Cryptocurrencies: bit-heads or bit-tails?
Cryptocurrencies and the underlying technology of the blockchain have the potential to upend the way sensitive information is stored and transmitted. While blockchain as a system is new, it's built on the backs of preexisting concepts in mathematics:
Elliptic Curve Digital Signature Algorithm (ECDSA) is the main component of the blockchain. This allows people to sign their transactions and allows other people to verify those transactions. It is a complicated concept, but at the fundamental level is related to algebra and geometry.
Hash functions are functions that take a variable length input and allow you to output something of fixed length. They can be designed to be one-way, meaning they are incredibly difficult to reverse. The RIPEMD-160 cryptographic hash function is used in Bitcoin.
Both of these relate to an even more fundamental component of statistics that is crucial to the success of any cryptocurrency: probability. Perhaps you've already invested in a fluctuating cryptocurrency or two, experimenting in this brave new world. Without the BoA controlling your money and The Fed backing them up, how do you know your money is safe? Because of statistics.
If you've ever bet on the likelihood of Bitcoin's success, then you've used statistical probability. What you probably didn't realize is that Bitcoin's existence hinges on probabilities (as well as improbabilities), too.
Probability is easy to grasp, and factors into business all the time, from sales forecasts to risk events. You're subconsciously using probability all the time, whenever you say “the odds are...” Probability is the likelihood that a future event will occur. All probabilities are between 0 and 1 and can be expressed as fractions, decimals, and percentages.
The equation for determining the probability of an event A is:
P (A) = possible ways A can occur / total number of outcomes
The simplest example is flipping a *physical* coin. If A is landing on “heads,” then P (A) = 1/2 or 50%.
Probability in Bitcoin is not much more complicated than flipping a coin or rolling dice, though the numbers are much larger. Bitcoin wallets contain private keys which are only visible to the owner and are applied to every transaction the owner makes from that wallet. Each transaction also generates a public key, which is visible to bitcoin miners who record and publish transactions. Private keys must be unique. Otherwise, two owners with the same key would withdraw from the same pool of funds.
The way bitcoin creators designed it, there are approximately 2^160 private keys possible, making a collision statistically improbable, though not impossible. The odds are, even in a scenario with 1 billion users with 10 wallets each, less than 0.000000000000000000000000000000000000684%.
What if someone wanted to steal your key? Could they just guess it and take all your Bitcoin? Say they had this password cracking machine, capable of 350,000,000,000 guesses per second. It will crack your Windows password in six hours. How long for your Bitcoin private key?
1.32x10^29 years. Considering the life expectancy of the earth is 7.8x10^9 years you can probably say your Bitcoin keys statistically safe.
Probability also determines the verification of transactions through the order by which they are recorded.
Confirmation is the process by which blocks containing records of transactions are added to the blockchain. Once a miner has solved a block, it must be confirmed by the network. Confirmation takes about 10 minutes. This ten-minute figure is based on a probability calculation that a block that has been mined will be found and added. About 2/3 of transactions are confirmed within that 10-minute timeframe, and about 95% are confirmed within 30 minutes.
Bitcoin's security is perhaps too reliant on these improbabilities. On the one hand, credit card numbers are a lot easier to guess, making fraud a lot easier with traditional transactions. On the other hand, because banks are centralized, reliable verification of payments is transparent and direct in comparison to Bitcoin's system.
Bitcoin's future remains unclear, but it has uncovered a wealth (maybe) of opportunities to look at current transactional systems and apply our latest knowledge of data to come up with innovative solutions.