# Viewing Keys

Each spending key has a corresponding collection of viewing keys, which represent different subsets of capability around creating and viewing transactions:

• the full viewing key represents all capability except for spend authorization, including viewing all incoming and outgoing transactions and creating proofs;
• the incoming viewing key represents the capability to scan the blockchain for incoming transactions;
• the outgoing viewing key represents the capability to recover information about sent transactions.

## Full Viewing Keys

The full viewing key consists of two components:

• , the spend verification key, a decaf377-rdsa verification key;
• , the nullifier key.

Their derivation is described in the previous section.

The spend verification key is used (indirectly) to verify spend authorizations. Using it directly would allow spends signed by the same key to be linkable to each other, so instead, each spend is signed by a randomization of the spend authorization key, and the proof statement includes a proof that the verification key provided in the spend description is a randomization of the (secret) spend verification key.

The nullifier key is used to derive the nullifier of a note sent to a particular user. Nullifiers are used for double-spend protection and so must be bound to the note contents, but it’s important that nullifiers cannot be derived solely from the contents of a note, so that the sender of a note cannot learn when the recipient spent it.

The full viewing key can be used to create transaction proofs, as well as to view all activity related to its spending authority.

## Incoming and Outgoing Viewing Keys

The incoming viewing key consists of two components:

• , the diversifier key, and
• , the incoming viewing key (component)1.

The diversifier key is used to derive diversifiers, which allow a single spend authority to have multiple, publicly unlinkable diversified addresses, as described in the next section. The incoming viewing key is used to scan the chain for transactions sent to every diversified address simultaneously.

The outgoing viewing key consists of one component:

• , the outgoing viewing key (component).

These components are derived as follows.

The and are not intended to be derived in a circuit. Define prf_expand(label, key, input) as BLAKE2b-512 with personalization label, key key, and input input. Define to_le_bytes(input) as the function that encodes an input integer in little-endian byte order. Define decaf377_encode(element) as the function that produces the canonical encoding of a decaf377 element. Then

dk  = prf_expand(b"Penumbra_ExpndVK", to_le_bytes(nk), decaf377_encode(ak))[ 0..32]
ovk = prf_expand(b"Penumbra_ExpndVK", to_le_bytes(nk), decaf377_encode(ak))[32..64]


The is intended to be derived in a circuit. Define poseidon_hash_2(label, x1, x2) to be rate-2 Poseidon hashing of inputs x1, x2 with the capacity initialized to the domain separator label. Define from_le_bytes(bytes) as the function that interprets its input bytes as an integer in little-endian order. Define decaf377_s(element) as the function that produces the -value used to encode the provided decaf377 element. Then

ivk = poseidon_hash_2(from_le_bytes(b"penumbra.derive.ivk"), nk, decaf377_s(ak)) mod r


i.e., we treat the Poseidon output (an element) as an integer, and reduce it modulo to get an element of .

1

In general, we refer to the combination of and as the “incoming viewing key” and the component just as , using the modifier “component” in case of ambiguity.