Ensure presence and correctness of validity checks

[piotr-roslaniec]

Revise Ferveo's whitepaper and docs. List all validity checks for the protocol. Revise the source code and make sure that those checks are present, correct, and tested. Devise green- and red path scenarios.

List of checks:

• Research and implement decryption share verification for simple tDec #42
• Verify PVSS transcript correctness #44 - moved, postponed
• Verify blinding of the key shares #45 - moved, postponed

---

• Ciphertext Validity Checking - must be done before creating a decryption share
• Validity checks #38

---

• Verifying Decryption Shares - must be done before combining decryption shares
  • batch_verify_decryption_shares
    • Used to be called in the original tpke benchmark
    • Checks that $e([\sum_j \alpha_{i,j} ] D_i, B_i)$ matches $e(\sum_j [ \sum_i \alpha_{i,j} ] U_j, -H)$ (?)
      - $B_i = [b_i] H$, blinding_key_prepared
  • Also described in docs
    • Validity checks #38
    • Existing implementation works for the fast tDec variant
    • Check for simple tDec variant is backlogged Research and implement decryption share verification for simple tDec #42

---

ferveo:

• verify_optimistic
  • Usage example
  • Already tested with positive and negative examples.
  • This one is effectively done, we just need to make sure we know what it does and whether we are happy with using it

[theref]

• Ciphertext Validity Checking - must be done before creating a decryption share
• Validity checks #38

tpke/src/iphertext.rs:

pub fn check_ciphertext_validity<E: PairingEngine>(
    c: &Ciphertext<E>,
    aad: &[u8],
) -> bool {
    let g_inv = E::G1Prepared::from(-E::G1Affine::prime_subgroup_generator());
    let hash_g2 = E::G2Prepared::from(construct_tag_hash::<E>(
        c.commitment,
        &c.ciphertext[..],
        aad,
    ));

    E::product_of_pairings(&[
        (E::G1Prepared::from(c.commitment), hash_g2),
        (g_inv, E::G2Prepared::from(c.auth_tag)),
    ]) == E::Fqk::one()
}

which is used by pub fn checked_decrypt and fn decrypt_with_shared_secret.

Also, in file tpke/src/api we have:

    pub fn to_decryption_share(&self) -> DecryptionShare {
        // TODO: Add verification steps

Verification is missing from this function.

[theref]

• Verifying Decryption Shares - must be done before combining decryption shares

[theref]

• We don't use weights, but the indexing is still important

[theref]

• Are we going to be aggregating decryption shares?

[cygnusv]

• Are we going to be aggregating decryption shares?

No, my understanding is that this makes sense for Ferveo original implementation, where a node (with a single private blinding key ek_i) may have many private shares, and the corresponding decryption shares can be aggregated.

[theref]

yeah, i couldn't think of any scenario where it would make sense for our use case

[piotr-roslaniec]

I found some other checks that I would like to document and verify.

Moved to issue description

[theref]

oh nice, these are from the code and we need to verify the maths?

[piotr-roslaniec]

Yes, these are from the original Ferveo source code, and I'd like to figure out what they do, how to use them, whether we need them etc.

[piotr-roslaniec]

We don't use weights, but the indexing is still important

Marking as complete since ferveo validators have a share_index attributed to them.

Are we going to be aggregating decryption shares?

Marking as solved.

I've aggregated the remaining checks into the issue description.

[piotr-roslaniec]

Not sure how to compute 4.4.4 for a simple tDec variant. In this variant, $D_i$ is of type Fqk (product of pairing), but we need to be G1Prepared for $e(D_i, B_i)$ to work.

[piotr-roslaniec]

verify_blinding doesn't work i.e. the original code seems to be implemented incorrectly. I can't find a reference to this operation in the docs or in the whitepaper.

@cygnusv, is this something we would like to explore further, or should we drop verify_blinding?

[piotr-roslaniec]

If blinding_key, $B_i = [b] dk_i$, is the same as PublicKey::encryption_key of DKG validator, then verify_blinding in tpke is effectively the same check that verify_full in ferveo does:

• $e(G_1, \hat{Y}{i,\omega_j}) = e(A_{i,\omega_j}, ek_i)$ verify_full
• $e(g, Y_i) = e(A_i, [b] H)$, verify_blinding

If $B_i = [b] dk_i = b [H]$ doesn't hold, then I don't know what verify_blinding is supposed to check.

[piotr-roslaniec]

Not sure how to compute 4.4.4 for a simple tDec variant. In this variant, Di is of type Fqk (product of pairing), but we need to be G1Prepared for e(Di,Bi) to work.

The naive rewrite doesn't make sense here anyway, since in simple tDec decryption share is defined as $C_i=e(U,Z_i)$, and in fast tDec as $D_i=[b−1]U$.

Marking this as a candidate for a research item in #42

[piotr-roslaniec]

Found this earlier rewrite of verify_blinding.

[piotr-roslaniec]

Closing this as the work will be continued in separate issues mentioned in OP.