Golang : How to get ECDSA curve and parameters data?

Problem :

A reader asked :

"ECDSA cents have a parameters block which has the parameters for the curve. Any info regarding how those would be created and saved in Go?"

Solution :

In the previous tutorial on how to use ECDSA Elliptic curve algorithm functions. We learn how to generate a private key and extract the public key from the private key.

From the public key data structure, we can observe that the Curve data is embedded inside the public key.

 type PublicKey struct {
 elliptic.Curve
 X, Y *big.Int
 }

and from https://golang.org/pkg/crypto/elliptic/#Curve interface, we can use the Params() function to returns the parameters for the curve and retrieve other type of data as well.

 type Curve interface {
 // Params returns the parameters for the curve.
 Params() *CurveParams
 // IsOnCurve returns true if the given (x,y) lies on the curve.
 IsOnCurve(x, y *big.Int) bool
 // Add returns the sum of (x1,y1) and (x2,y2)
 Add(x1, y1, x2, y2 *big.Int) (x, y *big.Int)
 // Double returns 2*(x,y)
 Double(x1, y1 *big.Int) (x, y *big.Int)
 // ScalarMult returns k*(Bx,By) where k is a number in big-endian form.
 ScalarMult(x1, y1 *big.Int, k []byte) (x, y *big.Int)
 // ScalarBaseMult returns k*G, where G is the base point of the group
 // and k is an integer in big-endian form.
 ScalarBaseMult(k []byte) (x, y *big.Int)
 }

The following code example demonstrates how to extract the curve and parameters data.

 package main

 import (
 "crypto/ecdsa"
 "crypto/elliptic"
 "crypto/rand"
 "fmt"
 "os"
 )

 func main() {

 pubkeyCurve := elliptic.P256() //see http://golang.org/pkg/crypto/elliptic/#P256

 privatekey := new(ecdsa.PrivateKey)
 privatekey, err := ecdsa.GenerateKey(pubkeyCurve, rand.Reader) // this generates a public & private key pair

 if err != nil {
 fmt.Println(err)
 os.Exit(1)
 }

 var pubkey ecdsa.PublicKey
 pubkey = privatekey.PublicKey

 fmt.Println("Public Key : ")

 // PublicKey represents and ECDSA public key
 // type PublicKey struct {
 // elliptic.Curve
 // X, Y *big.Int
 //}

 fmt.Println("Curve : ", pubkey.Curve)

 // Access curve data type and parameters example

 // ---- https://golang.org/pkg/crypto/elliptic/#Curve

 curveParams := pubkey.Curve.Params()

 fmt.Println("P : ", curveParams.P)
 fmt.Println("N : ", curveParams.N)
 fmt.Println("B : ", curveParams.B)
 fmt.Printf("Gx, Gy : %v, %v\n", curveParams.Gx, curveParams.Gy)
 fmt.Println("BitSize : ", curveParams.BitSize)

 fmt.Println("Is On Curve ? ", pubkey.Curve.IsOnCurve(pubkey.X, pubkey.Y))

 fmt.Println("X : ", pubkey.X)
 fmt.Println("Y : ", pubkey.Y)
 }

Sample output :

Public Key :

Curve : {0x20824e450}

P : 115792089210356248762697446949407573530086143415290314195533631308867097853951

N : 115792089210356248762697446949407573529996955224135760342422259061068512044369

B : 41058363725152142129326129780047268409114441015993725554835256314039467401291

Gx, Gy : 48439561293906451759052585252797914202762949526041747995844080717082404635286, 36134250956749795798585127919587881956611106672985015071877198253568414405109

BitSize : 256

Is On Curve ? true

X : 81954825413260908377823288112466052223174308460634959356324006972238863306292

Y : 104045399658056244122317769635250651827793337497571819907947708147764927071641

References :

https://golang.org/pkg/crypto/ecdsa/#PublicKey

https://golang.org/pkg/crypto/elliptic/#Curve

https://www.socketloop.com/tutorials/golang-saving-private-and-public-key-to-files#comment-2131136983