ecc

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README

btcec

Build Status ISC License GoDoc

Package btcec implements elliptic curve cryptography needed for working with Bitcoin (secp256k1 only for now). It is designed so that it may be used with the standard crypto/ecdsa packages provided with go. A comprehensive suite of test is provided to ensure proper functionality. Package btcec was originally based on work from ThePiachu which is licensed under the same terms as Go, but it has signficantly diverged since then. The btcsuite developers original is licensed under the liberal ISC license.

Although this package was primarily written for btcd, it has intentionally been designed so it can be used as a standalone package for any projects needing to use secp256k1 elliptic curve cryptography.

Installation and Updating

$ go get -u github.com/btcsuite/btcd/ecc

Examples

  • Sign Message
    Demonstrates signing a message with a secp256k1 private key that is first parsed form raw bytes and serializing the generated signature.

  • Verify Signature
    Demonstrates verifying a secp256k1 signature against a public key that is first parsed from raw bytes. The signature is also parsed from raw bytes.

  • Encryption Demonstrates encrypting a message for a public key that is first parsed from raw bytes, then decrypting it using the corresponding private key.

  • Decryption Demonstrates decrypting a message using a private key that is first parsed from raw bytes.

GPG Verification Key

All official release tags are signed by Conformal so users can ensure the code has not been tampered with and is coming from the btcsuite developers. To verify the signature perform the following:

  • Download the public key from the Conformal website at https://opensource.conformal.com/GIT-GPG-KEY-conformal.txt

  • Import the public key into your GPG keyring:

    gpg --import GIT-GPG-KEY-conformal.txt

  • Verify the release tag with the following command where TAG_NAME is a placeholder for the specific tag:

    git tag -v TAG_NAME

License

Package btcec is licensed under the copyfree ISC License except for btcec.go and btcec_test.go which is under the same license as Go.

Documentation

Overview

Package btcec implements support for the elliptic curves needed for bitcoin.

Bitcoin uses elliptic curve cryptography using koblitz curves (specifically secp256k1) for cryptographic functions. See http://www.secg.org/collateral/sec2_final.pdf for details on the standard.

This package provides the data structures and functions implementing the crypto/elliptic Curve interface in order to permit using these curves with the standard crypto/ecdsa package provided with go. Helper functionality is provided to parse signatures and public keys from standard formats. It was designed for use with btcd, but should be general enough for other uses of elliptic curve crypto. It was originally based on some initial work by ThePiachu, but has significantly diverged since then.

Example (DecryptMessage)

This example demonstrates decrypting a message using a private key that is first parsed from raw bytes. 

package main

import (
	"encoding/hex"
	"fmt"

	"github.com/cybriq/p9/pkg/ecc"
)

func main() {
	// Decode the hex-encoded private key.
	pkBytes, err := hex.DecodeString("a11b0a4e1a132305652ee7a8eb7848f6ad" +
		"5ea381e3ce20a2c086a2e388230811",
	)
	if err != nil {
		fmt.Println(err)
		return
	}

	privKey, _ := ecc.PrivKeyFromBytes(ecc.S256(), pkBytes)

	ciphertext, err := hex.DecodeString("35f644fbfb208bc71e57684c3c8b437402ca" +
		"002047a2f1b38aa1a8f1d5121778378414f708fe13ebf7b4a7bb74407288c1958969" +
		"00207cf4ac6057406e40f79961c973309a892732ae7a74ee96cd89823913b8b8d650" +
		"a44166dc61ea1c419d47077b748a9c06b8d57af72deb2819d98a9d503efc59fc8307" +
		"d14174f8b83354fac3ff56075162",
	)

	// Try decrypting the message.
	plaintext, err := ecc.Decrypt(privKey, ciphertext)
	if err != nil {
		fmt.Println(err)
		return
	}

	fmt.Println(string(plaintext))

}

Output:

test message
Example (EncryptMessage)

This example demonstrates encrypting a message for a public key that is first parsed from raw bytes, then decrypting it using the corresponding private key. 

package main

import (
	"encoding/hex"
	"fmt"

	"github.com/cybriq/p9/pkg/ecc"
)

func main() {
	// Decode the hex-encoded pubkey of the recipient.
	pubKeyBytes, err := hex.DecodeString("04115c42e757b2efb7671c578530ec191a1" +
		"359381e6a71127a9d37c486fd30dae57e76dc58f693bd7e7010358ce6b165e483a29" +
		"21010db67ac11b1b51b651953d2",
	) // uncompressed pubkey
	if err != nil {
		fmt.Println(err)
		return
	}
	pubKey, err := ecc.ParsePubKey(pubKeyBytes, ecc.S256())
	if err != nil {
		fmt.Println(err)
		return
	}

	// Encrypt a message decryptable by the private key corresponding to pubKey
	message := "test message"
	ciphertext, err := ecc.Encrypt(pubKey, []byte(message))
	if err != nil {
		fmt.Println(err)
		return
	}

	// Decode the hex-encoded private key.
	pkBytes, err := hex.DecodeString("a11b0a4e1a132305652ee7a8eb7848f6ad" +
		"5ea381e3ce20a2c086a2e388230811",
	)
	if err != nil {
		fmt.Println(err)
		return
	}
	// note that we already have corresponding pubKey
	privKey, _ := ecc.PrivKeyFromBytes(ecc.S256(), pkBytes)

	// Try decrypting and verify if it's the same message.
	plaintext, err := ecc.Decrypt(privKey, ciphertext)
	if err != nil {
		fmt.Println(err)
		return
	}

	fmt.Println(string(plaintext))

}

Output:

test message
Example (SignMessage)

This example demonstrates signing a message with a secp256k1 private key that is first parsed form raw bytes and serializing the generated signature. 

package main

import (
	"encoding/hex"
	"fmt"

	"github.com/cybriq/p9/pkg/chainhash"
	"github.com/cybriq/p9/pkg/ecc"
)

func main() {
	// Decode a hex-encoded private key.
	pkBytes, err := hex.DecodeString("22a47fa09a223f2aa079edf85a7c2d4f87" +
		"20ee63e502ee2869afab7de234b80c",
	)
	if err != nil {
		fmt.Println(err)
		return
	}
	privKey, pubKey := ecc.PrivKeyFromBytes(ecc.S256(), pkBytes)

	// Sign a message using the private key.
	message := "test message"
	messageHash := chainhash.DoubleHashB([]byte(message))
	signature, err := privKey.Sign(messageHash)
	if err != nil {
		fmt.Println(err)
		return
	}

	// Serialize and display the signature.
	fmt.Printf("Serialized Signature: %x\n", signature.Serialize())

	// Verify the signature for the message using the public key.
	verified := signature.Verify(messageHash, pubKey)
	fmt.Printf("Signature Verified? %v\n", verified)

}

Output:

Serialized Signature: 304402201008e236fa8cd0f25df4482dddbb622e8a8b26ef0ba731719458de3ccd93805b022032f8ebe514ba5f672466eba334639282616bb3c2f0ab09998037513d1f9e3d6d
Signature Verified? true
Example (VerifySignature)

This example demonstrates verifying a secp256k1 signature against a public key that is first parsed from raw bytes. The signature is also parsed from raw bytes. 

package main

import (
	"encoding/hex"
	"fmt"

	"github.com/cybriq/p9/pkg/chainhash"
	"github.com/cybriq/p9/pkg/ecc"
)

func main() {
	// Decode hex-encoded serialized public key.
	pubKeyBytes, err := hex.DecodeString("02a673638cb9587cb68ea08dbef685c" +
		"6f2d2a751a8b3c6f2a7e9a4999e6e4bfaf5",
	)
	if err != nil {
		fmt.Println(err)
		return
	}
	pubKey, err := ecc.ParsePubKey(pubKeyBytes, ecc.S256())
	if err != nil {
		fmt.Println(err)
		return
	}

	// Decode hex-encoded serialized signature.
	sigBytes, err := hex.DecodeString("30450220090ebfb3690a0ff115bb1b38b" +
		"8b323a667b7653454f1bccb06d4bbdca42c2079022100ec95778b51e707" +
		"1cb1205f8bde9af6592fc978b0452dafe599481c46d6b2e479",
	)

	if err != nil {
		fmt.Println(err)
		return
	}
	signature, err := ecc.ParseSignature(sigBytes, ecc.S256())
	if err != nil {
		fmt.Println(err)
		return
	}

	// Verify the signature for the message using the public key.
	message := "test message"
	messageHash := chainhash.DoubleHashB([]byte(message))
	verified := signature.Verify(messageHash, pubKey)
	fmt.Println("Signature Verified?", verified)

}

Output:

Signature Verified? true

Index

Examples

Constants

View Source 
const (
	PubKeyBytesLenCompressed   = 33
	PubKeyBytesLenUncompressed = 65
	PubKeyBytesLenHybrid       = 65
)

These constants define the lengths of serialized public keys.

View Source 
const MinSigLen = 8

MinSigLen is the minimum length of a DER encoded signature and is when both R and S are 1 byte each. 0x30 + <1-byte> + 0x02 + 0x01 + <byte> + 0x2 + 0x01 + <byte>

View Source 
const PrivKeyBytesLen = 32

PrivKeyBytesLen defines the length in bytes of a serialized private key.

Variables

View Source 
var (
	// ErrInvalidMAC occurs when Message Authentication Check (MAC) fails
	// during decryption. This happens because of either invalid private key or
	// corrupt ciphertext.
	ErrInvalidMAC = errors.New("invalid mac hash")
)

Functions

func Decrypt 

func Decrypt(priv *PrivateKey, in []byte) ([]byte, error)

Decrypt decrypts data that was encrypted using the Encrypt function.

func Encrypt 

func Encrypt(pubkey *PublicKey, in []byte) ([]byte, error)

Encrypt encrypts data for the target public key using AES-256-CBC. It also generates a private key (the pubkey of which is also in the output). The only supported curve is secp256k1. The `structure' that it encodes everything into is: 

struct {
	// Initialization Vector used for AES-256-CBC
	IV [16]byte
	// Public Key: curve(2) + len_of_pubkeyX(2) + pubkeyX +
	// len_of_pubkeyY(2) + pubkeyY (curve = 714)
	PublicKey [70]byte
	// Cipher text
	Data []byte
	// HMAC-SHA-256 Message Authentication Code
	HMAC [32]byte
}

The primary aim is to ensure byte compatibility with Pyelliptic. Also, refer to section 5.8.1 of ANSI X9.63 for rationale on this format.

func GenerateSharedSecret 

func GenerateSharedSecret(privkey *PrivateKey, pubkey *PublicKey) []byte

GenerateSharedSecret generates a shared secret based on a private key and a public key using Diffie-Hellman key exchange (ECDH) (RFC 4753). RFC5903 Section 9 states we should only return x.

func IsCompressedPubKey 

func IsCompressedPubKey(pubKey []byte) bool

IsCompressedPubKey returns true the the passed serialized public key has been encoded in compressed format, and false otherwise.

func NAF 

func NAF(k []byte) ([]byte, []byte)

NAF takes a positive integer k and returns the Non-Adjacent Form (NAF) as two byte slices. The first is where 1s will be. The second is where -1s will be. NAF is convenient in that on average, only 1/3rd of its values are non-zero. This is algorithm 3.30 from [GECC].

Essentially, this makes it possible to minimize the number of operations since the resulting ints returned will be at least 50% 0s.

func PrivKeyFromBytes 

func PrivKeyFromBytes(curve elliptic.Curve, pk []byte) (*PrivateKey,
	*PublicKey)

PrivKeyFromBytes returns a private and public key for `curve' based on the private key passed as an argument as a byte slice.

func SignCompact 

func SignCompact(curve *KoblitzCurve, key *PrivateKey,
	hash []byte, isCompressedKey bool) ([]byte, error)

SignCompact produces a compact signature of the data in hash with the given private key on the given koblitz curve. The isCompressed parameter should be used to detail if the given signature should reference a compressed public key or not. If successful the bytes of the compact signature will be returned in the format: <(byte of 27+public key solution)+4 if compressed >< padded bytes for signature R><padded bytes for signature S> where the R and S parameters are padde up to the bitlengh of the curve.

Types

type KoblitzCurve 

type KoblitzCurve struct {
	*elliptic.CurveParams

	H int // cofactor of the curve.
	// contains filtered or unexported fields
}

KoblitzCurve supports a koblitz curve implementation that fits the ECC Curve interface from crypto/elliptic.

func S256 

func S256() *KoblitzCurve

S256 returns a Curve which implements secp256k1.

func (*KoblitzCurve) Add 

func (curve *KoblitzCurve) Add(x1, y1, x2, y2 *big.Int) (*big.Int, *big.Int)

Add returns the sum of (x1,y1) and (x2,y2). Part of the elliptic.Curve interface.

func (*KoblitzCurve) Double 

func (curve *KoblitzCurve) Double(x1, y1 *big.Int) (*big.Int, *big.Int)

Double returns 2*(x1,y1). Part of the elliptic.Curve interface.

func (*KoblitzCurve) EndomorphismVectors 

func (curve *KoblitzCurve) EndomorphismVectors() (a1, b1, a2, b2 *big.Int)

EndomorphismVectors runs the first 3 steps of algorithm 3.74 from [GECC] to generate the linearly independent vectors needed to generate a balanced length-two representation of a multiplier such that k = k1 + k2λ (mod N) and returns them. Since the values will always be the same given the fact that N and λ are fixed, the final results can be accelerated by storing the precomputed values with the curve.

func (*KoblitzCurve) IsOnCurve 

func (curve *KoblitzCurve) IsOnCurve(x, y *big.Int) bool

IsOnCurve returns boolean if the point (x,y) is on the curve. Part of the elliptic.Curve interface. This function differs from the crypto/elliptic algorithm since a = 0 not -3.

func (*KoblitzCurve) Params 

func (curve *KoblitzCurve) Params() *elliptic.CurveParams

Params returns the parameters for the curve.

func (*KoblitzCurve) Q 

func (curve *KoblitzCurve) Q() *big.Int

Q returns the (P+1)/4 constant for the curve for use in calculating square roots via exponentiation.

func (*KoblitzCurve) QPlus1Div4 

func (curve *KoblitzCurve) QPlus1Div4() *big.Int

QPlus1Div4 returns the (P+1)/4 constant for the curve for use in calculating square roots via exponentiation.

DEPRECATED: The actual value returned is (P+1)/4, where as the original method name implies that this value is (((P+1)/4)+1)/4. This method is kept to maintain backwards compatibility of the API. Use Q() instead.

func (*KoblitzCurve) ScalarBaseMult 

func (curve *KoblitzCurve) ScalarBaseMult(k []byte) (*big.Int, *big.Int)

ScalarBaseMult returns k*G where G is the base point of the group and k is a big endian integer. Part of the elliptic.Curve interface.

func (*KoblitzCurve) ScalarMult 

func (curve *KoblitzCurve) ScalarMult(Bx, By *big.Int, k []byte) (*big.Int, *big.Int)

ScalarMult returns k*(Bx, By) where k is a big endian integer. Part of the elliptic.Curve interface.

func (*KoblitzCurve) SerializedBytePoints 

func (curve *KoblitzCurve) SerializedBytePoints() []byte

SerializedBytePoints returns a serialized byte slice which contains all of the possible points per 8-bit window. This is used to when generating secp256k1.go.

type PrivateKey 

type PrivateKey ecdsa.PrivateKey

PrivateKey wraps an ecdsa.PrivateKey as a convenience mainly for signing things with the the private key without having to directly import the ecdsa package.

func NewPrivateKey 

func NewPrivateKey(curve elliptic.Curve) (*PrivateKey, error)

NewPrivateKey is a wrapper for ecdsa.GenerateKey that returns a PrivateKey instead of the normal ecdsa.PrivateKey.

func (*PrivateKey) PubKey 

func (p *PrivateKey) PubKey() *PublicKey

PubKey returns the PublicKey corresponding to this private key.

func (*PrivateKey) Serialize 

func (p *PrivateKey) Serialize() []byte

Serialize returns the private key number d as a big-endian binary-encoded number, padded to a length of 32 bytes.

func (*PrivateKey) Sign 

func (p *PrivateKey) Sign(hash []byte) (*Signature, error)

Sign generates an ECDSA signature for the provided hash (which should be the result of hashing a larger message) using the private key. Produced signature is deterministic (same message and same key yield the same signature) and canonical in accordance with RFC6979 and BIP0062.

func (*PrivateKey) ToECDSA 

func (p *PrivateKey) ToECDSA() *ecdsa.PrivateKey

ToECDSA returns the private key as a *ecdsa.PrivateKey.

type PublicKey 

type PublicKey ecdsa.PublicKey

PublicKey is an ecdsa.PublicKey with additional functions to serialize in uncompressed, compressed, and hybrid formats.

func ParsePubKey 

func ParsePubKey(pubKeyStr []byte, curve *KoblitzCurve) (key *PublicKey, err error)

ParsePubKey parses a public key for a koblitz curve from a bytestring into a ecdsa.Publickey, verifying that it is valid. It supports compressed, uncompressed and hybrid signature formats.

func RecoverCompact 

func RecoverCompact(curve *KoblitzCurve, signature,
	hash []byte) (*PublicKey, bool, error)

RecoverCompact verifies the compact signature "signature" of "hash" for the Koblitz curve in "curve". If the signature matches then the recovered public key will be returned as well as a boolean if the original key was compressed or not, else an error will be returned.

func (*PublicKey) IsEqual 

func (p *PublicKey) IsEqual(otherPubKey *PublicKey) bool

IsEqual compares this PublicKey instance to the one passed, returning true if both PublicKeys are equivalent. A PublicKey is equivalent to another, if they both have the same X and Y coordinate.

func (*PublicKey) SerializeCompressed 

func (p *PublicKey) SerializeCompressed() []byte

SerializeCompressed serializes a public key in a 33-byte compressed format.

func (*PublicKey) SerializeHybrid 

func (p *PublicKey) SerializeHybrid() []byte

SerializeHybrid serializes a public key in a 65-byte hybrid format.

func (*PublicKey) SerializeUncompressed 

func (p *PublicKey) SerializeUncompressed() []byte

SerializeUncompressed serializes a public key in a 65-byte uncompressed format.

func (*PublicKey) ToECDSA 

func (p *PublicKey) ToECDSA() *ecdsa.PublicKey

ToECDSA returns the public key as a *ecdsa.PublicKey.

type Signature 

type Signature struct {
	R *big.Int
	S *big.Int
}

Signature is a type representing an ecdsa signature.

func ParseDERSignature 

func ParseDERSignature(sigStr []byte, curve elliptic.Curve) (*Signature, error)

ParseDERSignature parses a signature in DER format for the curve type `curve` into a Signature type. If parsing according to the less strict BER format is needed, use ParseSignature.

func ParseSignature 

func ParseSignature(sigStr []byte, curve elliptic.Curve) (*Signature, error)

ParseSignature parses a signature in BER format for the curve type `curve' into a Signature type, perfoming some basic sanity checks. If parsing according to the more strict DER format is needed, use ParseDERSignature.

func (*Signature) IsEqual 

func (sig *Signature) IsEqual(otherSig *Signature) bool

IsEqual compares this Signature instance to the one passed, returning true if both Signatures are equivalent. A signature is equivalent to another, if they both have the same scalar value for R and S.

func (*Signature) Serialize 

func (sig *Signature) Serialize() []byte

Serialize returns the ECDSA signature in the more strict DER format. Note that the serialized bytes returned do not include the appended hash type used in Bitcoin signature scripts.

encoding/asn1 is broken so we hand roll this output:

0x30 <length> 0x02 <length r> r 0x02 <length s> s

func (*Signature) Verify 

func (sig *Signature) Verify(hash []byte, pubKey *PublicKey) bool

Verify calls ecdsa.Verify to verify the signature of hash using the public key. It returns true if the signature is valid, false otherwise.

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