Go implementation of the Schnorr BIP
This is a Go implementation of the standard 64-byte Schnorr signature scheme over the elliptic curve secp256k1.
The code is based upon the initial proposal of Pieter Wuille when it didn't have a BIP number assigned yet.
The current version passes all test vectors provided here. But the author does not give any guarantees that the algorithm is implemented correctly for every edge case!
Table of Contents
- Usage
- API
- Sign(privateKey *big.Int, message [32]byte) ([64]byte, error)
- Verify(publicKey [33]byte, message [32]byte, signature [64]byte) (bool, error)
- BatchVerify(publicKeys [][33]byte, messages [][32]byte, signatures [][64]byte) (bool, error)
- AggregateSignatures(privateKeys []*big.Int, message [32]byte) ([64]byte, error)
- Benchmark
- Credit
Usage
Install using:
go get -u github.com/hbakhtiyor/schnorrIn your code:
import "github.com/hbakhtiyor/schnorr"
signature, err := schnorr.Sign(privateKey, message)
result, err := schnorr.Verify(publicKey, message, signature)
result, err := schnorr.BatchVerify(publicKeys, messages, signatures)
signature, err := schnorr.AggregateSignatures(privateKeys, message)API
Requiring the module gives an object with four methods:
Sign(privateKey *big.Int, message [32]byte) ([64]byte, error)
Sign a 32-byte message with the private key, returning a 64-byte signature. Read more
Arguments
- privateKey (*big.Int): The integer secret key in the range 1..n-1.
- message ([32]byte): The 32-byte array message.
Returns
([64]byte, error): A 64-byte array signature. An error if signing fails.
Examples
var message [32]byte
privateKey, _ := new(big.Int).SetString("B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF", 16)
msg, _ := hex.DecodeString("243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89")
copy(message[:], msg)
signature, err := schnorr.Sign(privateKey, message)
if err != nil {
fmt.Printf("The signing is failed: %v\n", err)
}
fmt.Printf("The signature is: %x\n", signature)Verify(publicKey [33]byte, message [32]byte, signature [64]byte) (bool, error)
Verify a 64-byte signature of a 32-byte message against the public key. Read more
Arguments
- publicKey ([33]byte): The 33-byte array public key.
- message ([32]byte): The 32-byte array message.
- signature ([64]byte): The 64-byte array signature.
Returns
(bool, error): True if signature is valid, An error if verification fails.
Examples
var (
publicKey [33]byte
message [32]byte
signature [64]byte
)
pk, _ := hex.DecodeString("02DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659")
copy(publicKey[:], pk)
msg, _ := hex.DecodeString("243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89")
copy(message[:], msg)
sig, _ := hex.DecodeString("2A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D1E51A22CCEC35599B8F266912281F8365FFC2D035A230434A1A64DC59F7013FD")
copy(signature[:], sig)
if result, err := schnorr.Verify(publicKey, message, signature); err != nil {
fmt.Printf("The signature verification failed: %v\n", err)
} else if result {
fmt.Println("The signature is valid.")
}BatchVerify(publicKeys [][33]byte, messages [][32]byte, signatures [][64]byte) (bool, error)
Verify a list of 64-byte signatures of a 32-byte messages against the public keys. Read more
Arguments
- publicKeys ([][33]byte): The list of 33-byte array public keys.
- messages ([][32]byte): The list of 32-byte array messages.
- signatures ([][64]byte): The list of 64-byte array signatures.
Returns
(bool, error): True if all signatures are valid, An error if one verification fails.
Examples
var (
publicKey [33]byte
message [32]byte
signature [64]byte
publicKeys [][33]byte
messages [][32]byte
signatures [][64]byte
)
pk, _ := hex.DecodeString("02DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659")
copy(publicKey[:], pk)
publicKeys = append(publicKeys, publicKey)
pk, _ = hex.DecodeString("03FAC2114C2FBB091527EB7C64ECB11F8021CB45E8E7809D3C0938E4B8C0E5F84B")
copy(publicKey[:], pk)
publicKeys = append(publicKeys, publicKey)
pk, _ = hex.DecodeString("026D7F1D87AB3BBC8BC01F95D9AECE1E659D6E33C880F8EFA65FACF83E698BBBF7")
copy(publicKey[:], pk)
publicKeys = append(publicKeys, publicKey)
msg, _ := hex.DecodeString("243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89")
copy(message[:], msg)
messages = append(messages, message)
msg, _ = hex.DecodeString("5E2D58D8B3BCDF1ABADEC7829054F90DDA9805AAB56C77333024B9D0A508B75C")
copy(message[:], msg)
messages = append(messages, message)
msg, _ = hex.DecodeString("B2F0CD8ECB23C1710903F872C31B0FD37E15224AF457722A87C5E0C7F50FFFB3")
copy(message[:], msg)
messages = append(messages, message)
sig, _ := hex.DecodeString("2A298DACAE57395A15D0795DDBFD1DCB564DA82B0F269BC70A74F8220429BA1D1E51A22CCEC35599B8F266912281F8365FFC2D035A230434A1A64DC59F7013FD")
copy(signature[:], sig)
signatures = append(signatures, signature)
sig, _ = hex.DecodeString("00DA9B08172A9B6F0466A2DEFD817F2D7AB437E0D253CB5395A963866B3574BE00880371D01766935B92D2AB4CD5C8A2A5837EC57FED7660773A05F0DE142380")
copy(signature[:], sig)
signatures = append(signatures, signature)
sig, _ = hex.DecodeString("68CA1CC46F291A385E7C255562068357F964532300BEADFFB72DD93668C0C1CAC8D26132EB3200B86D66DE9C661A464C6B2293BB9A9F5B966E53CA736C7E504F")
copy(signature[:], sig)
signatures = append(signatures, signature)
if result, err := schnorr.BatchVerify(publicKeys, messages, signatures); err != nil {
fmt.Printf("The signature verification failed: %v\n", err)
} else if result {
fmt.Println("The signature is valid.")
}AggregateSignatures(privateKeys []*big.Int, message [32]byte) ([64]byte, error)
Aggregate multiple signatures of different private keys over the same message into a single 64-byte signature.
Arguments
- privateKeys ([]*big.Int): The list of integer secret keys in the range 1..n-1.
- message ([32]byte): The list of 32-byte array messages.
Returns
(bool, error): True if all signatures are valid, An error if one verification fails. ([64]byte, error): A 64-byte array signature. An error if signing fails.
Examples
var (
publicKey [33]byte
message [32]byte
)
privateKey1, _ := new(big.Int).SetString("B7E151628AED2A6ABF7158809CF4F3C762E7160F38B4DA56A784D9045190CFEF", 16)
privateKey2, _ := new(big.Int).SetString("C90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74020BBEA63B14E5C7", 16)
msg, _ := hex.DecodeString("243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89")
copy(message[:], msg)
privateKeys := []*big.Int{privateKey1, privateKey2}
signature, _ := schnorr.AggregateSignatures(privateKeys, message)
// verifying an aggregated signature
pk, _ := hex.DecodeString("02DFF1D77F2A671C5F36183726DB2341BE58FEAE1DA2DECED843240F7B502BA659")
copy(publicKey[:], pk)
P1x, P1y := schnorr.Unmarshal(Curve, publicKey[:])
pk, _ = hex.DecodeString("03FAC2114C2FBB091527EB7C64ECB11F8021CB45E8E7809D3C0938E4B8C0E5F84B")
copy(publicKey[:], pk)
P2x, P2y := schnorr.Unmarshal(Curve, publicKey[:])
Px, Py := Curve.Add(P1x, P1y, P2x, P2y)
copy(publicKey[:], schnorr.Marshal(Curve, Px, Py))
if result, err := schnorr.Verify(publicKey, message, signature); err != nil {
fmt.Printf("The signature verification failed: %v\n", err)
} else if result {
fmt.Println("The signature is valid.")
}Benchmarks
BenchmarkSign-4 2000 1015337 ns/op 45812 B/op 814 allocs/op
BenchmarkVerify-4 200 8555659 ns/op 217884 B/op 3622 allocs/op
BenchmarkBatchVerify-4 100 12114966 ns/op 148343 B/op 2220 allocs/op
BenchmarkAggregateSignatures-4 2000 593665 ns/op 21981 B/op 400 allocs/op
Hardware used
- Intel® Core™ i3-2310M CPU @ 2.10GHz × 4
- 4Gb RAM
Versions
- Go 1.11.2
- Ubuntu 18.04.01 LTS x86_64 OS
- 4.15.0-39-generic kernel