A proof of concept of a public key derivation for ECDSA (without knowledge of the private key)

WARNING! Do not use this code in production. It was never validated by a real specialist in cryptography.

Also be aware, knowing the child private key and the derivation key is enough to easily restore the parent private key.

Simple

It is a demonstration of how to implement a simple key derivation algorithm for public keys without knowledge of private keys. This works for any asymmetric crypto algorithm with distributive property enabled for public key. The idea is very simple:

Let's imagine s0 is the private key, then public key would be P0 = s0*B (where B is the basepoint of the curve). So if a new private key is derived as s1 = s0 + d then a new public key could be derived as P1 = s1*B = (s0+d)*B. Thus new public key is: P1 = s0*B + d*B = P0 + d*B. That's it.

Demonstration

See the unit test:

func TestDerivePublic(t *testing.T) {
	randReader := rand.New(rand.NewSource(0))
	derivationKey := []byte{1, 2, 3}

	privKey, err := ecdsa.GenerateKey(elliptic.P521(), randReader)
	require.NoError(t, err)

	derivedPubKey := DerivePublic(privKey.Public().(*ecdsa.PublicKey), derivationKey)

	derivedPrivKey := DerivePrivate(privKey, derivationKey)
	require.NotEqual(t, privKey, derivedPrivKey)

	require.Equal(t,
		derivedPrivKey.Public().(*ecdsa.PublicKey),
		derivedPubKey,
	)
}

result:

xaionaro@void:~/go/src/github.com/xaionaro-go/ecdsakeyderivation$ go test ./... -count=1
ok  	github.com/xaionaro-go/ecdsakeyderivation	0.101s