DID SATOSHI NAKAMOTO PLAN THE DEATH OF BITCOIN? — CHAPTER I: “CRYPTOGRAPHY”
February 30, 2023 — the crypto winter continues to wear us down with its seemingly unchanging stillness. Bitcoin continues to hover around the $18,000 mark, and even the bad news seems to stop raining. And yet, that night, our on-chain data detectives notice something that was no longer expected. Satoshi Nakamoto had transferred his one million Bitcoins to another wallet. Death warrant for Bitcoin?
ULTIMATE DOOMSDAY SCENARIO OR RETURN OF THE PRODIGAL SON?
This is a widely discussed and debated scenario in the crypto sphere. What would happen if a movement on Satoshi Nakamoto’s wallet was noticed?
One can easily imagine the panic that this discovery would bring. Some people would think of a hidden message from its creator to announce that his invention has failed. Others would rationalize the situation by convincing themselves that moving is not selling.
But what if the reality was quite different? What if this hoard of about $20 billion at the moment has a very specific function for the very security of Bitcoin? This topic will be the culmination of a series of articles in which I will share with you the history of cryptography. How could it be turned upside down if, one day, one of the mathematical problems of the millennium were to be solved?
A good reason to finally understand, in a popularized way, all the workings and foundations of cryptography at the heart of Bitcoin. Better late than never!
THE ELECTRONIC SIGNATURE
Even before talking about blockchain, the electronic signature is the first fundamental brick of our beloved cryptocurrency. One of the elementary components of its cryptographic mechanisms. A decentralized blockchain-based electronic signature registry, which enables the exchange of a digital asset through its ability to keep track of all transactions made. That’s what Bitcoin is. But why are they necessary?
Let’s take your Facebook connection as an example. What would happen if your login request included your password and username in clear text? A hacker could intervene when sending your data to the server, pretend to be Facebook and steal it. Even encryption doesn’t seem to be enough. Because the hacker could directly transmit the encrypted credentials to connect on your behalf.
So how can you be sure that you are communicating with Facebook? This is where the need for an electronic signature comes in, necessary for any kind of secure authentication on the web. Whether it is to sign a document, or to connect to your favorite social network. An authentication, sometimes without even having to reveal your password or your private key. But how does it work?
Before answering this question, let’s look at the properties that a signature must satisfy in order to allow your authentication through the example of our handwritten signatures:
- Authenticity: the signature must allow to find the identity or the pseudonym of the signer. Not very obvious when you look at the scribbles we use to sign our bank checks.
- Infalifiability: the signature must prove that only you are able to provide it and that it cannot come from an impersonator. So much for our parents’ handwritten signatures, successfully copied into our correspondence books in our early school years.
- Non reusability: the signature needs to be unique and associated with each signed document. This is perhaps the only property that handwritten signatures meet with sufficient robustness.
- Unalterability: once a document is signed, it must become unalterable in order to avoid any modification that you would not have approved. This is why we avoid signing a blank check. You will not be able to dispute the written amount later.
- Irrevocability: Finally, the signature must be irrevocable. If it meets all the above properties, the signatory is necessarily the author of it and must not be able to deny it. This can quickly cause problems when a handwritten signature or a paper document is not immutable.
The security of handwritten signatures is therefore very imperfect. On the other hand, these properties are imperative for protocols such as Bitcoin.
To return to my Facebook example, in order to allow your connection to be secure, the platform must authenticate itself to the server to ensure that it is not a hacker trying to impersonate you. To do this, an asymmetric cryptography protocol is used, just like when you sign transactions on the blockchain. Once authenticated, Facebook and the server will exchange data using symmetric cryptography, which is simpler and less resource-intensive.
The very functioning of the electronic signature is intrinsically linked to the chosen cryptographic protocol.
THE TWO MAIN TYPES OF CRYPTOGRAPHY
There are two main types of cryptography. Symmetric cryptography, where you and your interlocutor have a single key to encrypt and decrypt your exchanges. And asymmetric cryptography, where you each have two keys, one public and one private.
To explain how symmetric cryptography works, let’s take a simple example:
To communicate secretly, Alice and Bob agree on a random number, 12. In order to send each other a message, they will encrypt it by shifting each letter of their messages in the alphabet by 12 ranks. The letter A will become M, the letter B will become N, etc. When they receive a message, they just have to shift all the letters of the message in the opposite direction again to find its original meaning. Not very robust, you will agree. But other systems are conceivable. For example, a mathematical sequence that would change the encryption key with each letter of the message.
But symmetric cryptography has a flaw. To be able to speak secretly, Alice and Bob must first agree on the encryption key to be used. But this agreement is not encrypted and cannot be perfectly secret. It therefore seems impossible to speak secretly without having spoken non-secretly beforehand. Until the invention of the Diffie-Hellman key exchange which will lead to the advent of asymmetric cryptography.
This mechanism was first conceived by cryptographers Whitfield Diffie and Martin Hellman in 1976. It allows two interlocutors who have never communicated before to secretly exchange an encryption key that will be used in future conversations.
This system is based on the use of what is called a one-way mathematical function. It acts in such a way that the result of this function applied to a number is easily calculated. On the contrary, the reverse path, i.e. finding the initial number starting from the result, is a very complex calculation and impossible in a humanly reasonable time. This computational security is called the Diffie-Hellman decision hypothesis. Even if the encryption function were to become public, there would be no need to worry, the message would remain undecipherable.
Let’s take our two interlocutors Alice and Bob again:
Alice and Bob will choose in a non-secret way a number that will be used as a public key, let’s call it g, and they each have a private key, respectively a and b. In order to agree on a symmetric encryption key for their future conversations, named C, they will perform the following calculations:
- Alice performs the calculation A = g^a and sends the result A to Bob.
- Bob performs the calculation B = g^b and sends the result B to Alice.
- Alice receives the number B and then performs the calculation C = B^a = (g^b)^a.
- Bob receives the number A and performs the calculation C = A^b = (g^a)^b.
If you haven’t forgotten your middle school math lessons, you will have noticed that the calculations g^b^a and g^a^b lead to the same result! So Alice and Bob have found a common secret key to do symmetric cryptography without ever exchanging it and without anyone else being able to calculate it, as long as their private key stays… private!
The power function serves as a one-way function. If a third person has access to the entire exchange between Alice and Bob and knows the numbers g, A and B, this person will not be able to find the private keys a and b and the final result C.
In order to ensure that these calculations cannot be performed in the reverse path, a and b must be very large numbers. For cryptography lovers, I have deliberately left out the modular mathematics part. It is used to simplify Alice’s and Bob’s calculations (and to make sure that neither of them can calculate the private key of his friend) so that nobody is drowned. Just understand that this is a mathematical trick that allows you to achieve powers of numbers very easily. Even the biggest calculators in the world would not be able to calculate for example 6³⁰⁰⁰. If you want to understand more in depth, I suggest you wait for my next article!
The Diffie-Hellman key exchange brings a whole new way of seeing cryptography. It allows an end-to-end confidentiality as well as a robustness that far exceeds what our most powerful computers are able to compute as long as the users’ private keys are large enough numbers. But it does not yet meet all the requirements that an electronic signature must have. We’re only touching Bitcoin’s asymmetric cryptography with our fingertips. To go further, we’ll look at RSA encryption and then move on to the encryption that Bitcoin uses, ECDSA encryption.
But how on earth could these great cryptographic principles and the security they imply lead to the “death of Bitcoin”? I’ll save this for my next articles, so you’ll have to be patient and come back next week!
