The previous section gives a fairly low-level description of a circuit. When implementing circuits we will typically use a higher-level API which aims for the desirable characteristics of auditability, efficiency, modularity, and expressiveness.

Some of the terminology and concepts used in this API are taken from an analogy with integrated circuit design and layout. As for integrated circuits, the above desirable characteristics are easier to obtain by composing chips that provide efficient pre-built implementations of particular functionality.

For example, we might have chips that implement particular cryptographic primitives such as a hash function or cipher, or algorithms like scalar multiplication or pairings.

In PLONKish circuits, it is possible to build up arbitrary logic just from standard gates that do field multiplication and addition. However, very significant efficiency gains can be obtained by using custom gates.

Using our API, we define chips that "know" how to use particular sets of custom gates. This creates an abstraction layer that isolates the implementation of a high-level circuit from the complexity of using custom gates directly.

Even if we sometimes need to "wear two hats", by implementing both a high-level circuit and the chips that it uses, the intention is that this separation will result in code that is easier to understand, audit, and maintain/reuse. This is partly because some potential implementation errors are ruled out by construction.

Gates in PLONKish circuits refer to cells by relative references, i.e. to the cell in a given column, and the row at a given offset relative to the one in which the gate's selector is set. We call this an offset reference when the offset is nonzero (i.e. offset references are a subset of relative references).

Relative references contrast with absolute references used in equality constraints, which can point to any cell.

The motivation for offset references is to reduce the number of columns needed in the configuration, which reduces proof size. If we did not have offset references then we would need a column to hold each value referred to by a custom gate, and we would need to use equality constraints to copy values from other cells of the circuit into that column. With offset references, we not only need fewer columns; we also do not need equality constraints to be supported for all of those columns, which improves efficiency.

In R1CS (another arithmetization which may be more familiar to some readers, but don't worry if it isn't), a circuit consists of a "sea of gates" with no semantically significant ordering. Because of offset references, the order of rows in a PLONKish circuit, on the other hand, is significant. We're going to make some simplifying assumptions and define some abstractions to tame the resulting complexity: the aim will be that, at the gadget level where we do most of our circuit construction, we will not have to deal with relative references or with gate layout explicitly.

We will partition a circuit into regions, where each region contains a disjoint subset of cells, and relative references only ever point within a region. Part of the responsibility of a chip implementation is to ensure that gates that make offset references are laid out in the correct positions in a region.

Given the set of regions and their shapes, we will use a separate floor planner to decide where (i.e. at what starting row) each region is placed. There is a default floor planner that implements a very general algorithm, but you can write your own floor planner if you need to.

Floor planning will in general leave gaps in the matrix, because the gates in a given row did not use all available columns. These are filled in —as far as possible— by gates that do not require offset references, which allows them to be placed on any row.

Chips can also define lookup tables. If more than one table is defined for the same lookup argument, we can use a tag column to specify which table is used on each row. It is also possible to perform a lookup in the union of several tables (limited by the polynomial degree bound).

Composing chips

In order to combine functionality from several chips, we compose them in a tree. The top-level chip defines a set of fixed, advice, and instance columns, and then specifies how they should be distributed between lower-level chips.

In the simplest case, each lower-level chips will use columns disjoint from the other chips. However, it is allowed to share a column between chips. It is important to optimize the number of advice columns in particular, because that affects proof size.

The result (possibly after optimization) is a PLONKish configuration. Our circuit implementation will be parameterized on a chip, and can use any features of the supported lower-level chips via the top-level chip.

Our hope is that less expert users will normally be able to find an existing chip that supports the operations they need, or only have to make minor modifications to an existing chip. Expert users will have full control to do the kind of circuit optimizations that ECC is famous for 🙂.