BLS Signatures implementation

NOTE: THIS LIBRARY IS A DRAFT AND NOT YET REVIEWED FOR SECURITY

Implements BLS signatures with aggregation as in Boneh, Drijvers, Neven 2018, using relic toolkit for cryptographic primitives (pairings, EC, hashing). The BLS12-381 curve is used. The spec is here.

Features:

• Non-interactive signature aggregation on identical or distinct messages
• Aggregate aggregates (trees)
• Efficient verification (only one pairing per distinct message)
• Security against rogue public key attack
• Aggregate public keys and private keys
• HD (BIP32) key derivation
• Key and signature serialization
• Batch verification
• Signature division (divide an aggregate by a previously verified signature)
• Python bindings
• Pure python bls12-381 and signatures

Import the library

#include "bls.hpp"

Creating keys and signatures

// Example seed, used to generate private key. Always use
// a secure RNG with sufficient entropy to generate a seed.
uint8_t seed[] = {0, 50, 6, 244, 24, 199, 1, 25, 52, 88, 192,
                  19, 18, 12, 89, 6, 220, 18, 102, 58, 209,
                  82, 12, 62, 89, 110, 182, 9, 44, 20, 254, 22};

bls::PrivateKey sk = bls::PrivateKey::FromSeed(seed, sizeof(seed));
bls::PublicKey pk = sk.GetPublicKey();

uint8_t msg[] = {100, 2, 254, 88, 90, 45, 23};

bls::Signature sig = sk.Sign(msg, sizeof(msg));

Serializing keys and signatures to bytes

uint8_t skBytes[bls::PrivateKey::PRIVATE_KEY_SIZE];  // 32 byte array
uint8_t pkBytes[bls::PublicKey::PUBLIC_KEY_SIZE];    // 48 byte array
uint8_t sigBytes[bls::Signature::SIGNATURE_SIZE];    // 96 byte array

sk.Serialize(skBytes);   // 32 bytes
pk.Serialize(pkBytes);   // 48 bytes
sig.Serialize(sigBytes); // 96 bytes

Loading keys and signatures from bytes

// Takes array of 32 bytes
sk = bls::PrivateKey::FromBytes(skBytes);

// Takes array of 48 bytes
pk = bls::PublicKey::FromBytes(pkBytes);

// Takes array of 96 bytes
sig = bls::Signature::FromBytes(sigBytes);

Verifying signatures

// Add information required for verification, to sig object
sig.SetAggregationInfo(bls::AggregationInfo::FromMsg(pk, msg, sizeof(msg)));

bool ok = sig.Verify();

Aggregate signatures for a single message

// Generate some more private keys
seed[0] = 1;
bls::PrivateKey sk1 = bls::PrivateKey::FromSeed(seed, sizeof(seed));
seed[0] = 2;
bls::PrivateKey sk2 = bls::PrivateKey::FromSeed(seed, sizeof(seed));

// Generate first sig
bls::PublicKey pk1 = sk1.GetPublicKey();
bls::Signature sig1 = sk1.Sign(msg, sizeof(msg));

// Generate second sig
bls::PublicKey pk2 = sk2.GetPublicKey();
bls::Signature sig2 = sk2.Sign(msg, sizeof(msg));

// Aggregate signatures together
vector<bls::Signature> sigs = {sig1, sig2};
bls::Signature aggSig = bls::Signature::Aggregate(sigs);

// For same message, public keys can be aggregated into one.
// The signature can be verified the same as a single signature,
// using this public key.
vector<bls::PublicKey> pubKeys = {pk1, pk2};
bls::PublicKey aggPubKey = bls::Signature::Aggregate(pubKeys);

Aggregate signatures for different messages

// Generate one more key and message
seed[0] = 3;
bls::PrivateKey sk3 = bls::PrivateKey::FromSeed(seed, sizeof(seed));
bls::PublicKey pk3 = sk3.GetPublicKey();
uint8_t msg2[] = {100, 2, 254, 88, 90, 45, 23};

// Generate the signatures, assuming we have 3 private keys
sig1 = sk1.Sign(msg, sizeof(msg));
sig2 = sk2.Sign(msg, sizeof(msg));
bls::Signature sig3 = sk3.Sign(msg2, sizeof(msg2));

// They can be noninteractively combined by anyone
// Aggregation below can also be done by the verifier, to
// make batch verification more efficient
vector<bls::Signature> sigsL = {sig1, sig2};
bls::Signature aggSigL = bls::Signature::Aggregate(sigsL);

// Arbitrary trees of aggregates
vector<bls::Signature> sigsFinal = {aggSigL, sig3};
bls::Signature aggSigFinal = bls::Signature::Aggregate(sigsFinal);

// Serialize the final signature
aggSigFinal.Serialize(sigBytes);

Verify aggregate signature for different messages

// Deserialize aggregate signature
aggSigFinal = bls::Signature::FromBytes(sigBytes);

// Create aggregation information (or deserialize it)
bls::AggregationInfo a1 = bls::AggregationInfo::FromMsg(pk1, msg, sizeof(msg));
bls::AggregationInfo a2 = bls::AggregationInfo::FromMsg(pk2, msg, sizeof(msg));
bls::AggregationInfo a3 = bls::AggregationInfo::FromMsg(pk3, msg2, sizeof(msg2));
vector<bls::AggregationInfo> infos = {a1, a2};
bls::AggregationInfo a1a2 = bls::AggregationInfo::MergeInfos(infos);
vector<bls::AggregationInfo> infos2 = {a1a2, a3};
bls::AggregationInfo aFinal = bls::AggregationInfo::MergeInfos(infos2);

// Verify final signature using the aggregation info
aggSigFinal.SetAggregationInfo(aFinal);
ok = aggSigFinal.Verify();

// If you previously verified a signature, you can also divide
// the aggregate signature by the signature you already verified.
ok = aggSigL.Verify();
vector<bls::Signature> cache = {aggSigL};
aggSigFinal = aggSigFinal.DivideBy(cache);

// Final verification is now more efficient
ok = aggSigFinal.Verify();

Aggregate private keys

vector<bls::PrivateKey> privateKeysList = {sk1, sk2};
vector<bls::PublicKey> pubKeysList = {pk1, pk2};

// Create an aggregate private key, that can generate
// aggregate signatures
const bls::PrivateKey aggSk = bls::PrivateKey::Aggregate(
        privateKeys, pubKeys);

bls::Signature aggSig3 = aggSk.Sign(msg, sizeof(msg));

HD keys

// Random seed, used to generate master extended private key
uint8_t seed[] = {1, 50, 6, 244, 24, 199, 1, 25, 52, 88, 192,
                  19, 18, 12, 89, 6, 220, 18, 102, 58, 209,
                  82, 12, 62, 89, 110, 182, 9, 44, 20, 254, 22};

bls::ExtendedPrivateKey esk = bls::ExtendedPrivateKey::FromSeed(
        seed, sizeof(seed));

bls::ExtendedPublicKey epk = esk.GetExtendedPublicKey();

// Use i >= 2^31 for hardened keys
bls::ExtendedPrivateKey skChild = esk.PrivateChild(0)
                                .PrivateChild(5);

bls::ExtendedPublicKey pkChild = epk.PublicChild(0)
                               .PublicChild(5);

// Serialize extended keys
uint8_t buffer1[bls::ExtendedPublicKey::ExtendedPublicKeySize]   // 93 bytes
uint8_t buffer2[bls::ExtendedPrivateKey::ExtendedPrivateKeySize] // 77 bytes

pkChild.Serialize(buffer1);
skChild.Serialize(buffer2);

Build

Cmake, a c++ compiler, and python3 (for bindings) are required for building.

git submodule update --init --recursive
mkdir build
cd build
cmake ../
cmake --build . -- -j 6

Run tests

./build/src/runtest

Run benchmarks

./build/src/runbench

Link the library to use it

g++ -Wl,-no_pie  -Ibls-signatures/contrib/relic/include -Ibls-signatures/build/contrib/relic/incl
ude -Ibls-signatures/src/  -L./bls-signatures/build/ -l bls  yourfile.cpp

Notes on dependencies

Changes performed to relic: Added config files for Chia, and added gmp include in relic.h, new ep_map and ep2_map, new ep_pck and ep2_pck. Custom inversion function. Note: relic is used with the Apache 2.0 license.

Libsodium and GMP are optional dependencies: libsodium gives secure memory allocation, and GMP speeds up the library by ~ 3x. To install them, either download them from github and follow the instructions for each repo, or use a package manager like APT or brew.

Discussion

Discussion about this library and other Chia related development is on Keybase. Install Keybase, and run the following to join the Chia public channels:

keybase team request-access chia_network.public

Code style

• Always use uint8_t for bytes
• Use size_t for size variables
• Uppercase method names
• Prefer static constructors
• Avoid using templates
• Objects allocate and free their own memory
• Use cpplint with default rules

TODO

• Serialize aggregation info
• Secure allocation during signing, key derivation
• Threshold signatures
• Remove unnecessary dependency files
• Constant time and side channel attacks
• Adaptor signatures / Blind signatures
• More tests vectors (failed verifications, etc)

Specification and test vectors

The specification and test vectors can be found here. Test vectors can also be seen in the python or cpp test files.