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Extracting Uncompressed Public Key from Compressed Private Key in OpenSSL

When working with cryptographic keys, particularly those of the Elliptic Curve Cryptosystem (ECC) like ECDSA, it’s essential to understand how to extract the uncompressed public key from a compressed private key. In this article, we’ll delve into the process and provide an example code snippet using the OpenSSL library.

Compressed Private Key Format

The compressed private key format used by ECC keys is based on the Curve25519 key structure, which consists of several fields:

• ec_point: The elliptic curve point.

• base_string: A base string containing the compressed public key (more on this later).

• length: The length of the base string in bytes.

Compressed Public Key Format

The uncompressed public key format is similar but uses a different base string and has some differences:

• ec_point: Still an elliptic curve point.

• base_string: A base string containing the uncompressed public key (more on this later).

• length: The length of the base string in bytes.

Extracting Uncompressed Public Key from Compressed Private Key

To extract the uncompressed public key, you need to first decompress the compressed private key using OpenSSL’s ecdk library. This will provide you with a Base64 encoded string, which can be decoded to obtain the uncompressed public key.

Here’s an example code snippet in C++:

#include 

#include 

#include 


int main() {

    // Load your private key from a file or buffer

    EC_KEY* pKey = NULL;

    int ret = EC_KEY_new_by_curve_name(NID_secp256k1, NULL);

    if (ret != 0) {

        std::cerr << "Error loading private key" << std::endl;

        return 1;

    }


    // Decompress the compressed private key

    unsigned char* base64Enc = NULL; // Your compressed private key here

    ret = Base64_decode(base64Enc, NULL);

    if (ret != 0) {

        std::cerr << "Error decompressing private key" << std::endl;

        EC_KEY_free(pKey);

        return 1;

    }


    int len = strlen((char*)base64Enc); // Get the length of the base string

    unsigned char* uncompressedBase64 = new unsigned char[len];

    ret = Base64_decode(uncompressedBase64, NULL, len);

    if (ret != 0) {

        std::cerr << "Error decompressing private key" << std::endl;

        delete[] base64Enc; // Don't forget to free the memory!

        EC_KEY_free(pKey);

        return 1;

    }


    // Convert the uncompressed base string to a public key

    unsigned char* publicKey = NULL;

    ret = ECDP_key_from_bytes(&publicKey, uncompressedBase64, len);

    if (ret != 0) {

        std::cerr << "Error converting private key to public key" << std::endl;

        delete[] base64Enc; // Don't forget to free the memory!

        EC_KEY_free(pKey);

        return 1;

    }


    // Print the uncompressed public key

    unsigned char* pubStr = new unsigned char[256]; // Allocate some space for the string

    ret = ECDP_pub_key_to_str(publicKey, pubStr, 256);

    if (ret != 0) {

        std::cerr << "Error converting public key to string" << std::endl;

        delete[] base64Enc; // Don't forget to free the memory!

        EC_KEY_free(pKey);

        return 1;

    }


    // Free all allocated memory

    delete[] base64Enc;

    delete[] uncompressedBase64;

    delete[] publicKey;


    std::cout << "Uncompressed public key: " << pubStr << std::endl;


    // Clean up the private key (not necessary in this example)

    EC_KEY_free(pKey);


    return 0;

}

Note that you’ll need to replace base64Enc with your actual compressed private key.

Example Use Case

This code snippet is just a demonstration of how to extract an uncompressed public key from a compressed private key using OpenSSL.