// getNotaryPredicate gets the predicate for the proof of correctness of notary ciphertexts:
// R_j = r_j*g-hat AND (S_j = -r_j*g_l AND ...)
// Since we can't put the minus sign in a predicate, we actually use the following equivalent statement:
// R_j = r_j*g-hat AND (S_j = r_j*(-g_l) AND ...)
func getNotaryPredicate(amount int) proof.Predicate {
preds := make([]proof.Predicate, amount+1)
preds[0] = proof.Rep("R_j", "r_j", "g_hat")
for l := 0; l < amount; l++ {
preds[l+1] = proof.Rep("S_j,"+strconv.Itoa(l), "r_j", "-g_"+strconv.Itoa(l))
}
return proof.And(preds...)
}
// GetUserPredicate gets the predicate for the proof of correctness of user ciphertexts:
// ( R_i = r_i*g-hat AND (C_{i,l} = r_i*g_l AND ...) OR Y = y*g )
// Here R_i = \sum_{j} R_{ij}; same for r_i; C_{i,l} is the l-th ciphertext;
// g_l is the l-th base point and Y is the slot owner public key
func GetUserPredicate(amount int) proof.Predicate {
preds := make([]proof.Predicate, amount+1)
preds[0] = proof.Rep("R_i", "r_i", "g_hat")
for l := 0; l < amount; l++ {
preds[l+1] = proof.Rep("C_i,"+strconv.Itoa(l), "r_i", "g_"+strconv.Itoa(l))
}
return proof.Or(proof.And(preds...), proof.Rep("Y", "y", "g"))
}
/* Verifies that a blameProof proves a share to be maliciously constructed.
*
* Arguments
* i = the index of the share subject to blame
* proof = blameProof that alleges the Dealer to have constructed a bad share.
*
* Return
* an error if the blame is unjustified or nil if the blame is justified.
*/
func (p *Deal) verifyBlame(i int, bproof *blameProof) error {
// Basic sanity checks
if i < 0 || i >= p.n {
return errors.New("Invalid index. Expected 0 <= i < n")
}
if err := p.verifySignature(i, &bproof.signature, sigBlameMsg); err != nil {
return err
}
// Verify the Diffie-Hellman shared secret was constructed properly
pval := map[string]abstract.Point{"D": bproof.diffieKey, "P": p.pubKey}
pred := proof.Rep("D", "x", "P")
verifier := pred.Verifier(p.suite, pval)
err := proof.HashVerify(p.suite, protocolName, verifier,
bproof.proof)
if err != nil {
return err
}
// Verify the share is bad.
diffieSecret := p.diffieHellmanSecret(bproof.diffieKey)
share := p.suite.Secret().Sub(p.secrets[i], diffieSecret)
if p.pubPoly.Check(i, share) {
return errors.New("Unjustified blame. The share checks out okay.")
}
return nil
}
/* Create a blameProof that the Dealer maliciously constructed a shared secret.
* This should be called if verifyShare fails due to the public polynomial
* check failing. If it failed for other reasons (such as a bad index) it is not
* advised to call this function since the share might actually be valid.
*
* Arguments
* i = the index of the malicious shared secret
* gKeyPair = the long term key pair of the insurer of share i
*
* Return
* A blameProof that the Dealer is malicious or nil if an error occurs
* An error object denoting the status of the blameProof construction
*
* TODO: Consider whether it is worthwile to produce some form of blame if
* the Dealer gives an invalid index.
*/
func (p *Deal) blame(i int, gKeyPair *config.KeyPair) (*blameProof, error) {
diffieKey := p.suite.Point().Mul(p.pubKey, gKeyPair.Secret)
insurerSig := p.sign(i, gKeyPair, sigBlameMsg)
choice := make(map[proof.Predicate]int)
pred := proof.Rep("D", "x", "P")
choice[pred] = 1
rand := p.suite.Cipher(abstract.RandomKey)
sval := map[string]abstract.Secret{"x": gKeyPair.Secret}
pval := map[string]abstract.Point{"D": diffieKey, "P": p.pubKey}
prover := pred.Prover(p.suite, sval, pval, choice)
proof, err := proof.HashProve(p.suite, protocolName, rand, prover)
if err != nil {
return nil, err
}
return new(blameProof).init(p.suite, diffieKey, proof, insurerSig), nil
}
func bifflePred() proof.Predicate {
// Branch 0 of either/or proof (for bit=0)
rep000 := proof.Rep("Xbar0-X0", "beta0", "G")
rep001 := proof.Rep("Ybar0-Y0", "beta0", "H")
rep010 := proof.Rep("Xbar1-X1", "beta1", "G")
rep011 := proof.Rep("Ybar1-Y1", "beta1", "H")
// Branch 1 of either/or proof (for bit=1)
rep100 := proof.Rep("Xbar0-X1", "beta1", "G")
rep101 := proof.Rep("Ybar0-Y1", "beta1", "H")
rep110 := proof.Rep("Xbar1-X0", "beta0", "G")
rep111 := proof.Rep("Ybar1-Y0", "beta0", "H")
and0 := proof.And(rep000, rep001, rep010, rep011)
and1 := proof.And(rep100, rep101, rep110, rep111)
or := proof.Or(and0, and1)
return or
}
// Get the proof predicate for decryption proofs:
// PK{ (x) : h = g^x and c2/m = c1^x }
func getProofPredicate() proof.Predicate {
return proof.And(proof.Rep("h", "x", "g"), proof.Rep("c2/m", "x", "c1"))
}