39 KiB
Binary format for R1CS
eip: title: r1cs binary format author: Jordi Baylina jordi@baylina.cat discussions-to: status: draft type: Standards Track category: ERC created: 2019-09-24 requires:
Simple Summary
This standard defines a standard format for a binery representation of a r1cs constraint system.
Abstract
Motivation
The zero knowledge primitives, requires the definition of a statment that wants to be proved. This statment can be expressed as a deterministric program or an algebraic circuit. Lots of primitives like zkSnarks, bulletProofs or aurora, requires to convert this statment to a rank-one constraint system.
This standard specifies a format for a r1cs and allows the to connect a set of tools that compiles a program or a circuit to r1cs that can be used for the zksnarks or bulletproofs primitives.
Specification
General considerations
The standard extension is .r1cs
A deterministic program (or circuit) is a program that generates a set of deterministic values given an input. All those values are labeled from l_{0} to l_{n_labels}
This file defines a map beween l_{i} -> w_{j} and defines a series a R1CS of the form
$$
\left{ \begin{array}{rclclcl}
(a_{0,0}w_0 + a_{0,1}w_1 + ... + a_{0,n}w_{n}) &\cdot& (b_{0,0} w_0 + b_{0,1} w_1 + ... + b_{0,n} w_{n}) &-& (c_{0,0} w_0 + c_{0,1} w_1 + ... + c_{0,n}w_{n}) &=& 0 \
(a_{1,0}w_0 + a_{1,1}w_1 + ... + a_{1,n}w_{n}) &\cdot& (b_{1,0} w_0 + b_{1,1} w_1 + ... + b_{1,n} w_{n}) &-& (c_{1,0} w_0 + c_{1,1}w_1 + ... + c_{1,n}w_{n}) &=& 0 \
...\
(a_{m-1,0}w_0 + a_{m-1,1}w_1 + ... + a_{m-1,n}w_{n}) &\cdot& (b_{m-1,0} w_0 + b_{m-1,1} w_1 + ... + b_{m-1,n} w_{n}) &-& (c_{m-1,0} w_0 + c_{m-1,1}w_1 + ... + c_{m-1,n}w_{n}) &=& 0
\end{array} \right.
$$
Wire 0 must be always mapped to label 0 and it's an input forced to value "1" implicitly
Format of the file
┏━━━━┳━━━━━━━━━━━━━━━━━┓
┃ 4 │ 72 31 63 73 ┃ Magic "r1cs"
┗━━━━┻━━━━━━━━━━━━━━━━━┛
┏━━━━┳━━━━━━━━━━━━━━━━━┓
┃ 4 │ 01 00 00 00 ┃ Version 1
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┃ 4 │ 03 00 00 00 ┃ Number of Sections
┗━━━━┻━━━━━━━━━━━━━━━━━┛
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┃ 4 │ sectionType ┃ 8 │ SectionSize ┃
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛
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┃ Section Content ┃
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┃ 4 │ sectionType ┃ 8 │ SectionSize ┃
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛
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┃ ┃
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┃ Section Content ┃
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┗━━━━━━━━━━━━━━━━━━━━━┛
...
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Magic Number
Size: 4 bytes The file start with a constant 4 bytes (magic number) "r1cs"
0x72 0x31 0x63 0x73
Version
Size: 4 bytes Format: Little-Endian
For this standard it's fixed to
0x01 0x00 0x00 0x00
Number of Sections
Size: 4 bytes Format: Little-Endian
Number of sections contained in the file
SectionType
Size: 4 bytes Format: Little-Endian
Type of the section.
Currently there are 3 types of sections defined:
- 0x00000001 : Header Section
- 0x00000002 : Constraint Section
- 0x00000003 : Wire2LabelId Map Section
If the file contain other types, the format is valid, but they MUST be ignored.
Any order of the section must be accepted.
Example:
0x01 0x00 0x00 0x00
SectionSize
Size: ws bytes
Format: Little-Endian
Size in bytes of the section
Header Section
Section Type: 0x01
┏━━━━┳━━━━━━━━━━━━━━━━━┓
┃ 4 │ 20 00 00 00 ┃ Field Size in bytes (fs)
┗━━━━┻━━━━━━━━━━━━━━━━━┛
┏━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ fs │ 010000f0 93f5e143 9170b979 48e83328 5d588181 b64550b8 29a031e1 724e6430 ┃ Prime size
┗━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
┏━━━━┳━━━━━━━━━━━━━━━━━┓
┃ 32 │ 01 00 00 00 ┃ nWires
┗━━━━┻━━━━━━━━━━━━━━━━━┛
┏━━━━┳━━━━━━━━━━━━━━━━━┓
┃ 32 │ 01 00 00 00 ┃ nPubOut
┗━━━━┻━━━━━━━━━━━━━━━━━┛
┏━━━━┳━━━━━━━━━━━━━━━━━┓
┃ 32 │ 01 00 00 00 ┃ nPubIn
┗━━━━┻━━━━━━━━━━━━━━━━━┛
┏━━━━┳━━━━━━━━━━━━━━━━━┓
┃ 32 │ 01 00 00 00 ┃ nPrvIn
┗━━━━┻━━━━━━━━━━━━━━━━━┛
┏━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 64 │ 01 00 00 00 00 00 00 00 ┃ nLabels
┗━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
┏━━━━┳━━━━━━━━━━━━━━━━━┓
┃ 32 │ 01 00 00 00 ┃ mConstraints
┗━━━━┻━━━━━━━━━━━━━━━━━┛
field Size (fs)
Size: 4 bytes Format: Little-Endian
Size in bytes of a field element. Mast be a multiple of 8.
Example:
0x00 0x0 0x00 0x00
Prime
Prime Number of the field
Example:
0x010000f0_93f5e143_9170b979_48e83328_5d588181_b64550b8_29a031e1_724e6430
Number of wires
Size: 4 bytes Format: Little-Endian
Total Number of wires including ONE signal (Index 0).
Number of public outputs
Size: 4 bytes Format: Little-Endian
Total Number of wires public output wires. They should be starting at idx 1
Number of public inputs
Size: 4 bytes Format: Little-Endian
Total Number of wires public input wires. They should be starting just after the public output
Number of private inputs
Size: 4 bytes Format: Little-Endian
Total Number of wires private input wires. They should be starting just after the public inputs
Number of Labels
Size: 8 bytes Format: Little-Endian
Total Number of wires private input wires. They should be starting just after the public inputs
Number of constraints (m)
Size: 4 bytes Format: Little-Endian
Total Number of constraints
Constraints section
Section Type: 0x02
┏━━━━┳━━━━━━━━━━━━━━━━━┓ ╲
┃ 32 │ nA ┃ ╲
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ ╲
┃ 32 │ wireId_1 ┃ fs │ a_{0,wireId_1} ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━┫ │
┃ 32 │ wireId_2 ┃ fs │ a_{0,wireId_2} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
... ... │
┏━━━━┳━━━━━━━━━━━━━━━━━┳━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_nA ┃ fs │ a_{0,wireId_nA} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
┏━━━━┳━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ nB ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_1 ┃ fs │ b_{0,wireId_1} ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━┫ ╲
┃ 32 │ wireId_2 ┃ fs │ b_{0,wireId_2} ┃ ╲
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ ╱ Constraint_0
... ... ╱
┏━━━━┳━━━━━━━━━━━━━━━━━┳━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_nB ┃ fs │ b_{0,wireId_nB} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
┏━━━━┳━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ nC ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_1 ┃ fs │ c_{0,wireId_1} ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━┫ │
┃ 32 │ wireId_2 ┃ fs │ c_{0,wireId_2} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
... ... │
┏━━━━┳━━━━━━━━━━━━━━━━━┳━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_nC ┃ fs │ c_{0,wireId_nC} ┃ ╱
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ ╱
╱
┏━━━━┳━━━━━━━━━━━━━━━━━┓ ╲
┃ 32 │ nA ┃ ╲
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ ╲
┃ 32 │ wireId_1 ┃ fs │ a_{1,wireId_1} ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━┫ │
┃ 32 │ wireId_2 ┃ fs │ a_{1,wireId_2} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
... ... │
┏━━━━┳━━━━━━━━━━━━━━━━━┳━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_nA ┃ fs │ a_{1,wireId_nA} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
┏━━━━┳━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ nB ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_1 ┃ fs │ b_{1,wireId_1} ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━┫ ╲
┃ 32 │ wireId_2 ┃ fs │ b_{1,wireId_2} ┃ ╲
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ ╱ Constraint_1
... ... ╱
┏━━━━┳━━━━━━━━━━━━━━━━━┳━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_nB ┃ fs │ b_{1,wireId_nB} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
┏━━━━┳━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ nC ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_1 ┃ fs │ c_{1,wireId_1} ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━┫ │
┃ 32 │ wireId_2 ┃ fs │ c_{1,wireId_2} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
... ... │
┏━━━━┳━━━━━━━━━━━━━━━━━┳━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_nC ┃ fs │ c_{1,wireId_nC} ┃ ╱
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ ╱
╱
...
...
...
┏━━━━┳━━━━━━━━━━━━━━━━━┓ ╲
┃ 32 │ nA ┃ ╲
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ ╲
┃ 32 │ wireId_1 ┃ fs │ a_{m-1,wireId_1} ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━┫ │
┃ 32 │ wireId_2 ┃ fs │ a_{m-1,wireId_2} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
... ... │
┏━━━━┳━━━━━━━━━━━━━━━━━┳━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_nA ┃ fs │ a_{m-1,wireId_nA} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
┏━━━━┳━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ nB ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_1 ┃ fs │ b_{m-1,wireId_1} ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━┫ ╲
┃ 32 │ wireId_2 ┃ fs │ b_{m-1,wireId_2} ┃ ╲
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ ╱ Constraint_{m-1}
... ... ╱
┏━━━━┳━━━━━━━━━━━━━━━━━┳━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_nB ┃ fs │ b_{m-1,wireId_nB} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
┏━━━━┳━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ nC ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_1 ┃ fs │ c_{m-1,wireId_1} ┃ │
┣━━━━╋━━━━━━━━━━━━━━━━━╋━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━┫ │
┃ 32 │ wireId_2 ┃ fs │ c_{m-1,wireId_2} ┃ │
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ │
... ... │
┏━━━━┳━━━━━━━━━━━━━━━━━┳━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓ │
┃ 32 │ wireId_nC ┃ fs │ c_{m-1,wireId_nC} ┃ ╱
┗━━━━┻━━━━━━━━━━━━━━━━━┻━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━┛ ╱
╱
Constraints
Each constraint contains 3 linear combinations A, B, C.
The constraint is such that:
A*B-C = 0
Linear combination
Each linear combination is of the form:
$$ a_{j,0}w_0 + a_{j,1}w_1 + ... + a_{j,n}w_{n} $$
Number of nonZero Factors
Size: 4 bytes Format: Little-Endian
Total number of non Zero factors in the linear compination.
The factors MUST be sorted in ascending order.
Factor
For each factor we have the index of the factor and the value of the factor.
WireId of the factor
Size: 4 bytes Format: Little-Endian
WireId of the nonZero Factor
Value of the factor
This is the factor that multiplies the associated wire in the linear convination.
For example, to represent the linear combination:
$$ 5w_4 +8w_5 + 260w_{886} $$
The linear combination would be represented as:
┏━━━━━━━━━━━━━━━━━┓
┃ 03 00 00 00 ┃
┣━━━━━━━━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 04 00 00 00 ┃ 05000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┣━━━━━━━━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ 05 00 00 00 ┃ 08000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┣━━━━━━━━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ 76 03 00 00 ┃ 04010000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┗━━━━━━━━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
WireId2LabelId Map Section
Section Type: 0x03
┏━━┳━━━━━━━━━━━━━━━━━━━┳━━┳━━━━━━━━━━━━━━━━━━━┓ ┏━━┳━━━━━━━━━━━━━━━━━━━┓
┃64│ labelId of Wire_0 ┃64│ labelId of Wire_1 ┃ ... ┃64│ labelId of Wire_n ┃
┗━━┻━━━━━━━━━━━━━━━━━━━┻━━┻━━━━━━━━━━━━━━━━━━━┛ ┗━━┻━━━━━━━━━━━━━━━━━━━┛
Rationale
Variable size for field elements allows to shrink the size of the file and allows to work with any field.
Version allows to update the format.
Have a very good comprasion ratio for sparse r1cs as it's the normal case.
The motivation of having a map between l and w is that this allows optimizers to calculate equivalent r1cs systems but keeping the original values geneated by the circuit.
Backward Compatibility
N.A.
Test Cases
Example
Given this r1cs in a 256 bit Field:
$$
\left{ \begin{array}{rclclcl}
(3w_5 + 8w_6) &\cdot& (2w_0 + 20w_2 + 12w_3) &-& (5w_0 + 7w_2) &=& 0 \
(4w_1 + 8w_4 + 3w_5) &\cdot& (6w_6 + 44w_3) && &=& 0 \
(4w_6) &\cdot& (6w_0 + 5w_3 + 11s_2) &-& (600w_6) &=& 0
\end{array} \right.
$$
And a Wire to label map.
$$
w_0 := l_0 \
w_1 := l_3 \
w_2 := l_{10} \
w_3 := l_{11} \
w_4 := l_{12} \
w_5 := l_{15} \
w_6 := l_{324} \
$$
The format will be:
┏━━━━━━━━━━┓
┃ 72316377 ┃ Magic
┣━━━━━━━━━━┫
┃ 01000000 ┃ Version
┣━━━━━━━━━━┫
┃ 03000000 ┃ nSections
┗━━━━━━━━━━┛
┏━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━┓
┃ 01000000 ┃ 40000000 00000000 ┃ SectionType: Header
┗━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━┛
┏━━━━━━━━━━┓
┃ 20000000 ┃ Field Size
┣━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 010000f0 93f5e143 9170b979 48e83328 5d588181 b64550b8 29a031e1 724e6430 ┃
┣━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
┃ 07000000 ┃ # of wires
┣━━━━━━━━━━┫
┃ 01000000 ┃ # Public Outs
┣━━━━━━━━━━┫
┃ 02000000 ┃ # Public Ins
┣━━━━━━━━━━┫
┃ 03000000 ┃ # Private Ins
┣━━━━━━━━━━┻━━━━━━━━┓
┃ e8030000 00000000 ┃ # Labels
┣━━━━━━━━━━┳━━━━━━━━┛
┃ 03000000 ┃ # Constraints
┗━━━━━━━━━━┛
┏━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━┓
┃ 02000000 ┃ 88200000 00000000 ┃ SectionType: Constraints
┗━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━┛
┏━━━━━━━━━━┓ Constraint 0: (3w_5 + 8w_6) * (2w_0 + 20w_2 + 12w_3) - (5w_0 + 7w_2) = 0
┃ 02000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 05000000 ┃ 03000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ 06000000 ┃ 01000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┗━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
┏━━━━━━━━━━┓
┃ 03000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 00000000 ┃ 02000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ 02000000 ┃ 01140000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ 03000000 ┃ 0C000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┗━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
┏━━━━━━━━━━┓
┃ 02000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 00000000 ┃ 05000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ 02000000 ┃ 07000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┗━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
┏━━━━━━━━━━┓ Constraint 1: (4w_1 + 8w_4 + 3w_5) * (6w_6 + 44w_3) = 0
┃ 03000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 01000000 ┃ 04000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ 04000000 ┃ 08000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ 05000000 ┃ 03000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┗━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
┏━━━━━━━━━━┓
┃ 02000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 03000000 ┃ 2C000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ 06000000 ┃ 06000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┗━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
┏━━━━━━━━━━┓
┃ 00000000 ┃
┗━━━━━━━━━━┛
┏━━━━━━━━━━┓ Constraint 2: (4w_6) * (6w_0 + 5w_3 + 11w_2) - (600w_6) = 0
┃ 01000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 06000000 ┃ 04000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┗━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
┏━━━━━━━━━━┓
┃ 03000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 00000000 ┃ 06000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ 02000000 ┃ 0B000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┫
┃ 03000000 ┃ 05000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┗━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
┏━━━━━━━━━━┓
┃ 01000000 ┃
┣━━━━━━━━━━╋━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ 06000000 ┃ 58020000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 ┃
┗━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
┏━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━┓
┃ 03000000 ┃ 38000000 00000000 ┃ Wire to Label Map
┗━━━━━━━━━━┻━━━━━━━━━━━━━━━━━━━┛
┏━━━━━━━━━━━━━━━━━━━┓
┃ 00000000 00000000 ┃
┣━━━━━━━━━━━━━━━━━━━┫
┃ 03000000 00000000 ┃
┣━━━━━━━━━━━━━━━━━━━┫
┃ 0a000000 00000000 ┃
┣━━━━━━━━━━━━━━━━━━━┫
┃ 0b000000 00000000 ┃
┣━━━━━━━━━━━━━━━━━━━┫
┃ 0c000000 00000000 ┃
┣━━━━━━━━━━━━━━━━━━━┫
┃ 0f000000 00000000 ┃
┣━━━━━━━━━━━━━━━━━━━┫
┃ 44010000 00000000 ┃
┗━━━━━━━━━━━━━━━━━━━┛
And the binary representation in Hex:
72316377
01000000
03000000
01000000 40000000 00000000
20000000
010000f0 93f5e143 9170b979 48e83328 5d588181 b64550b8 29a031e1 724e6430
07000000
01000000
02000000
03000000
e8030000 00000000
03000000
02000000 88200000 00000000
02000000
05000000 03000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
06000000 01000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
03000000
00000000 02000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
02000000 01140000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
03000000 0C000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
02000000
00000000 05000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
02000000 07000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
03000000
01000000 04000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
04000000 08000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
05000000 03000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
02000000
03000000 2C000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
06000000 06000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
00000000
01000000
06000000 04000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
03000000
00000000 06000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
02000000 0B000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
03000000 05000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
01000000
06000000 58020000 00000000 00000000 00000000 00000000 00000000 00000000 00000000
03000000 38000000 00000000
00000000 00000000
03000000 00000000
0a000000 00000000
0b000000 00000000
0c000000 00000000
0f000000 00000000
44010000 00000000
Implementation
circom will output this format.
Copyright
Copyright and related rights waived via CC0.