Terminology

The key words "MUST", "MUST NOT", "SHOULD NOT", and "MAY" in this document are to be interpreted as described in BCP 14 1 when, and only when, they appear in all capitals.

The following functions are defined in the Zcash Protocol Specification 2 according to the type (Sapling or Orchard) of note plaintext being processed:

• let \(\mathsf{ToScalar}\) be \(\mathsf{ToScalar^{Sapling}}\) defined in section 4.2.2 5 or \(\mathsf{ToScalar^{Orchard}}\) defined in section 4.2.3 6;
• let \(\mathsf{DiversifyHash}\) be \(\mathsf{DiversifyHash^{Sapling}}\) or \(\mathsf{DiversifyHash^{Orchard}}\) defined in section 5.4.1.6 12;
• let \(\mathsf{KA}\) be \(\mathsf{KA^{Sapling}}\) defined in section 5.4.5.3 13 or \(\mathsf{KA^{Orchard}}\) defined in section 5.4.5.5 14;
• let \(\mathsf{NoteCommit}\) be \(\mathsf{NoteCommit^{Sapling}}\) or \(\mathsf{NoteCommit^{Orchard}}\) defined in section 4.1.8 4.

Abstract

This ZIP proposes a new note plaintext format for Sapling Outputs (later extended to include Orchard Actions) in transactions. The new format allows recipients to verify that the sender of an Output or Action knows the private key corresponding to the ephemeral Diffie–Hellman key, in order to avoid an assumption on zk-SNARK soundness for preventing diversified address linkability.

Motivation

The Sapling and Orchard payment protocols have a feature called "diversified addresses" which allows a single incoming viewing key to receive payments on an enormous number of distinct and unlinkable payment addresses. This feature allows users to maintain many payment addresses without paying additional overhead during blockchain scanning.

The feature works by allowing payment addresses to become a tuple \((\mathsf{pk_d}, \mathsf{d})\) of a public key \(\mathsf{pk_d}\) and \(88\!\) -bit diversifier \(\mathsf{d}\) such that \(\mathsf{pk_d} = [\mathsf{ivk}]\, \mathsf{DiversifyHash}(\mathsf{d})\) for some incoming viewing key \(\mathsf{ivk}\!\) . The hash function \(\mathsf{DiversifyHash}(\mathsf{d})\) maps from a diversifier to prime-order elements of the Jubjub or Pallas elliptic curve. It is possible for a user to choose many \(\mathsf{d}\) to create several distinct and unlinkable payment addresses of this form.

In order to make a payment to a Sapling or Orchard address, an ephemeral secret \(\mathsf{esk}\) is sampled by the sender and an ephemeral public key \(\mathsf{epk} = [\mathsf{esk}]\, \mathsf{DiversifyHash}(\mathsf{d})\) is included in the Output or Action description. Then, a shared Diffie-Hellman secret is computed by the sender as \(\mathsf{KA.Agree}(\mathsf{esk}, \mathsf{pk_d})\!\) . The recipient can recover this shared secret without knowledge of the particular \(\mathsf{d}\) by computing \(\mathsf{KA.Agree}(\mathsf{ivk}, \mathsf{epk})\!\) . This shared secret is then used as part of note decryption.

Naïvely, the recipient cannot know which \((\mathsf{pk_d}, \mathsf{d})\) was used to compute the shared secret, but the sender is asked to include the \(\mathsf{d}\) within the note plaintext to reconstruct the note. However, if the recipient has more than one known address, an attacker could use a different payment address to perform secret exchange and, by observing the behavior of the recipient, link the two diversified addresses together. (This attacker strategy was discovered by Brian Warner earlier in the design of the Sapling protocol.)

In order to prevent this attack before activation of this ZIP, the protocol forced the sender to prove knowledge of the discrete logarithm of \(\mathsf{epk}\) with respect to the \(\mathsf{g_d} = \mathsf{DiversifyHash}(\mathsf{d})\) included within the note commitment. This \(\mathsf{g_d}\) is determined by \(\mathsf{d}\) and recomputed during note decryption, and so either the note decryption will fail, or the sender will be unable to produce the proof that requires knowledge of the discrete logarithm.

However, the latter proof was part of the Sapling Output statement, and so relied on the soundness of the underlying Groth16 zk-SNARK — hence on relatively strong cryptographic assumptions and a trusted setup. It is preferable to force the sender to transfer sufficient information in the note plaintext to allow deriving \(\mathsf{esk}\!\) , so that, during note decryption, the recipient can check that \(\mathsf{epk} = [\mathsf{esk}]\, \mathsf{g_d}\) for the expected \(\mathsf{g_d}\!\) , and ignore the payment as invalid otherwise. For Sapling, this forms a line of defense in the case that soundness of the zk-SNARK does not hold. For Orchard, this check is essential because (for efficiency and simplicity) \(\mathsf{epk} = [\mathsf{esk}]\, \mathsf{g_d}\) is not checked in the Action statement.

Merely sending \(\mathsf{esk}\) to the recipient in the note plaintext would require us to enlarge the note plaintext, but also would compromise the proof of IND-CCA2 security for in-band secret distribution. We avoid both of these concerns by using a key derivation to obtain both \(\mathsf{esk}\) and \(\mathsf{rcm}\!\) .

Specification

Pseudo random functions (PRFs) are defined in section 4.1.2 of the Zcash Protocol Specification 3. We will be adapting \(\mathsf{PRF^{expand}}\) for the purposes of this ZIP. This function is keyed by a 256-bit key \(\mathsf{sk}\) and takes an arbitrary length byte sequence as input, returning a \(64\!\) -byte sequence as output.

Rationale

The attack that this prevents is an interactive attack that requires an adversary to be able to break critical soundness properties of the zk-SNARKs underlying Sapling. It is potentially valid to assume that this cannot occur, due to other damaging effects on the system such as undetectable counterfeiting. However, we have attempted to avoid any instance in the protocol where privacy (even against interactive attacks) depended on strong cryptographic assumptions. Acting differently here would be confusing for users that have previously been told that "privacy does not depend on zk-SNARK soundness" or similar claims.

It would have been possible to infringe on the length of the memo field and ask the sender to provide \(\mathsf{esk}\) within the existing note plaintext without modifying the transaction format, but this would have harmed users who have come to expect a \(512\!\) -byte memo field to be available to them. Changes to the memo field length should be considered in a broader context than changes made for cryptographic purposes.

It would be possible to transmit a signature of knowledge of a correct \(\mathsf{esk}\) rather than \(\mathsf{esk}\) itself, but this appears to be an unnecessary complication and is likely slower than just supplying \(\mathsf{esk}\!\) .

The grace period is intended to mitigate loss-of-funds risk due to non-conformant sending wallet implementations. The intention is that during the grace period (of about 4 weeks), it will be possible to identify wallets that are still sending plaintexts according to the old specification, and cajole their developers to make the required updates. For the avoidance of doubt, such wallets are non-conformant because it is a "MUST" requirement to immediately switch to sending note plaintexts with lead byte \(\mathtt{0x02}\) (and the other changes in this specification) at the upgrade. Note that nodes will clear their mempools when the upgrade activates, which will clear all plaintexts with lead byte \(\mathtt{0x01}\) that were sent conformantly and not mined before the upgrade.

Historical note: in practice some note plaintexts with lead byte \(\mathtt{0x01}\) were non-conformantly sent even after the end of the specified grace period. ZecWallet extended its implementation of the grace period by a further 161280 blocks (approximately 20 weeks) in order to allow for recovery of these funds 20.

Security and Privacy Considerations

The changes made in this proposal prevent an interactive attack that could link together diversified addresses by only breaking the knowledge soundness assumption of the zk-SNARK. It is already assumed that the adversary cannot defeat the EC-DDH assumption of the Jubjub (or Pallas) elliptic curve, for it could perform a linkability attack trivially in that case.

In the naïve case where the protocol is modified so that \(\mathsf{esk}\) is supplied directly to the recipient (rather than derived through \(\mathsf{rseed}\!\) ) this would lead to an instance of key-dependent encryption, which is difficult or perhaps impossible to prove secure using existing security notions. Our approach of using a key derivation, which ultimately queries an oracle, allows a proof for IND-CCA2 security to be written by reprogramming the oracle to return bogus keys when necessary.

Deployment

This proposal will be deployed with the Canopy network upgrade. 18

Reference Implementation

In zcashd:

• https://github.com/zcash/zcash/pull/4578

In librustzcash:

• https://github.com/zcash/librustzcash/pull/258

Acknowledgements

The discovery that diversified address unlinkability depended on the zk-SNARK knowledge assumption was made by Sean Bowe and Zooko Wilcox.

References