Output Descriptions

Each output contains an OutputBody and a zk-SNARK output proof.

Clients using the ephemeral public key $epk$ provided in an output body to decrypt a note payload MUST check:

$epk=[esk]B_d$

Output zk-SNARK Statements

The output proof demonstrates the properties enumerated below for the private witnesses known by the prover:

• Note amount $v$ (interpreted as an ${\mathbb{F}}_q$) and asset ID $\in \mathbb{G}$
• Blinding factor $rcm\in {\mathbb{F}}_q$ used to blind the note commitment
• Diversified basepoint $B_d\in \mathbb{G}$ corresponding to the address
• Transmission key $p{k}_d\in \mathbb{G}$ corresponding to the address
• Clue key $\mathsf{c}{\mathsf{k}}_{\mathsf{d}}\in {\mathbb{F}}_q$ corresponding to the address
• Blinding factor $\tilde{v}\in {\mathbb{F}}_r$ used to blind the balance commitment

And the corresponding public inputs:

• Balance commitment $cv\in G$ to the value balance
• Note commitment $cm\in {\mathbb{F}}_q$

Note Commitment Integrity

The zk-SNARK certifies that the public input note commitment $cm$ was derived as:

$cm=has{h}_6(ds,(rcm,v,ID,B_d,p{k}_d,c{k}_d))$.

using the above witnessed values and where ds is a constant domain separator:

ds = from_le_bytes(BLAKE2b-512(b"penumbra.notecommit")) mod q

Balance Commitment Integrity

The zk-SNARK certifies that the public input balance commitment $cv$ was derived from the witnessed values as:

$cv=[v]G_v+[\tilde{v}]G_{\tilde{v}}$

where $G_{\tilde{v}}$ is a constant generator and $G_v$ is an asset-specific generator point derived as described in Value Commitments.

Diversified Base is not Identity

The zk-SNARK certifies that the diversified basepoint $B_d$ is not identity.

Note that we do not check the integrity of the ephemeral public key $epk$ in the zk-SNARK. Instead this check should be performed at note decryption time as described above.