|
|
# Binary format for R1CS
---eip:title: r1cs binary formatauthor: Jordi Baylina <jordi@baylina.cat>discussions-to:status: drafttype: Standards Trackcategory: ERCcreated: 2019-09-24requires:---
## 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
````
โโโโโโณโโโโโโโโโโโโโโโโโโ โ 4 โ 72 31 63 73 โ Magic "r1cs" โโโโโโปโโโโโโโโโโโโโโโโโโ โโโโโโณโโโโโโโโโโโโโโโโโโ โ 4 โ 01 00 00 00 โ Version 1 โโโโโโปโโโโโโโโโโโโโโโโโโ โโโโโโณโโโโโโโโโโโโโโโโโโ โ 4 โ 03 00 00 00 โ Number of Sections โโโโโโปโโโโโโโโโโโโโโโโโโ โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ 4 โ sectionType โ 8 โ SectionSize โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโโโโโโโโโ โ โ โ โ โ โ โ Section Content โ โ โ โ โ โ โ โโโโโโโโโโโโโโโโโโโโโโโ
โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ 4 โ sectionType โ 8 โ SectionSize โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโโโโโโโโโ โ โ โ โ โ โ โ Section Content โ โ โ โ โ โ โ โโโโโโโโโโโโโโโโโโโโโโโ
... ... ...````
#### Magic Number
Size: 4 bytesThe file start with a constant 4 bytes (magic number) "r1cs"
```0x72 0x31 0x63 0x73```
#### Version
Size: 4 bytesFormat: Little-Endian
For this standard it's fixed to
```0x01 0x00 0x00 0x00```
#### Number of Sections
Size: 4 bytesFormat: Little-Endian
Number of sections contained in the file
#### SectionType
Size: 4 bytesFormat: 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` bytesFormat: Little-Endian
Size in bytes of the section
### Header Section
Section Type: 0x01```` โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโณโโโโโโโโโโณโโโโโโโโโโโโโโโโโ โ 4 โ FieldDefSize โ 4 โFieldDef โ field Id โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโปโโโโโโโโโโปโโโโโโโโโโโโโโโโโ โโโโโโณโโโโโโโโโโโโโโโโโโ โ 4 โ 00 00 00 00 โ bigInt Format โโโโโโปโโโโโโโโโโโโโโโโโโ โโโโโโณโโโโโโโโโโโโโโโโโโ โ 4 โ is โ Id size ( Normally 4 (32bits)) โโโโโโปโโโโโโโโโโโโโโโโโโ โโโโโโณโโโโโโโโโโโโโโโโโโ โ is โ 01 00 00 00 โ nWires โโโโโโปโโโโโโโโโโโโโโโโโโ โโโโโโณโโโโโโโโโโโโโโโโโโ โ is โ 01 00 00 00 โ nPubOut โโโโโโปโโโโโโโโโโโโโโโโโโ โโโโโโณโโโโโโโโโโโโโโโโโโ โ is โ 01 00 00 00 โ nPubIn โโโโโโปโโโโโโโโโโโโโโโโโโ โโโโโโณโโโโโโโโโโโโโโโโโโ โ is โ 01 00 00 00 โ nPrvIn โโโโโโปโโโโโโโโโโโโโโโโโโ โโโโโโณโโโโโโโโโโโโโโโโโโ โ is โ 01 00 00 00 โ nLabels โโโโโโปโโโโโโโโโโโโโโโโโโ โโโโโโณโโโโโโโโโโโโโโโโโโ โ is โ 01 00 00 00 โ mConstraints โโโโโโปโโโโโโโโโโโโโโโโโโ
````
#### fieldDefSize
Size: 4 bytesFormat: Little-Endian
Size of the field Definition
Example:```0x00 0x0 0x00 0x00```
#### fieldDef
Field dfinition the first 4 bytes are the type in LE. 0x0000001 Ar prime fields.
For the prime fields, the next bytes are the prime in variable length LE base 256 format.
NOTE: This number is independent of the bigInt Format defined next
#### bigInt Format
Size: 4 bytesFormat: Little-Endian
0 Means that the Big Int are variable size LE.That is the First byte indicates the size and the remaining bytes are the number in little enfian (LSB first) base 256.
Numbers from 1 to 16383 are fixed size Litle endian format base 256.
Example:```0x00 0x00 0x00 0x00```
#### Id Size (is)
Size: 4 bytesFormat: Little-Endian
Size of the identifiers for wires, labels and constraints. In small circuits this is going to be 4 (32 bits)but can be increaset to 8 for bigger circiuits.
The only possible numbers are 4 or 8
#### Number of wires
Size: `is` bytesFormat: Little-Endian
Total Number of wires including ONE signal (Index 0).
#### Number of public outputs
Size: `is` bytesFormat: Little-Endian
Total Number of wires public output wires. They should be starting at idx 1
#### Number of public inputs
Size: `is` bytesFormat: Little-Endian
Total Number of wires public input wires. They should be starting just after the public output
#### Number of private inputs
Size: `is` bytesFormat: Little-Endian
Total Number of wires private input wires. They should be starting just after the public inputs
#### Number of constraints (m)
Size: `รฌs` bytesFormat: Little-Endian
Total Number of constraints
### Constraints section
Section Type: 0x02
```` โโโโโโณโโโโโโโโโโโโโโโโโโ โฒ โ is โ nA โ โฒ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โฒ โ is โ wireId_1 โ V โ a_{0,wireId_1} โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโซ โ โ is โ wireId_2 โ V โ a_{0,wireId_2} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ ... ... โ โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_nA โ V โ a_{0,wireId_nA} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ โโโโโโณโโโโโโโโโโโโโโโโโโ โ โ is โ nB โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_1 โ V โ b_{0,wireId_1} โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโซ โฒ โ is โ wireId_2 โ V โ b_{0,wireId_2} โ โฒ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โฑ Constraint_0 ... ... โฑ โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_nB โ V โ b_{0,wireId_nB} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ โโโโโโณโโโโโโโโโโโโโโโโโโ โ โ is โ nC โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_1 โ V โ c_{0,wireId_1} โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโซ โ โ is โ wireId_2 โ V โ c_{0,wireId_2} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ ... ... โ โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_nC โ V โ c_{0,wireId_nC} โ โฑ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โฑ โฑ
โโโโโโณโโโโโโโโโโโโโโโโโโ โฒ โ is โ nA โ โฒ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โฒ โ is โ wireId_1 โ V โ a_{1,wireId_1} โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโซ โ โ is โ wireId_2 โ V โ a_{1,wireId_2} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ ... ... โ โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_nA โ V โ a_{1,wireId_nA} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ โโโโโโณโโโโโโโโโโโโโโโโโโ โ โ is โ nB โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_1 โ V โ b_{1,wireId_1} โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโซ โฒ โ is โ wireId_2 โ V โ b_{1,wireId_2} โ โฒ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โฑ Constraint_1 ... ... โฑ โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_nB โ V โ b_{1,wireId_nB} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ โโโโโโณโโโโโโโโโโโโโโโโโโ โ โ is โ nC โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_1 โ V โ c_{1,wireId_1} โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโซ โ โ is โ wireId_2 โ V โ c_{1,wireId_2} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ ... ... โ โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_nC โ V โ c_{1,wireId_nC} โ โฑ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โฑ โฑ
... ... ...
โโโโโโณโโโโโโโโโโโโโโโโโโ โฒ โ is โ nA โ โฒ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โฒ โ is โ wireId_1 โ V โ a_{m-1,wireId_1} โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโซ โ โ is โ wireId_2 โ V โ a_{m-1,wireId_2} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ ... ... โ โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_nA โ V โ a_{m-1,wireId_nA} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ โโโโโโณโโโโโโโโโโโโโโโโโโ โ โ is โ nB โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_1 โ V โ b_{m-1,wireId_1} โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโซ โฒ โ is โ wireId_2 โ V โ b_{m-1,wireId_2} โ โฒ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โฑ Constraint_{m-1} ... ... โฑ โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_nB โ V โ b_{m-1,wireId_nB} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ โโโโโโณโโโโโโโโโโโโโโโโโโ โ โ is โ nC โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_1 โ V โ c_{m-1,wireId_1} โ โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโซ โ โ is โ wireId_2 โ V โ c_{m-1,wireId_2} โ โ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โ ... ... โ โโโโโโณโโโโโโโโโโโโโโโโโโณโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโ โ โ is โ wireId_nC โ V โ c_{m-1,wireId_nC} โ โฑ โโโโโโปโโโโโโโโโโโโโโโโโโปโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโ โฑ โฑ โฑ````
#### 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: `รฌs` bytesFormat: 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: `is` bytesFormat: Little-Endian
WireId of the nonZero Factor
#### Value of the factor
The first byte indicate the length N in bytes of the number in the upcoming bytes.
The next N bytes represent the value in Little Endian format.
For example, to represent the linear combination:
$$5w_4 +8w_5 + 260w_{886}$$
The linear combination would be represented as:
```` โโโโโโโโโโโโโโโโโโโ โ 03 00 00 00 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ 04 00 00 00 โ 01 05 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโซ โ 05 00 00 00 โ 01 08 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโซ โ 76 03 00 00 โ 02 04 01 โ โโโโโโโโโโโโโโโโโโโปโโโโโโโโโโโโโโโโโโ````
### WireId2LabelId Map Section
Section Type: 0x03
````โโโโณโโโโโโโโโโโโโโโโโโโโณโโโณโโโโโโโโโโโโโโโโโโโโ โโโโณโโโโโโโโโโโโโโโโโโโโโisโ labelId of Wire_0 โisโ labelId of Wire_1 โ ... โisโ labelId of Wire_n โโโโโปโโโโโโโโโโโโโโโโโโโโปโโโปโโโโโโโโโโโโโโโโโโโโ โโโโปโโโโโโโโโโโโโโโโโโโโ````
## 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:
```` โโโโโโโโโโโโโโโโ โ 72 31 63 73 โ Magic โฃโโโโโโโโโโโโโโโซ โ 01 00 00 00 โ Version โฃโโโโโโโโโโโโโโโซ โ 03 00 00 00 โ nSections โโโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโ โ 01 00 00 00 โ 49 00 00 00 โ SectionType: Header โโโโโโโโโโโโโโโโปโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโ โ 25 00 00 00 โ 10 00 00 00 โ FieldDefSize FieldDef โฃโโโโโโโโโโโโโโโปโโโโโโโโโโโโโโปโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ 20 010000f0 93f5e143 9170b979 48e83328 5d588181 b64550b8 29a031e1 724e6430โ โฃโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ 00 00 00 00 โ Big Int format โฃโโโโโโโโโโโโโโโซ โ 04 00 00 00 โ Id Size โฃโโโโโโโโโโโโโโโซ โ 07 00 00 00 โ # of wires โฃโโโโโโโโโโโโโโโซ โ 01 00 00 00 โ # Public Outs โฃโโโโโโโโโโโโโโโซ โ 02 00 00 00 โ # Public Ins โฃโโโโโโโโโโโโโโโซ โ 03 00 00 00 โ # Private Ins โฃโโโโโโโโโโโโโโโซ โ e8 03 00 00 โ # Labels โฃโโโโโโโโโโโโโโโซ โ 03 00 00 00 โ # Constraints โโโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโ โ 02 00 00 00 โ 8b 00 00 00 โ SectionType: Constraints โโโโโโโโโโโโโโโโปโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโโ Constraint 0: (3w_5 + 8w_6) * (2w_0 + 20w_2 + 12w_3) - (5w_0 + 7w_2) = 0 โ 02 00 00 00 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโ โ 05 00 00 00 โ 01 03 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโซ โ 06 00 00 00 โ 01 08 โ โโโโโโโโโโโโโโโโปโโโโโโโโโ โโโโโโโโโโโโโโโโ โ 03 00 00 00 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโ โ 00 00 00 00 โ 01 02 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโซ โ 02 00 00 00 โ 01 14 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโซ โ 03 00 00 00 โ 01 0C โ โโโโโโโโโโโโโโโโปโโโโโโโโโ โโโโโโโโโโโโโโโโ โ 02 00 00 00 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโ โ 00 00 00 00 โ 01 05 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโซ โ 02 00 00 00 โ 01 07 โ โโโโโโโโโโโโโโโโปโโโโโโโโโ
โโโโโโโโโโโโโโโโ Constraint 1: (4w_1 + 8w_4 + 3w_5) * (6w_6 + 44w_3) = 0 โ 03 00 00 00 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโ โ 01 00 00 00 โ 01 04 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโซ โ 04 00 00 00 โ 01 08 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโซ โ 05 00 00 00 โ 01 03 โ โโโโโโโโโโโโโโโโปโโโโโโโโโโ โโโโโโโโโโโโโโโโ โ 02 00 00 00 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโ โ 03 00 00 00 โ 01 2C โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโซ โ 06 00 00 00 โ 01 06 โ โโโโโโโโโโโโโโโโปโโโโโโโโโโ โโโโโโโโโโโโโโโโ โ 00 00 00 00 โ โโโโโโโโโโโโโโโโ
โโโโโโโโโโโโโโโโ Constraint 2: (4w_6) * (6w_0 + 5w_3 + 11w_2) - (600w_6) = 0 โ 01 00 00 00 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโ โ 06 00 00 00 โ 01 04 โ โโโโโโโโโโโโโโโโปโโโโโโโโโโ โโโโโโโโโโโโโโโโ โ 03 00 00 00 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโ โ 00 00 00 00 โ 01 06 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโซ โ 02 00 00 00 โ 01 0B โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโซ โ 03 00 00 00 โ 01 05 โ โโโโโโโโโโโโโโโโปโโโโโโโโโโ โโโโโโโโโโโโโโโโ โ 01 00 00 00 โ โฃโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ โ 06 00 00 00 โ 02 58 02 โ โโโโโโโโโโโโโโโโปโโโโโโโโโโโโโโ
โโโโโโโโโโโโโโโโณโโโโโโโโโโโโโโ โ 03 00 00 00 โ 1c 00 00 00 โ Wire to Label Map โโโโโโโโโโโโโโโโปโโโโโโโโโโโโโโ โโโโโโโโโโโโโโโโ โ 00 00 00 00 โ โฃโโโโโโโโโโโโโโโซ โ 03 00 00 00 โ โฃโโโโโโโโโโโโโโโซ โ 0a 00 00 00 โ โฃโโโโโโโโโโโโโโโซ โ 0b 00 00 00 โ โฃโโโโโโโโโโโโโโโซ โ 0c 00 00 00 โ โฃโโโโโโโโโโโโโโโซ โ 0f 00 00 00 โ โฃโโโโโโโโโโโโโโโซ โ 44 01 00 00 โ โโโโโโโโโโโโโโโโ````
And the binary representation in Hex:
````72 31 63 7701 00 00 0003 00 00 0001 00 00 00 49 00 00 0025 00 00 00 10 00 00 0020 010000f0 93f5e143 9170b979 48e83328 5d588181 b64550b8 29a031e1 724e643000 00 00 0004 00 00 0007 00 00 0001 00 00 0002 00 00 0003 00 00 00e8 03 00 0003 00 00 0002 00 00 00 8b 00 00 0002 00 00 0005 00 00 00 01 0306 00 00 00 01 0803 00 00 0000 00 00 00 01 0202 00 00 00 01 1403 00 00 00 01 0C02 00 00 0000 00 00 00 01 0502 00 00 00 01 0703 00 00 0001 00 00 00 01 0404 00 00 00 01 0805 00 00 00 01 0302 00 00 0003 00 00 00 01 2C06 00 00 00 01 0600 00 00 0001 00 00 0006 00 00 00 01 0403 00 00 0000 00 00 00 01 0602 00 00 00 01 0B03 00 00 00 01 0501 00 00 0006 00 00 00 02 58 0203 00 00 00 1c 00 00 0000 00 00 0003 00 00 000a 00 00 000b 00 00 000c 00 00 000f 00 00 0044 01 00 00
````
## Implementation
circom will output this format.
## Copyright
Copyright and related rights waived via [CC0](https://creativecommons.org/publicdomain/zero/1.0/).
|
