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book: Use M for number-of-circuit-instances in proof encoding

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Jack Grigg 2021-06-01 17:25:31 +01:00
parent 9a7f331f1b
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18
book/src/design/implementation/proofs.md
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@ -58,27 +58,27 @@ In the encoding description below, we will use the following circuit-specific co
- $Q_A$ - the number of advice column queries.
- $Q_F$ - the number of fixed column queries.
- $Q_I$ - the number of instance column queries.
- $N$ - the number of instances of the circuit that are being proven simultaneously.
- $M$ - the number of instances of the circuit that are being proven simultaneously.
As the proof encoding directly follows the transcript, we can break the encoding into
sections matching the Halo 2 protocol:
- PLONK commitments:
- $A$ points (repeated $N$ times).
- $2L$ points (repeated $N$ times).
- $P$ points (repeated $N$ times).
- $L$ points (repeated $N$ times).
- $A$ points (repeated $M$ times).
- $2L$ points (repeated $M$ times).
- $P$ points (repeated $M$ times).
- $L$ points (repeated $M$ times).
- Vanishing argument:
- $D - 1$ points.
- $Q_I$ scalars (repeated $N$ times).
- $Q_A$ scalars (repeated $N$ times).
- $Q_I$ scalars (repeated $M$ times).
- $Q_A$ scalars (repeated $M$ times).
- $Q_F$ scalars.
- $D - 1$ scalars.
- PLONK evaluations:
- $(2 + \textsf{Col}_P) \times P$ scalars (repeated $N$ times).
- $5L$ scalars (repeated $N$ times).
- $(2 + \textsf{Col}_P) \times P$ scalars (repeated $M$ times).
- $5L$ scalars (repeated $M$ times).
- Multiopening argument:
- 1 point.