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)
    • Arguments
    • Returns
    • Examples
  • Verify(publicKey [33]byte, message [32]byte, signature [64]byte) (bool, error)
    • Arguments
    • Returns
    • Examples
  • BatchVerify(publicKeys [][33]byte, messages [][32]byte, signatures [][64]byte) (bool, error)
    • Arguments
    • Returns
    • Examples
  • AggregateSignatures(privateKeys []*big.Int, message [32]byte) ([64]byte, error)
    • Arguments
    • Returns
    • Examples
• Benchmark
  • Hardware used
  • Version
• Credit

Usage

Install using:

go get -u github.com/hbakhtiyor/schnorr

In 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

1. privateKey (*big.Int): The integer secret key in the range 1..n-1.
2. 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

1. publicKey ([33]byte): The 33-byte array public key.
2. message ([32]byte): The 32-byte array message.
3. 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

1. publicKeys ([][33]byte): The list of 33-byte array public keys.
2. messages ([][32]byte): The list of 32-byte array messages.
3. 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

1. privateKeys ([]*big.Int): The list of integer secret keys in the range 1..n-1.
2. 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

Credits

• https://github.com/guggero/bip-schnorr
• https://github.com/sipa/bips/tree/bip-schnorr/bip-schnorr