# Cryptographic Protocol

This chapter describes the cryptographic design of the Penumbra protocol, described in more detail in the following sections:

• The Addressses and Keys section describes the Penumbra key hierarchy and diversified addresses.

• The Notes section describes Penumbra’s private notes and their contents.

## Notation

We use the following notation in this chapter:

• denotes the decaf377 group;
• denotes the BLS12-377 scalar field of order ;
• denotes the decaf377 scalar field of order .