Deriving an ECDSA uncompressed public key from a compressed one ποΈ is a simple and important step when working with cryptographic signatures π. To get started, take the compressed key, which is shorter in size (33 bytes) βοΈ, and apply some mathematical magic π§ββοΈ to it (involved in elliptic curve cryptography). This magic includes using the rules of the elliptic curve π to perform calculations π’, and finally, you’ll get the longer, 65-bytes ECDSA uncompressed public key π as a result! VoilΓ ! βοΈπ Now you can use your uncompressed key in various cryptographic applications with ease and confidence ππ!

Table of Contents

# π Unlocking the Secrets: Converting a Compressed ECDSA Public Key into an Uncompressed Format π€―

## Dive Deeper into the World of Cryptography and Ethereum π°

## Introduction

Hey there, cryptography enthusiasts! π Are you ready to unlock a secret? Today we have an exciting journey to embark on! We will be exploring the nifty world of cryptographyπ, specifically understanding how to convert a compressed ECDSA (Elliptic Curve Digital Signature Algorithm) public key into an uncompressed format. π

What are we waiting for? Let’s dive right in! π

## Table of Content:

- Overview of ECDSA and Public Keys
- Compressed vs. Uncompressed Public Keys
- Conversion Process: Step-by-Step Guide
- Practical Applications
- Conclusion

## 1οΈβ£ Overview of ECDSA and Public Keys

### π What is ECDSA?

ECDSA, which stands for Elliptic Curve Digital Signature Algorithm, is a cryptographic algorithm primarily used for digital signatures, secure transactions, and authentication πΌ. It is based on elliptic curve cryptography (ECC), which provides us with the same security levels as other public-key cryptographies, like RSA or Diffie-Hellman π, but with much smaller key sizes. π

This vital feature of smaller key size makes ECDSA more efficient, faster, and requires minimal processing power π₯. No wonder it is widely used in many applications, such as Bitcoin and Ethereum!

### π Public Keys in ECDSA

In ECDSA, the public key is essentially a point on an elliptic curve π. Just like other algorithms, a user has a keypair β including a private key and a public key. The private key is a large, secret integer value. On the other hand, the public key is derived from this private key using an elliptic curve point multiplication operation.

The public key can be widely distributed β‘, while the private key must be kept secret. The public key is used for verifying digital signatures, while the private key is used for signing messages or transactions. Simple yet elegant! π

## 2οΈβ£ Compressed vs. Uncompressed Public Key

Now that we have understood ECDSA and public keys, let’s delve deeper into our main topic: Compressed and Uncompressed public keys. π§

- Uncompressed Public Key: An uncompressed public key consists of the ‘x’ and ‘y’ coordinates of the elliptic curve point π―. This point represents the public key itself! Usually, uncompressed public keys are represented by a prefix “04,” followed by the x and y coordinates.
- Compressed Public Key: As the name suggests, a compressed public key is a shorter representation for the same public key value π€. It includes the ‘x’ coordinate and an additional flag (either “02” or “03”) that indicates which half of the curve the point lies on. This flag helps in recovering the ‘y’ coordinate when needed.

## 3οΈβ£ Conversion Process: Step-by-Step Guide

π‘ Are you eager to learn how to convert a compressed ECDSA public key into an uncompressed format? Follow this step-by-step guide! π

#### Prerequisites:

- Python 3.x π»
- install ecdsa package (Run
`pip install ecdsa`

to install)

#### Step 1: Import Libraries π

Import the required libraries by including the following lines in your Python script:

```
from ecdsa import VerifyingKey, SECP256k1
import codecs
```

#### Step 2: Define and Initialize the Compressed Public Key ποΈ

Next, define and initialize the compressed public key as a hexadecimal value like this:

```
compressed_public_key = "021a0d0321374027cd2f3bc3a5df5f5e5d7e123716207368dcb7f45bd08478295e"
```

Remember to replace “compressed_public_key” with your key value π.

#### Step 3: Convert Compressed Public Key to Uncompressed Format π

Now, let’s write a function to perform the actual conversion π

```
def convert_compressed_to_uncompressed_public_key(comp_key):
vk = VerifyingKey.from_string(codecs.decode(comp_key[2:], "hex"), curve=SECP256k1, hashfunc=None)
uncompressed_public_key = "04" + hex(vk.pubkey.point.x())[2:] + hex(vk.pubkey.point.y())[2:]
return uncompressed_public_key
```

In this function, we:

- Create a VerifyingKey object from the compressed key
- Recover the X and Y coordinates from the key object
- Reconstruct the uncompressed public key using the X and Y coordinates

#### Step 4: Call the Conversion Function and Print the Uncompressed Public Key π

Let’s put it all together now! Call the conversion function, passing the compressed public key as an argument, as shown below.

```
uncompressed_public_key = convert_compressed_to_uncompressed_public_key(compressed_public_key)
print("Uncompressed Public Key: ", uncompressed_public_key.upper())
```

Run the script, and voila! You should see the uncompressed public key displayed in the output. π₯³

## 4οΈβ£ Practical Applications

The process of converting a compressed public key to an uncompressed format has many practical uses, including:

- Deriving Ethereum addresses π¦
- Verifying transactions in Bitcoin and Ethereum networks πΈ
- Decoding transactions and developing blockchain tools π§
- Ensuring cryptographic integrity for secure communication π¬

## 5οΈβ£ Conclusion

And that’s a wrap! π We have successfully unlocked the secret to converting a compressed ECDSA public key into an uncompressed format. Now you can use your new-found knowledge to explore the exciting world of ECDSA and Ethereum even further! π

So, keep experimenting and have fun! Until next time, happy coding! π€π¨βπ»π©βπ»

**Disclaimer**: *We cannot guarantee that all information in this article is correct. THIS IS NOT INVESTMENT ADVICE! We may hold one or multiple of the securities mentioned in this article. NotSatoshi authors are coders, not financial advisors.*