// Verifies that the 'message' is included in the signature and that it
// is correct.
// Message is your own hash, and reply contains the inclusion proof + signature
// on the aggregated message
func VerifySignature(suite abstract.Suite, reply *StampSignature, public abstract.Point, message []byte) bool {
// Check if aggregate public key is correct
if !public.Equal(reply.AggPublic) {
dbg.Lvl1("Aggregate-public-key check: FAILED (maybe you have an outdated config file of the tree)")
return false
}
// First check if the challenge is ok
if err := VerifyChallenge(suite, reply); err != nil {
dbg.Lvl1("Challenge-check: FAILED (", err, ")")
return false
}
dbg.Lvl2("Challenge-check: OK")
// Incorporate the timestamp in the message since the verification process
// is done by reconstructing the challenge
var b bytes.Buffer
if err := binary.Write(&b, binary.LittleEndian, reply.Timestamp); err != nil {
dbg.Lvl1("Error marshaling the timestamp for signature verification")
return false
}
msg := append(b.Bytes(), []byte(reply.MerkleRoot)...)
if err := VerifySchnorr(suite, msg, public, reply.Challenge, reply.Response); err != nil {
dbg.Lvl1("Signature-check: FAILED (", err, ")")
return false
}
dbg.Lvl2("Signature-check: OK")
// finally check the proof
if !proof.CheckProof(suite.Hash, reply.MerkleRoot, hashid.HashId(message), reply.Prf) {
dbg.Lvl2("Inclusion-check: FAILED")
return false
}
dbg.Lvl2("Inclusion-check: OK")
return true
}
// Pick a [pseudo-]random curve point with optional embedded data,
// filling in the point's x,y coordinates
// and returning any remaining data not embedded.
func (c *curve) pickPoint(P point, data []byte, rand cipher.Stream) []byte {
// How much data to embed?
dl := c.pickLen()
if dl > len(data) {
dl = len(data)
}
// Retry until we find a valid point
var x, y nist.Int
var Q abstract.Point
for {
// Get random bits the size of a compressed Point encoding,
// in which the topmost bit is reserved for the x-coord sign.
l := c.PointLen()
b := make([]byte, l)
rand.XORKeyStream(b, b) // Interpret as little-endian
if data != nil {
b[0] = byte(dl) // Encode length in low 8 bits
copy(b[1:1+dl], data) // Copy in data to embed
}
util.Reverse(b, b) // Convert to big-endian form
xsign := b[0] >> 7 // save x-coordinate sign bit
b[0] &^= 0xff << uint(c.P.BitLen()&7) // clear high bits
y.M = &c.P // set y-coordinate
y.SetBytes(b)
if !c.solveForX(&x, &y) { // Corresponding x-coordinate?
continue // none, retry
}
// Pick a random sign for the x-coordinate
if c.coordSign(&x) != uint(xsign) {
x.Neg(&x)
}
// Initialize the point
P.initXY(&x.V, &y.V, c.self)
if c.full {
// If we're using the full group,
// we just need any point on the curve, so we're done.
return data[dl:]
}
// We're using the prime-order subgroup,
// so we need to make sure the point is in that subgroup.
// If we're not trying to embed data,
// we can convert our point into one in the subgroup
// simply by multiplying it by the cofactor.
if data == nil {
P.Mul(P, &c.cofact) // multiply by cofactor
if P.Equal(c.null) {
continue // unlucky; try again
}
return data[dl:]
}
// Since we need the point's y-coordinate to make sense,
// we must simply check if the point is in the subgroup
// and retry point generation until it is.
if Q == nil {
Q = c.self.Point()
}
Q.Mul(P, &c.order)
if Q.Equal(c.null) {
return data[dl:]
}
// Keep trying...
}
}
// Simple helper to verify Theta elements,
// by checking whether A^a*B^-b = T.
// P,Q,s are simply "scratch" abstract.Point/Scalars reused for efficiency.
func thver(A, B, T, P, Q abstract.Point, a, b, s abstract.Scalar) bool {
P.Mul(A, a)
Q.Mul(B, s.Neg(b))
P.Add(P, Q)
return P.Equal(T)
}
