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

## Ultimate apocalyptic scenario or return of the prodigal son?

This is a much discussed and debated scenario in the cryptosphere. What would happen if we noticed a movement on the wallet of **Satoshi Nakamoto** ?

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

What if the reality was completely different? And if this crowd of approx **20 billion dollars** currently had a specific function for **Security** same as **Bitcoin** ? This subject will be the purpose of**a number of articles** which I want to share with you** history of cryptography**. How could this be disturbed if one day one of the **millennial math problems**should be solved?

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 we even talk about blockchain, **Electronic signature** is the first basic building block of our beloved cryptocurrency. One of the elementary components of its cryptographic mechanisms. A decentralized on-chain electronic signature ledger that enables the exchange of a digital asset through its ability to keep track of all transactions made. It is what **Bitcoin**. But why are they necessary?

Let’s take your connection as an example **Facebook**. What would happen if your login request included your username and password **clear** ? A hacker can intervene when you send your** data** to the server, pretend to be Facebook to the latter and **steal them**. Even encryption doesn’t seem to be enough. Because this hacker could directly transfer the encrypted identifiers to connect on your behalf.

So how can you be sure you communicate well with **Facebook** ? This is where the need for a** Electronic signature**necessary for every species **Approval** **sure** on the Internet. 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 we answer this question, let’s look at **Properties** which a signature must meet 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 we use to sign our bank checks.

**Obvious manipulation**: the signature must prove that only you are able to deliver it and that it cannot come**of a usurper**. Missing because of our parents’ manual signatures, successfully copied in our correspondence notebooks during our young years in college.

**Non-reusability**: the signature must be**unique and associated**with each signed document. Perhaps the only feature to which the handwritten signature responds with sufficient robustness.

**Immutability**: when a document is signed, it must remain unchanged to avoid possible**modification**which you would not approve. Therefore, we avoid signing a blank cheque. You will not be able to dispute the amount written afterwards.

**Irrevocability**: finally, the signature must be irrevocable. If it meets all the above characteristics, the signatory is necessarily**the author**of it and must not be able to**refuse**. This can quickly cause problems when a handwritten signature or 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**.

Going back to my example of** Facebook**, to allow your connection in a secure way, the platform must authenticate with the server to ensure that it is not a hacker trying to usurp your identity. To do this, **an asymmetric cryptography protocol** is used, just like when you sign transactions on the blockchain. Once approved, Facebook and the server will exchange data per **symmetric cryptography**because it is simpler and less resource-intensive.

The function of the electronic signature itself is inextricably linked to the chosen cryptographic protocol.

## The two main types of cryptography

### Symmetric cryptography

It exists **by them** main types of cryptography. L**has 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**. To send a message to each other, they will **cipher** by moving each letter of their messages in the 12-row alphabet. The letter **HAVE** will be **M**the letter **B** will be **DOES NOT**etc. When they receive a message, all they have to do is move all the letters in the message back in **the opposite direction** to regain its original meaning. Not very robust, you will agree. But other systems can be thought of. For example, a mathematical sequence that would change the encryption key with each letter in the message.

But it has symmetric cryptography **a mistake**. To be able to speak secretly, **Alice and Bob** must agree in advance which encryption key is to be used. But this agreement is not encrypted and cannot be completely secret. It therefore seems impossible to speak secretly without first speaking non-secretly. Until the invention of **Diffie-Hellman key exchange **which will lead to the emergence 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 Hellmann** in 1976. It allows two interlocutors who have never communicated before to secretly exchange an encryption key that will be used during their future conversations.

This system is based on the use of what is called** a one-way math function**. It thus appears that the result of this function applied to a number is **easy** calculable. Conversely, the reverse path, i.e. to find the initial number based on the result, a very complex calculation and **impossible** in a humanly reasonable time. This computational certainty is called** The Diffie-Hellman decision hypothesis**. Even if the encryption function became public, no worries, the message would remain **indescribable**.

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

**Alice** and **Bob** will in a non-secret way choose a number that acts as **public key**let’s call it **g** and each has one **private key**respectively, **have** and **b**. To agree on **a symmetric encryption key** for their future conversations, named **vs**they will perform the following calculations:

**Alice**perform the calculation**A = g^a**and send the result**HAVE**on**Bob**.**Bob**perform the calculation**B = g^b**and send the result**B**on**Alice**.**Alice**receives the number**B**and then perform the calculation**C = B^a = (g^b)^a**.**Bob**receives the number**HAVE**and do the calculation**C = A^b = (g^a)^b**.

If you haven’t forgotten your math classes in college, you’ve noticed that the calculations** g^b^a** and **g^a^b** lead to the same result! **Alice** and **Bob** therefore found a shared 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 works as **one-way function**. If a third person has access to all exchanges between **Alice** and **Bob** and know the numbers **g**, **HAVE** and **B**the latter will not be able to find the private keys **have** and **b** as well as the end result **vs**.

To ensure that it is impossible to perform these calculations in the opposite way, **have** and **b** must be **very large numbers**. For cryptography lovers, I have deliberately omitted the part **modular mathematics**. It is used to simplify the calculations of**Alice** and off **Bob** (and so neither of them can calculate his mate’s private key) so as not to drown anyone. Just understand that it is **a mathematical trick** which makes it possible to realize gigantic numbers forces very easily. Even the biggest calculators in the world would not be able to calculate e.g **6^3000**. If you want to understand more in depth, I suggest you wait for my next article!

**Diffie-Hellman key exchange **therefore bringing a whole new way of looking at crypto. It allows one **privacy** end-to-end as well as a robustness that far exceeds what our most powerful computers are capable of calculating, 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. Moving on, we’ll 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 will save this for my next articles, you will have to arm yourself with patience and come back **next week** !

*In crypto, do not skimp 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. Don’t wait to secure your capital (commercial link)!*