential computing power in the world to see how it stacks up against bitcoin’s security model.

Currently, all of the world’s computing power is measured to be around 1 zettabyte. 1 yottabyte is equal to 1000 zettabytes. To track every potential private key, you would need approximately 25 yottabytes, or 25,000 times the world’s current computing power. Luckily for bitcoin holders, there isn’t enough gas and electricity for all of humanity to be able to run 25 yottabytes worth of computing power.

Ultimately the best evidence for bitcoin wallet security is the staggering amount of wealth held in them. For more than a decade, some wallets have been sitting idle on the blockchain with 9 or 10 figures of value stored in them. While this is a massive target for hackers, none of these wallets have been infiltrated. The math in this article should help to explain why that is. Bitcoin is a public ledger that is protected by numbers so large that we cannot comprehend them.

Private Key Best Practices

If you want to achieve maximum security for your bitcoin wallet, it is important to note that public and private keys can and should be generated while offline.

This will eliminate the possibility that software connected to the internet has scooped up your private key in the process of creating it. Once you’ve gone offline and generated a new private key, and subsequent public key, you can restore your internet and safely apply your private keys to a transaction so that it may be completed.

Holding bitcoin in an offline wallet is referred to as cold storage and provides the most protection against hackers, giving them virtually no avenues through which they can obtain your private keys.

The second-best alternative to cold storage is leaving your funds with a reputable and insured cryptocurrency exchange. As exchanges have prioritized regulatory compliance the prospect of leaving your coins there is much more attractive. This stems from the risks associated with a hot wallet, or a wallet that is connected to the internet. In the event that a hacker takes the coins in your hot wallet, you have no recourse and have lost your coins. However, if your coins were taken by a hacker who gained access to your exchange account, you may have the ability to recoup your funds, depending on the exchange.

To recap, in order from most to least secure, cold storage wallets are the most secure, followed by wallets controlled by a reputable exchange or custodial service. Storing your bitcoin in a hot wallet is by far the least secure method and should be avoided at all times.

When holding assets on Beaxy Exchange, your cryptocurrency is protected by Curv’s advanced multi-party computation (MPC) algorithm and fiat holdings are backed by FDIC insurance for up to $250,000 per account.

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