While Bitcoin's pseudonymous nature offers a level of privacy, all transactions are public on the blockchain, allowing for potential analysis that could link identities to transactions. To enhance privacy and security, advanced cryptographic techniques such as homomorphic encryption can be applied. using Microsoft SEAL, a C++ library for homomorphic encryption, to demonstrate how privacy could be further protected in Bitcoin transactions, particularly in privacy-focused protocols like CoinJoin.
Homomorphic encryption allows computations on encrypted data without needing to decrypt it first. This property can be particularly useful in Bitcoin transactions for various reasons... Users can participate in transactions without revealing their transaction amounts or other sensitive data to other parties or the public blockchain.
Secure Multi-party Computations, enables the creation of complex multi-party protocols where inputs are kept private.
Setting up Encryption Each participant uses a common encryption scheme set up using Microsoft SEAL. This ensures all parties can operate on the data homomorphically. users encrypt their UTXO values. This encryption does not reveal the amount of bitcoins each user intends to mix, but allows operations to be performed on the encrypted values.
Ciphertext encrypted_utxo = encrypt_utxo_amount(context, utxo_amount, public_key, encryptor);
Serialize and Share Encrypted UTXOs, Once encrypted, UTXO data can be serialized and securely shared with other participants or a coordinating server without revealing the actual values.
string serialized_utxo = serialize_encrypted_utxo(encrypted_utxo);
Aggregate Encrypted UTXOs, A trusted coordinator or the participants themselves can aggregate the encrypted UTXOs. This aggregation is performed homomorphically, ensuring that no individual inputs are exposed.
Ciphertext aggregated_utxos = aggregate_utxos({encrypted_utxo1, encrypted_utxo2}, evaluator);
Check Aggregated UTXOs Against Threshold: To ensure the transaction meets certain criteria (e.g., minimum input threshold for a CoinJoin), a homomorphic operation checks if the aggregated encrypted value meets the required threshold.
bool meets_threshold = check_threshold(context, aggregated_utxos, threshold, decryptor, encoder);
Finalize Transaction: If the check passes, the transaction can proceed. This step would typically require converting the homomorphically encrypted data into a format suitable for a Bitcoin transaction, which may involve securely decrypting the data under strict protocols or through a zero-knowledge proof mechanism to maintain confidentiality.
#include
#include "seal/seal.h"
using namespace std;
using namespace seal;
// setup the encryption context
shared_ptr setup_context() {
EncryptionParameters parms(scheme_type::ckks);
size_t poly_modulus_degree = 8192;
parms.set_poly_modulus_degree(poly_modulus_degree);
parms.set_coeff_modulus(CoeffModulus::Create(poly_modulus_degree, { 60, 40, 40, 60 }));
auto context = SEALContext::Create(parms);
return context;
}
// encrypt a UTXO amount
Ciphertext encrypt_utxo_amount(shared_ptr context, double amount, PublicKey public_key, Encryptor& encryptor) {
CKKSEncoder encoder(context);
Plaintext plain;
double scale = pow(2.0, 40);
vector input{ amount };
encoder.encode(input, scale, plain);
Ciphertext encrypted;
encryptor.encrypt(plain, encrypted);
return encrypted;
}
// serialize a ciphertext (for sharing or storage)
string serialize_encrypted_utxo(const Ciphertext& encrypted) {
stringstream ss;
encrypted.save(ss);
return ss.str();
}
// deserialize a ciphertext
Ciphertext deserialize_encrypted_utxo(shared_ptr context, const string& data) {
stringstream ss(data);
Ciphertext encrypted(context);
encrypted.load(context, ss);
return encrypted;
}
// aggregate encrypted UTXOs
Ciphertext aggregate_utxos(const vector& utxos, Evaluator& evaluator) {
Ciphertext aggregated = utxos[0];
for (size_t i = 1; i < utxos.size(); ++i) {
evaluator.add_inplace(aggregated, utxos[i]);
}
return aggregated;
}
// check if aggregated UTXOs meet the threshold
bool check_threshold(shared_ptr context, const Ciphertext& aggregated, double threshold, Decryptor& decryptor, CKKSEncoder& encoder) {
// Subtract the threshold homomorphically
Plaintext plain_threshold;
encoder.encode(vector{threshold}, aggregated.scale(), plain_threshold);
Ciphertext encrypted_threshold;
Encryptor encryptor(context, decryptor.public_key());
encryptor.encrypt(plain_threshold, encrypted_threshold);
Ciphertext result;
Evaluator evaluator(context);
evaluator.sub(aggregated, encrypted_threshold, result);
// Decrypt
Plaintext result_plain;
decryptor.decrypt(result, result_plain);
vector result_vector;
encoder.decode(result_plain, result_vector);
return result_vector[0] >= 0;
}
int main() {
auto context = setup_context();
KeyGenerator keygen(context);
PublicKey public_key = keygen.public_key();
SecretKey secret_key = keygen.secret_key();
Encryptor encryptor(context, public_key);
Decryptor decryptor(context, secret_key);
CKKSEncoder encoder(context);
Ciphertext encrypted_utxo1 = encrypt_utxo_amount(context, 2.5, public_key, encryptor);
Ciphertext encrypted_utxo2 = encrypt_utxo_amount(context, 1.7, public_key, encryptor);
vector utxos{ encrypted_utxo1, encrypted_utxo2 };
Ciphertext aggregated = aggregate_utxos(utxos, Evaluator(context));
bool meets_threshold = check_threshold(context, aggregated, 4.0, decryptor, encoder);
cout << "Aggregated UTXOs meet threshold: " << (meets_threshold ? "true" : "false") << endl;
return 0;
}
While it's not 100% solid idea yet could be worth exploring further.
