Encrypting/decrypting text strings using OpenSSL ECC

Question

How can I use OpenSSL\'s ECC support to encrypt or decrypt a text string? I am able to generate ECC private/public keys using OpenSSL APIs, but I don\'t know how to encrypt plai

Answer 1

ECC itself doesn't really define any encryption/decryption operations - algorithms built on elliptic curves do.

One example is Elliptic-Curve Diffie-Hellman. You could encrypt a message using ECDH by:

1. Generating an ephemeral EC key.
2. Using that key and the public key of the recipient, generate a secret using ECDH.
3. Use that secret as a key to encrypt the message with a symmetric cipher, like AES.
4. Transmit the encrypted message and the ephemeral public key generated in step 1.

To decrypt:

1. Load the ephemeral public key from the message.
2. Use that public key together with your recipient key to generate a secret using ECDH.
3. Use that secret as a key to decrypt the message with the symmetric cipher.

EDIT: The following is the basic idea to generate a secret using ECDH. First we need to define a key derivation function - this one uses the SHA1 hash.

void *KDF1_SHA1(const void *in, size_t inlen, void *out, size_t *outlen)
{
    if (*outlen < SHA_DIGEST_LENGTH)
        return NULL;
    else
        *outlen = SHA_DIGEST_LENGTH;
    return SHA1(in, inlen, out);
}

This is the ECDH code for the sender side. It assumes that the recipient's public key is already in "recip_key", and you have verified it with EC_KEY_check_key(). It also omits much important error checking, for the sake of brevity, which you will definitely want to include in production code.

EC_KEY *ephemeral_key = NULL;
const EC_GROUP *group = NULL;
unsigned char buf[SHA_DIGEST_LENGTH] = { 0 };

group = EC_KEY_get0_group(recip_key);
ephemeral_key = EC_KEY_new();
EC_KEY_set_group(ephemeral_key, group);

EC_KEY_generate_key(ephemeral_key);
ECDH_compute_key(buf, sizeof buf, EC_KEY_get0_public_key(recip_key), ephemeral_key, KDF1_SHA1);

After this the buffer 'buf' contains 20 bytes of material you can use for keying. This abbreviated example is based on the code in "ecdhtest.c" in the openssl source distribution - I suggest taking a look at it.

You will want to send the public key portion of ephemeral_key with the encrypted message, and securely discard the private key portion. A MAC over the data is also a good idea, and if you need more than 20 bytes of keying material a longer hash is probably in order.

The recipient does something similar, except that its private key already exists (since the sender had to know the corresponding public key beforehand), and the public key is recieved from the sender.

Answer 2

Since its so hard to find examples showing how to use ECC to encrypt data I thought I'd post some code for others to use. For the complete listing, check out my openssl-dev posting:

http://www.mail-archive.com/openssl-dev@openssl.org/msg28042.html

Basically its a flushed out usable version of how to use ECDH to secure a block of data. ECDH is used to generate a shared secret. The shared secret is then hashed using SHA 512. The resulting 512 bits are split up, with 256 serving as the key to the symmetric cipher (AES 256 in my example) and the other 256 bits used as the key for the HMAC. My implementation is loosely based on the ECIES standard outlined by SECG working group.

The key functions are ecies_encrypt() which accepts the public key in hex form and returns the encrypted data:

secure_t * ecies_encrypt(char *key, unsigned char *data, size_t length) {

void *body;
HMAC_CTX hmac;
int body_length;
secure_t *cryptex;
EVP_CIPHER_CTX cipher;
unsigned int mac_length;
EC_KEY *user, *ephemeral;
size_t envelope_length, block_length, key_length;
unsigned char envelope_key[SHA512_DIGEST_LENGTH], iv[EVP_MAX_IV_LENGTH], block[EVP_MAX_BLOCK_LENGTH];

// Simple sanity check.
if (!key || !data || !length) {
    printf("Invalid parameters passed in.\n");
    return NULL;
}

// Make sure we are generating enough key material for the symmetric ciphers.
if ((key_length = EVP_CIPHER_key_length(ECIES_CIPHER)) * 2 > SHA512_DIGEST_LENGTH) {
    printf("The key derivation method will not produce enough envelope key material for the chosen ciphers. {envelope = %i / required = %zu}", SHA512_DIGEST_LENGTH / 8,
            (key_length * 2) / 8);
    return NULL;
}

// Convert the user's public key from hex into a full EC_KEY structure.
if (!(user = ecies_key_create_public_hex(key))) {
    printf("Invalid public key provided.\n");
    return NULL;
}

// Create the ephemeral key used specifically for this block of data.
else if (!(ephemeral = ecies_key_create())) {
    printf("An error occurred while trying to generate the ephemeral key.\n");
    EC_KEY_free(user);
    return NULL;
}

// Use the intersection of the provided keys to generate the envelope data used by the ciphers below. The ecies_key_derivation() function uses
// SHA 512 to ensure we have a sufficient amount of envelope key material and that the material created is sufficiently secure.
else if (ECDH_compute_key(envelope_key, SHA512_DIGEST_LENGTH, EC_KEY_get0_public_key(user), ephemeral, ecies_key_derivation) != SHA512_DIGEST_LENGTH) {
    printf("An error occurred while trying to compute the envelope key. {error = %s}\n", ERR_error_string(ERR_get_error(), NULL));
    EC_KEY_free(ephemeral);
    EC_KEY_free(user);
    return NULL;
}

// Determine the envelope and block lengths so we can allocate a buffer for the result.
else if ((block_length = EVP_CIPHER_block_size(ECIES_CIPHER)) == 0 || block_length > EVP_MAX_BLOCK_LENGTH || (envelope_length = EC_POINT_point2oct(EC_KEY_get0_group(
        ephemeral), EC_KEY_get0_public_key(ephemeral), POINT_CONVERSION_COMPRESSED, NULL, 0, NULL)) == 0) {
    printf("Invalid block or envelope length. {block = %zu / envelope = %zu}\n", block_length, envelope_length);
    EC_KEY_free(ephemeral);
    EC_KEY_free(user);
    return NULL;
}

// We use a conditional to pad the length if the input buffer is not evenly divisible by the block size.
else if (!(cryptex = secure_alloc(envelope_length, EVP_MD_size(ECIES_HASHER), length, length + (length % block_length ? (block_length - (length % block_length)) : 0)))) {
    printf("Unable to allocate a secure_t buffer to hold the encrypted result.\n");
    EC_KEY_free(ephemeral);
    EC_KEY_free(user);
    return NULL;
}

// Store the public key portion of the ephemeral key.
else if (EC_POINT_point2oct(EC_KEY_get0_group(ephemeral), EC_KEY_get0_public_key(ephemeral), POINT_CONVERSION_COMPRESSED, secure_key_data(cryptex), envelope_length,
        NULL) != envelope_length) {
    printf("An error occurred while trying to record the public portion of the envelope key. {error = %s}\n", ERR_error_string(ERR_get_error(), NULL));
    EC_KEY_free(ephemeral);
    EC_KEY_free(user);
    secure_free(cryptex);
    return NULL;
}

// The envelope key has been stored so we no longer need to keep the keys around.
EC_KEY_free(ephemeral);
EC_KEY_free(user);

// For now we use an empty initialization vector.
memset(iv, 0, EVP_MAX_IV_LENGTH);

// Setup the cipher context, the body length, and store a pointer to the body buffer location.
EVP_CIPHER_CTX_init(&cipher);
body = secure_body_data(cryptex);
body_length = secure_body_length(cryptex);

// Initialize the cipher with the envelope key.
if (EVP_EncryptInit_ex(&cipher, ECIES_CIPHER, NULL, envelope_key, iv) != 1 || EVP_CIPHER_CTX_set_padding(&cipher, 0) != 1 || EVP_EncryptUpdate(&cipher, body,
        &body_length, data, length - (length % block_length)) != 1) {
    printf("An error occurred while trying to secure the data using the chosen symmetric cipher. {error = %s}\n", ERR_error_string(ERR_get_error(), NULL));
    EVP_CIPHER_CTX_cleanup(&cipher);
    secure_free(cryptex);
    return NULL;
}

// Check whether all of the data was encrypted. If they don't match up, we either have a partial block remaining, or an error occurred.
else if (body_length != length) {

    // Make sure all that remains is a partial block, and their wasn't an error.
    if (length - body_length >= block_length) {
        printf("Unable to secure the data using the chosen symmetric cipher. {error = %s}\n", ERR_error_string(ERR_get_error(), NULL));
        EVP_CIPHER_CTX_cleanup(&cipher);
        secure_free(cryptex);
        return NULL;
    }

    // Copy the remaining data into our partial block buffer. The memset() call ensures any extra bytes will be zero'ed out.
    memset(block, 0, EVP_MAX_BLOCK_LENGTH);
    memcpy(block, data + body_length, length - body_length);

    // Advance the body pointer to the location of the remaining space, and calculate just how much room is still available.
    body += body_length;
    if ((body_length = secure_body_length(cryptex) - body_length) < 0) {
        printf("The symmetric cipher overflowed!\n");
        EVP_CIPHER_CTX_cleanup(&cipher);
        secure_free(cryptex);
        return NULL;
    }

    // Pass the final partially filled data block into the cipher as a complete block. The padding will be removed during the decryption process.
    else if (EVP_EncryptUpdate(&cipher, body, &body_length, block, block_length) != 1) {
        printf("Unable to secure the data using the chosen symmetric cipher. {error = %s}\n", ERR_error_string(ERR_get_error(), NULL));
        EVP_CIPHER_CTX_cleanup(&cipher);
        secure_free(cryptex);
        return NULL;
    }
}

// Advance the pointer, then use pointer arithmetic to calculate how much of the body buffer has been used. The complex logic is needed so that we get
// the correct status regardless of whether there was a partial data block.
body += body_length;
if ((body_length = secure_body_length(cryptex) - (body - secure_body_data(cryptex))) < 0) {
    printf("The symmetric cipher overflowed!\n");
    EVP_CIPHER_CTX_cleanup(&cipher);
    secure_free(cryptex);
    return NULL;
}

else if (EVP_EncryptFinal_ex(&cipher, body, &body_length) != 1) {
    printf("Unable to secure the data using the chosen symmetric cipher. {error = %s}\n", ERR_error_string(ERR_get_error(), NULL));
    EVP_CIPHER_CTX_cleanup(&cipher);
    secure_free(cryptex);
    return NULL;
}

EVP_CIPHER_CTX_cleanup(&cipher);

// Generate an authenticated hash which can be used to validate the data during decryption.
HMAC_CTX_init(&hmac);
mac_length = secure_mac_length(cryptex);

// At the moment we are generating the hash using encrypted data. At some point we may want to validate the original text instead.
if (HMAC_Init_ex(&hmac, envelope_key + key_length, key_length, ECIES_HASHER, NULL) != 1 || HMAC_Update(&hmac, secure_body_data(cryptex), secure_body_length(cryptex))
        != 1 || HMAC_Final(&hmac, secure_mac_data(cryptex), &mac_length) != 1) {
    printf("Unable to generate a data authentication code. {error = %s}\n", ERR_error_string(ERR_get_error(), NULL));
    HMAC_CTX_cleanup(&hmac);
    secure_free(cryptex);
    return NULL;
}

HMAC_CTX_cleanup(&hmac);

return cryptex;
}

And ecies_decrypt() which takes the private key, again in hex form, and decrypts the previously secured buffer:

unsigned char * ecies_decrypt(char *key, secure_t *cryptex, size_t *length) {

HMAC_CTX hmac;
size_t key_length;
int output_length;
EVP_CIPHER_CTX cipher;
EC_KEY *user, *ephemeral;
unsigned int mac_length = EVP_MAX_MD_SIZE;
unsigned char envelope_key[SHA512_DIGEST_LENGTH], iv[EVP_MAX_IV_LENGTH], md[EVP_MAX_MD_SIZE], *block, *output;

// Simple sanity check.
if (!key || !cryptex || !length) {
    printf("Invalid parameters passed in.\n");
    return NULL;
}

// Make sure we are generating enough key material for the symmetric ciphers.
else if ((key_length = EVP_CIPHER_key_length(ECIES_CIPHER)) * 2 > SHA512_DIGEST_LENGTH) {
    printf("The key derivation method will not produce enough envelope key material for the chosen ciphers. {envelope = %i / required = %zu}", SHA512_DIGEST_LENGTH / 8,
            (key_length * 2) / 8);
    return NULL;
}

// Convert the user's public key from hex into a full EC_KEY structure.
else if (!(user = ecies_key_create_private_hex(key))) {
    printf("Invalid private key provided.\n");
    return NULL;
}

// Create the ephemeral key used specifically for this block of data.
else if (!(ephemeral = ecies_key_create_public_octets(secure_key_data(cryptex), secure_key_length(cryptex)))) {
    printf("An error occurred while trying to recreate the ephemeral key.\n");
    EC_KEY_free(user);
    return NULL;
}

// Use the intersection of the provided keys to generate the envelope data used by the ciphers below. The ecies_key_derivation() function uses
// SHA 512 to ensure we have a sufficient amount of envelope key material and that the material created is sufficiently secure.
else if (ECDH_compute_key(envelope_key, SHA512_DIGEST_LENGTH, EC_KEY_get0_public_key(ephemeral), user, ecies_key_derivation) != SHA512_DIGEST_LENGTH) {
    printf("An error occurred while trying to compute the envelope key. {error = %s}\n", ERR_error_string(ERR_get_error(), NULL));
    EC_KEY_free(ephemeral);
    EC_KEY_free(user);
    return NULL;
}

// The envelope key material has been extracted, so we no longer need the user and ephemeral keys.
EC_KEY_free(ephemeral);
EC_KEY_free(user);

// Use the authenticated hash of the ciphered data to ensure it was not modified after being encrypted.
HMAC_CTX_init(&hmac);

// At the moment we are generating the hash using encrypted data. At some point we may want to validate the original text instead.
if (HMAC_Init_ex(&hmac, envelope_key + key_length, key_length, ECIES_HASHER, NULL) != 1 || HMAC_Update(&hmac, secure_body_data(cryptex), secure_body_length(cryptex))
        != 1 || HMAC_Final(&hmac, md, &mac_length) != 1) {
    printf("Unable to generate the authentication code needed for validation. {error = %s}\n", ERR_error_string(ERR_get_error(), NULL));
    HMAC_CTX_cleanup(&hmac);
    return NULL;
}

HMAC_CTX_cleanup(&hmac);

// We can use the generated hash to ensure the encrypted data was not altered after being encrypted.
if (mac_length != secure_mac_length(cryptex) || memcmp(md, secure_mac_data(cryptex), mac_length)) {
    printf("The authentication code was invalid! The ciphered data has been corrupted!\n");
    return NULL;
}

// Create a buffer to hold the result.
output_length = secure_body_length(cryptex);
if (!(block = output = malloc(output_length + 1))) {
    printf("An error occurred while trying to allocate memory for the decrypted data.\n");
    return NULL;
}

// For now we use an empty initialization vector. We also clear out the result buffer just to be on the safe side.
memset(iv, 0, EVP_MAX_IV_LENGTH);
memset(output, 0, output_length + 1);

EVP_CIPHER_CTX_init(&cipher);

// Decrypt the data using the chosen symmetric cipher.
if (EVP_DecryptInit_ex(&cipher, ECIES_CIPHER, NULL, envelope_key, iv) != 1 || EVP_CIPHER_CTX_set_padding(&cipher, 0) != 1 || EVP_DecryptUpdate(&cipher, block,
        &output_length, secure_body_data(cryptex), secure_body_length(cryptex)) != 1) {
    printf("Unable to decrypt the data using the chosen symmetric cipher. {error = %s}\n", ERR_error_string(ERR_get_error(), NULL));
    EVP_CIPHER_CTX_cleanup(&cipher);
    free(output);
    return NULL;
}

block += output_length;
if ((output_length = secure_body_length(cryptex) - output_length) != 0) {
    printf("The symmetric cipher failed to properly decrypt the correct amount of data!\n");
    EVP_CIPHER_CTX_cleanup(&cipher);
    free(output);
    return NULL;
}

if (EVP_DecryptFinal_ex(&cipher, block, &output_length) != 1) {
    printf("Unable to decrypt the data using the chosen symmetric cipher. {error = %s}\n", ERR_error_string(ERR_get_error(), NULL));
    EVP_CIPHER_CTX_cleanup(&cipher);
    free(output);
    return NULL;
}

EVP_CIPHER_CTX_cleanup(&cipher);

*length = secure_orig_length(cryptex);
return output;
}

I'm posting this because I personally couldn't find any other examples of how to secure files using ECC and the OpenSSL library. That said its worth mentioning alternatives that don't use OpenSSL. One is seccure which follows a pattern similar to my example, only it relies libgcrypt. Since libgcrypt doesn't provide all of the underlying ECC functions needed, the seccure program fills in the gaps and implements the ECC logic missing from libgcrypt.

Another program worth looking at is SKS, which uses a similar ECC based encryption process as the example above, but doesn't have any external dependencies (so all the ECC code is right there for you to look at).