Did Satoshi Nakamoto Plan the Death of Bitcoin?

February 30, 2023 – the crypto winter continues to wear us down with its immobility which seems almost immutable. the bitcoin keep wandering around $18,000, and even the bad news seems to stop raining. And yet, this nightour on-chain data inspectors notice an event that was more expected. Satoshi Nakamoto transferred his million bitcoins to another wallet. Death warrant for Bitcoin?

Ultimate apocalyptic scenario or return of the prodigal son?

This is a widely discussed and debated scenario in the crypto sphere. What would happen if we noticed a movement on the wallet of Satoshi Nakamoto ?

One can easily imagine the wave of panic that this discovery would accompany. Some would think of a hidden message of its creator to announce that his invention failed. Others would rationalize the situation by convincing themselves that moving is not selling.

What if the reality was quite different? And if this hoard of about $20 billion currently had a specific function for Security same as Bitcoin ? This subject will be the purpose ofa series of articles in which I will share with you the history of cryptography. How could this be upset if, one day, one of the millennial math problemswas to be resolved?

A good reason to finally understand, in a popular way, all the cogs and foundations of cryptography at the heart of Bitcoin. Better late than never !

The electronic signature

Secure authentication

Before even talking about blockchain, electronic signature is the first fundamental building block of our beloved cryptocurrency. One of the elementary components of its cryptographic mechanisms. A decentralized on-chain electronic signature ledger, which enables the exchange of a digital asset through its ability to keep track of all transactions made. That’s what Bitcoin. But why are they necessary?

Let’s take as an example your connection to Facebook. What would happen if your login request included your username and password clear ? A hacker could intervene when sending your data to the server, pretend to be Facebook to the latter and steal them. Even encryption does not seem sufficient. Because this hacker could directly transmit the encrypted identifiers to connect on your behalf.

So how can you be sure that you are communicating well with Facebook ? This is where the need for a electronic signaturenecessary for any kind authentication secure on the Web. Whether it’s to sign a document, or connect to your favorite social network. Authentication, sometimes without even having to reveal your password or private key. But how does it work ?

The five components of a secure signature

Before answering this question, let’s look at Properties which a signature must satisfy in order to allow your authentication through the example of our handwritten signatures :

• Authenticity : the signature must make it possible to find identity or the pseudonym of the signatory. Not very obvious when you look at the scribbles that we use to sign our bank checks.

• Tamper-evident : the signature must prove that only you are able to provide it and that it cannot come of a usurper. Missed for the manual signatures of our parents, copied successfully in our correspondence notebooks during our young years of college.

• Non-reusability : the signature needs to be unique and associated with each signed document. Perhaps the only property to which the handwritten signature responds with enough robustness.

• Inalterability : when a document is signed, it must become unalterable in order to avoid any change that you wouldn’t approve of. This is why we avoid signing a blank check. You will not be able to dispute the amount written afterwards.

• Irrevocability : finally, the signature must be irrevocable. If it meets all the properties above, the signer is necessarily the author of it and must not be able deny. 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 imperatively necessary for protocols such as Bitcoin.

Going back to my example of Facebook, in order to allow your connection in a secure way, the platform must authenticate itself with the server in order to ensure that it is not a hacker who is trying to usurp your identity. 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 by symmetric cryptographybecause it 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

Symmetric Cryptography

It exists of them major types of cryptography. Lhas 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 number, at random, 12. In order to send a message to each other, they will cipher by shifting each letter of their messages in the alphabet by 12 rows. The letter HAS will become Mthe letter B will become NOT, etc. When they receive a message, they only have to shift again all the letters of the message in the opposite direction to regain 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 agree in advance 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 Diffie-Hellman key exchange which will lead to the advent of asymmetric cryptography.

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Diffie-Hellman key exchange and asymmetric cryptography

This mechanism was first thought of by cryptographers Whitfield Diffie and Martin Hellman in 1976. It allows two interlocutors who have never communicated before, to secretly exchange an encryption key which will be used during their future conversations.

This system is based on the use of what is called a one-way math function. It acts so that the result of this function applied to a number is easily calculable. Conversely, 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 became public, no worries, the message would remain indecipherable.

Let’s go back to our two interlocutors Alice and Bob :

Alice and Bob will choose in a non-secret way a number which will serve as public keylet’s call it g and each have a private keyrespectively, has and b. In order to agree on a symmetric encryption key for their future conversations, named VSthey will perform the following calculations:

• Alice perform the calculation A = g^a and send the result HAS at Bob.
• Bob perform the calculation B = g^b and send the result B at Alice.
• Alice receives the number B and then perform the calculation C = B^a = (g^b)^a.
• Bob receives the number HAS and do the calculation C = A^b = (g^a)^b.

If you haven’t forgotten your college math lessons, you’ll have noticed that the calculations g^b^a and g^a^b lead to the same result! Alice and Bob therefore found a common secret key to do symmetric cryptography without never exchange it and without anyone being able to calculate it… As long as their private key, the rest !

The power function serves as one-way function. If a third person having access to all the exchanges between Alice and Bob and knowing the numbers g, HAS and Bthe latter will not be able to find the private keys has and b as well as the end result VS.

In order to ensure that performing these calculations in the reverse path is impossible, has and b have to be very large numbers. For the cryptography lovers, I deliberately glossed over the part modular mathematics. It is used to simplify the calculations ofAlice and of Bob (and so that neither of them can calculate his comrade’s private key) so as not to drown anyone. Just understand that it is a math trick which makes it possible to realize gigantic powers of numbers very easily. Even the greatest calculators in the world would not be able to calculate for example 6^3000. If you want to understand more in depth, I suggest you wait for my next article!

The Diffie-Hellman key exchange therefore brings a whole new way of looking at crypto. It allows a privacy end-to-end as well as a robustness that far exceeds what our most powerful computers are able to calculate as long as the users’ private keys are sufficiently large numbers. big. But the latter does not yet meet all the conditions that an electronic signature must have. We only touch Bitcoin’s asymmetric cryptography with our fingertips. To go further, we will look at encryption RSA to finally address the encryption used by bitcoin, the encryption ECDSA.

But how on earth could these great cryptographic principles and the security they imply lead to the “death of Bitcoin”? I keep this for my next articles, you will have to arm yourself with patience and come back next week !

In crypto, do not economize on caution! So, to keep your crypto assets safe, the best solution is still a personal hardware wallet. At Ledger, there is something for all profiles and all cryptos. Do not wait to put your capital in safety (commercial link)!