Fix VRF uniqueness violation

* renamed c, cH, ... with s, sH

it is called s in the CONIKS paper/in KT (in the cfrg draft and other literature it is called c, though)

* Adopt VRF to update in CONIKS paper
- add unique identifier: also hash h=H1(m), g^x and h^x (the VRF output) and not only with random nonce r (g^r, h^r); additionally hash m into H2 (as before)
- like in the paper add the base-point and public-key
- skip outdated test-vectors
- unrelated: remove formatting version of test-output where no placeholder is used

fixes #175

crypto/internal/ed25519/edwards25519/const.go

@@ -23,6 +23,20 @@ var A = FieldElement{
 	486662, 0, 0, 0, 0, 0, 0, 0, 0, 0,
 }
 
+var extendedBaseEl = ExtendedGroupElement{
+	FieldElement{25485296, 5318399, 8791791, -8299916, -14349720, 6939349, -3324311, -7717049, 7287234, -6577708},
+	FieldElement{-758052, -1832720, 13046421, -4857925, 6576754, 14371947, -13139572, 6845540, -2198883, -4003719},
+	FieldElement{-947565, 6097708, -469190, 10704810, -8556274, -15589498, -16424464, -16608899, 14028613, -5004649},
+	FieldElement{6966464, -2456167, 7033433, 6781840, 28785542, 12262365, -2659449, 13959020, -21013759, -5262166},
+}
+
+// BaseBytes can be used to hash the base point if necessary
+var BaseBytes [32]byte
+
+func init() {
+	extendedBaseEl.ToBytes(&BaseBytes)
+}
+
 var bi = [8]PreComputedGroupElement{
 	{
 		FieldElement{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605},

crypto/vrf/vrf.go

@@ -120,14 +120,16 @@ func hashToCurve(m []byte) *edwards25519.ExtendedGroupElement {
 // same as returned by Compute(m).
 func (sk PrivateKey) Prove(m []byte) (vrf, proof []byte) {
 	x, skhr := sk.expandSecret()
-	var cH, rH [64]byte
-	var r, c, minusC, t, grB, hrB, iiB [32]byte
+	var sH, rH [64]byte
+	var r, s, minusS, t, gB, grB, hrB, hxB, hB [32]byte
 	var ii, gr, hr edwards25519.ExtendedGroupElement
 
-	hm := hashToCurve(m)
-	edwards25519.GeScalarMult(&ii, x, hm)
-	ii.ToBytes(&iiB)
+	h := hashToCurve(m)
+	h.ToBytes(&hB)
+	edwards25519.GeScalarMult(&ii, x, h)
+	ii.ToBytes(&hxB)
 
+	// use hash of private-, public-key and msg as randomness source:
 	hash := sha3.NewShake256()
 	hash.Write(skhr[:])
 	hash.Write(sk[32:]) // public key, as in ed25519
@@ -137,26 +139,32 @@ func (sk PrivateKey) Prove(m []byte) (vrf, proof []byte) {
 	edwards25519.ScReduce(&r, &rH)
 
 	edwards25519.GeScalarMultBase(&gr, &r)
-	edwards25519.GeScalarMult(&hr, &r, hm)
+	edwards25519.GeScalarMult(&hr, &r, h)
 	gr.ToBytes(&grB)
 	hr.ToBytes(&hrB)
+	gB = edwards25519.BaseBytes
 
+	// H2(g, h, g^x, h^x, g^r, h^r, m)
+	hash.Write(gB[:])
+	hash.Write(hB[:])
+	hash.Write(sk[32:]) // ed25519 public-key
+	hash.Write(hxB[:])
 	hash.Write(grB[:])
 	hash.Write(hrB[:])
 	hash.Write(m)
-	hash.Read(cH[:])
+	hash.Read(sH[:])
 	hash.Reset()
-	edwards25519.ScReduce(&c, &cH)
+	edwards25519.ScReduce(&s, &sH)
 
-	edwards25519.ScNeg(&minusC, &c)
-	edwards25519.ScMulAdd(&t, x, &minusC, &r)
+	edwards25519.ScNeg(&minusS, &s)
+	edwards25519.ScMulAdd(&t, x, &minusS, &r)
 
 	proof = make([]byte, ProofSize)
-	copy(proof[:32], c[:])
+	copy(proof[:32], s[:])
 	copy(proof[32:64], t[:])
-	copy(proof[64:96], iiB[:])
+	copy(proof[64:96], hxB[:])
 
-	hash.Write(iiB[:]) // const length: Size
+	hash.Write(hxB[:])
 	hash.Write(m)
 	vrf = make([]byte, Size)
 	hash.Read(vrf[:])
@@ -169,15 +177,15 @@ func (pkBytes PublicKey) Verify(m, vrfBytes, proof []byte) bool {
 	if len(proof) != ProofSize || len(vrfBytes) != Size || len(pkBytes) != PublicKeySize {
 		return false
 	}
-	var pk, c, cRef, t, vrf, iiB, ABytes, BBytes [32]byte
+	var pk, s, sRef, t, vrf, hxB, hB, gB, ABytes, BBytes [32]byte
 	copy(vrf[:], vrfBytes)
 	copy(pk[:], pkBytes[:])
-	copy(c[:32], proof[:32])
+	copy(s[:32], proof[:32])
 	copy(t[:32], proof[32:64])
-	copy(iiB[:], proof[64:96])
+	copy(hxB[:], proof[64:96])
 
 	hash := sha3.NewShake256()
-	hash.Write(iiB[:]) // const length
+	hash.Write(hxB[:]) // const length
 	hash.Write(m)
 	var hCheck [Size]byte
 	hash.Read(hCheck[:])
@@ -191,25 +199,33 @@ func (pkBytes PublicKey) Verify(m, vrfBytes, proof []byte) bool {
 	if !P.FromBytesBaseGroup(&pk) {
 		return false
 	}
-	if !ii.FromBytesBaseGroup(&iiB) {
+	if !ii.FromBytesBaseGroup(&hxB) {
 		return false
 	}
-	edwards25519.GeDoubleScalarMultVartime(&A, &c, &P, &t)
+	edwards25519.GeDoubleScalarMultVartime(&A, &s, &P, &t)
 	A.ToBytes(&ABytes)
+	gB = edwards25519.BaseBytes
 
-	hm := hashToCurve(m)
-	edwards25519.GeDoubleScalarMultVartime(&hmtP, &t, hm, &[32]byte{})
-	edwards25519.GeDoubleScalarMultVartime(&iicP, &c, &ii, &[32]byte{})
+	h := hashToCurve(m) // h = H1(m)
+	h.ToBytes(&hB)
+	edwards25519.GeDoubleScalarMultVartime(&hmtP, &t, h, &[32]byte{})
+	edwards25519.GeDoubleScalarMultVartime(&iicP, &s, &ii, &[32]byte{})
 	iicP.ToExtended(&iic)
 	hmtP.ToExtended(&B)
 	edwards25519.GeAdd(&B, &B, &iic)
 	B.ToBytes(&BBytes)
 
-	var cH [64]byte
-	hash.Write(ABytes[:]) // const length
-	hash.Write(BBytes[:]) // const length
+	var sH [64]byte
+	// sRef = H2(g, h, g^x, v, g^t·G^s,H1(m)^t·v^s, m), with v=H1(m)^x=h^x
+	hash.Write(gB[:])
+	hash.Write(hB[:])
+	hash.Write(pkBytes)
+	hash.Write(hxB[:])
+	hash.Write(ABytes[:]) // const length (g^t*G^s)
+	hash.Write(BBytes[:]) // const length (H1(m)^t*v^s)
 	hash.Write(m)
-	hash.Read(cH[:])
-	edwards25519.ScReduce(&cRef, &cH)
-	return cRef == c
+	hash.Read(sH[:])
+
+	edwards25519.ScReduce(&sRef, &sH)
+	return sRef == s
 }

crypto/vrf/vrf_test.go

@@ -23,10 +23,10 @@ func TestHonestComplete(t *testing.T) {
 	// fmt.Printf("aliceProof:   %X\n", aliceProof)
 
 	if !pk.Verify(alice, aliceVRF, aliceProof) {
-		t.Errorf("Gen -> Compute -> Prove -> Verify -> FALSE")
+		t.Error("Gen -> Compute -> Prove -> Verify -> FALSE")
 	}
 	if !bytes.Equal(aliceVRF, aliceVRFFromProof) {
-		t.Errorf("Compute != Prove")
+		t.Error("Compute != Prove")
 	}
 }
 
@@ -69,37 +69,37 @@ func sampleVectorTest(pk PublicKey, aliceVRF, aliceProof []byte, t *testing.T) {
 
 	// Positive test case
 	if !pk.Verify(alice, aliceVRF, aliceProof) {
-		t.Errorf("TestSampleVectors HonestVector Failed")
+		t.Error("TestSampleVectors HonestVector Failed")
 	}
 
 	// Negative test cases - try increment the first byte of every vector
 	pk[0]++
 	if pk.Verify(alice, aliceVRF, aliceProof) {
-		t.Errorf("TestSampleVectors ForgedVector (pk modified) Passed")
+		t.Error("TestSampleVectors ForgedVector (pk modified) Passed")
 	}
 	pk[0]--
 
 	alice[0]++
 	if pk.Verify(alice, aliceVRF, aliceProof) {
-		t.Errorf("TestSampleVectors ForgedVector (alice modified) Passed")
+		t.Error("TestSampleVectors ForgedVector (alice modified) Passed")
 	}
 	alice[0]--
 
 	aliceVRF[0]++
 	if pk.Verify(alice, aliceVRF, aliceProof) {
-		t.Errorf("TestSampleVectors ForgedVector (aliceVRF modified) Passed")
+		t.Error("TestSampleVectors ForgedVector (aliceVRF modified) Passed")
 	}
 	aliceVRF[0]--
 
 	aliceProof[0]++
 	if pk.Verify(alice, aliceVRF, aliceProof) {
-		t.Errorf("TestSampleVectors ForgedVector (aliceProof modified) Passed")
+		t.Error("TestSampleVectors ForgedVector (aliceProof modified) Passed")
 	}
 	aliceProof[0]--
 }
 
 func TestSampleVectorSets(t *testing.T) {
-
+	t.Skip("TODO: generate new test vectors or remove test")
 	var aliceVRF, aliceProof []byte
 	var pk []byte