BLS signature and multisignature schemas in Go and Solidity

This code demonstrates the following schemas. Sign functions signature are in GoLang, verifies are both in Golang and Solidity using Ethereum precompiled callbacks.

BLS signature scheme.

1. Alice signs a message.
2. Everyone verifies it using her public key.

secretKey, publicKey := bls.GenerateRandomKey()
signature := secretKey.Sign(message)
genuine := signature.Verify(publicKey, message)

Refer to sign_test.go for more code.

BLS signature aggregation (n-of-n multisignature).

1. A group of participants sign a message.
2. Their signatures are aggregated into one.
3. Everyone verifies the aggregated signature using the aggregated public key.

sig0 := priv0.Sign(msg)
sig1 := priv1.Sign(msg)
sig2 := priv2.Sign(msg)
genuine := sig0.Aggregate(sig1).Aggregate(sig2).Verify(pub0.Aggregate(pub2).Aggregate(pub1), message)

Refer to aggregated_test.go for more code.

Accountable-Subgroup Multisignatures (threshold signatures, m-of-n multisignatures).

1. A subgroup of a group of participants sign a message.
2. Their signatures are aggregated into one.
3. Everyone verifies the aggregated signature using
   • the aggregated signature,
   • the aggregated public key of the subgroup (who really signed),
   • the aggregated public key of all participants in the group (whether signed or not),
   • the bitmap representing the subgroup (who really signed) - this is what accountable is.

allPub := pub0.Aggregate(pub1).Aggregate(pub2)

// Setup phase - generate membership keys
mk0 := priv0.GenerateMembershipKeyPart(0, allPub, Simple).
    Aggregate(priv1.GenerateMembershipKeyPart(0, allPub, Simple)).
    Aggregate(priv2.GenerateMembershipKeyPart(0, allPub, Simple))
mk1 := priv0.GenerateMembershipKeyPart(1, allPub, Simple).
    Aggregate(priv1.GenerateMembershipKeyPart(1, allPub, Simple)).
    Aggregate(priv2.GenerateMembershipKeyPart(1, allPub, Simple))
mk2 := priv0.GenerateMembershipKeyPart(2, allPub, Simple).
    Aggregate(priv1.GenerateMembershipKeyPart(2, allPub, Simple)).
    Aggregate(priv2.GenerateMembershipKeyPart(2, allPub, Simple))

// Sign only by #0 and #2
mask := big.NewInt(0b101)
sig0 := priv0.Multisign(msg, allPub, mk0)
sig2 := priv2.Multisign(msg, allPub, mk2)
subSig := sig0.Aggregate(sig2)
subPub := pub0.Aggregate(pub2)

genuine := subSig.VerifyMultisig(allPub, subPub, msg, mask)

Refer to multisig_test.go for more code.

Inspired by

• https://gist.github.com/BjornvdLaan/ca6dd4e3993e1ef392f363ec27fe74c4
• https://github.com/ConsenSys/gpact/blob/main/common/common/src/main/solidity/BlsSignatureVerification.sol
• https://github.com/keep-network/keep-core/blob/main/solidity/contracts/cryptography/AltBn128.sol

References

1. Dan Boneh, Manu Drijvers, and Gregory Neven. Compact Multi-Signatures for Smaller Blockchains. https://crypto.stanford.edu/~dabo/pubs/abstracts/ASM.html
2. BLS signatures: better than Schnorr. https://medium.com/cryptoadvance/bls-signatures-better-than-schnorr-5a7fe30ea716
3. Dan Boneh, Victor Shoup. A Graduate Course in Applied Cryptography. Chapter 15: Elliptic curve cryptography and pairings. http://toc.cryptobook.us/
4. EIP-196: Precompiled contracts for addition and scalar multiplication on the elliptic curve alt_bn128. https://eips.ethereum.org/EIPS/eip-196

Prerequisites to run tests

1. Install go compiler: v1.16+ https://golang.org/doc/install

2. Install solc: v0.8+ https://docs.soliditylang.org/en/v0.8.6/installing-solidity.html

3. Install abigen:

    cd bls-crypto
    make dep
    cd $GOPATH/pkg/mod/github.com/ethereum/go-ethereum@*
    make devtools
   

Run tests

make test

Test parameters

Note that there are parameters specified in the aggregated_test.go file that affect the gas usage:

• MESSAGE_SIZE - size of the message being signed in bytes,
• PARTICIPANTS_NUMBER - total number of participants in a group who sign the message.