Vamp-IR

Vamp-IR is a language for specifying arithmetic circuits. The Vamp-IR compiler can transform an arithmetic circuit into a form that is compatible with any proving system backend.

• Design rationale / Spec

VAMP-IR stands for:

Vamp-IR Aliased Multivariate Polynomial Intermediate Representation

The Vamp-IR language consists of alias definitions and expressions defining an arithmetic circuit.

Trying Vamp-IR

Installation

git clone git@github.com:anoma/vamp-ir
cd vamp-ir
cargo build

Setup

Creates public parameters for proving and verifying and saves to params.pp:

./target/debug/vamp-ir setup params.pp

Compile

Compiles ./tests/alu.pir to alu.plonk using the setup:

./target/debug/vamp-ir compile ./tests/alu.pir params.pp alu.plonk

Prove

Create proof from alu.plonk and save to proof.plonk:

 ./target/debug/vamp-ir prove alu.plonk params.pp proof.plonk

Verify

Verify proof.plonk:

./target/debug/vamp-ir verify alu.plonk params.pp proof.plonk

Interface

The Vamp-IR compiler takes as input:

• A Vamp-IR document consisting of alias definitions and a circuit written with those aliases. (The alias definitions may come from Vamp-IR's standard library inwhich they don't need to included in the document itself, or they be written as custom aliases and included in the Vamp-IR document.)
• Target backend parameters, which may include a specification of the constraint system (R1CS, 3-Plonk, 4-Plonk, etc.), the order of the scalar field, elliptic curve parameters, and so on. These parameters help the Vamp-IR compiler transform the given circuit into an optimized form targetting the backend proving system and give important information that is needed to compute the values during prover runtime (for instance, field division requries knowledge of the order of the scalar field).
• (optionally) A precomputed prover input map which allows the Vamp-IR compiler to skip the prover runtime step.

The Vamp-IR compiler outputs:

• A portable, canonical form of the circuit as a .vampir document

Additionally, if connected to a backend proving system implementation that has a Vamp-IR -> Backend compiler and parameters for the backend, Vamp-IR can invoke the backend proving system and output:

• A proof in the backend proving system
• A verification of a proof provided in the backend proving system

Components

Vamp-IR consists of a parser, compiler, and a prover runtime.

• The parser parses the text input into an abstract structure tree.
• The compiler transforms the data in the tree in various ways, eventually arriving at a form that is compatible with some backend proving system implementation, according to target backend parameters which are supplied alongside the text input.
• The prover runtime takes the circuit IR and the prover's private initial inputs and executes the circuit steps to produce the intermediate values of the computation. These are organized and sent to the backend prover in the prover input map.

Vamp-IR language

Vamp-IR is a language for specifying arithmetic circuits. Circuits in Vamp-IR are written as a set of multivariable polynomial expressions. Vamp-IR allows a circuit writer to define their own custom, reusable circuits called aliases. Vamp-IR will also ship with a standard library of pre-defined aliases which are commonly needed.

A Vamp-IR document consists of a set of aliases and a circuit.

Circuit

A Vamp-IR circuit is a set of expressions.

Expressions

An expression in Vamp-IR is a multivariable polynomial constraint written with variables, constants, and the symbols +, -, *, ^, (, ), and =.

This constraint (which checks that $(x,y)$ is a point on a certain elliptic curve) is a Vamp-IR expression:

y^2 = x^3 + 3

Every expression is implicitly an equation in Vamp-IR. An expression written with no = is considered to be constrained to be equal to 0. Therefore, the equation above could be rewritten without the = as:

y^2 - (x^3 + 3)

These two forms of expressions are equivalent in Vamp-IR.

An example circuit

Here is a small circuit written in Vamp-IR. This circuit checks that two twisted Edwards elliptic curve points $(x_1, y_1)$ and $(x_2, y_2)$ add to a third point $(x_3, y_3)$ on the curve. (This curve uses twisted Edwards parameters $A=3$ and $D=2$.)

(1 + 2*x1*x2*y1*y2)*x3 = x1*y2 + y1*x2
(1 - 2*x1*x2*y1*y2)*y3 = y1*y2 - 3*x1*x2

Aliases

Since this circuit is likely to be used often, we can define an alias for it so it can be reused. An alias can include a signature which allows it to be used as a function by designating which internal wires can be considered inputs and outputs. The compiler then knows how to compose circuits together.

def alias_name[param1, param2, ...] input1 input2 ... -> output1 output2 ... {
  expression1
  expression2
  ...
}

Here is the circuit from earlier written as an alias:

def twisted_edwards_add[A, D] x1 y1 x2 y2 -> x3 y3 {
  (1 + D*x1*x2*y1*y2)*x3 = x1*y2 + y1*x2
  (1 - D*x1*x2*y1*y2)*y3 = y1*y2 - A*x1*x2
}

Then this alias can be called like a function inside a circuit:

twisted_edwards_add[3, 2] p1 q1 p2 q2

Example with expansion

Here is a collection of aliases constraining $x$ to be a 1, 2, 4, or 8 bit integer. Then a circuit checks that a triple $(a,b,c)$ satisfies the Pythagorean theorem and that both $a$ and $b$ are bytes.

// aliases

def range[1] x {
  x*x - x
}

def range[2] x {
  range[1] hi
  range[1] lo
  2*hi + lo - x
}

def range[4] x {
  range[2] hi
  range[2] lo
  4*hi + lo - x
}

def range[8] x {
  range[4] hi
  range[4] lo
  16*hi + lo - x
}


// circuit

a^2 + b^2 = c^2
range[8] a
range[8] b

Expanded form

The circuit above is expanded by the compiler into a set of polynomial constraints, using $w_k$ to stand in for auxiliary variables required by the invoked aliases.

a*a + b*b - c*c
w0*w0 - w0
w1*w1 - w1
2*w1 + w0 - w2
w3*w3 - w3
w4*w4 - w4
2*w4 + w3 - w5
4*w5 + w2 - w6
w7*w7 - w7
w8*w8 - w8
2*w8 + w7 - w9
w10*w10 - w10
w11*w11 - w11
2*w11 + w10 - w12
4*w12 + w9 - w13
8*w13 + w6 - a
w14*w14 - w14
w15*w15 - w15
2*w15 + w14 - w16
w17*w17 - w17
w18*w18 - w18
2*w18 + w17 - w19
4*w19 + w16 - w20
w21*w21 - w21
w22*w22 - w22
2*w22 + w21 - w23
w24*w24 - w24
w25*w25 - w25
2*w25 + w24 - w26
4*w26 + w23 - w27
8*w27 + w20 - b

Prover Input Map

The compiler can use the expanded list of constraints to compute the values of all variables including the auxiliary variables, from the initial inputs $(a, b, c)$ during the prover runtime process.

  a: 3    // b00000011
  b: 4    // b00000100
  c: 5    // b00000101
 w0: 1
 w1: 1
 w2: 3
 w3: 0
 w4: 0
 w5: 0
 w6: 3
 w7: 0
 w8: 0
 w9: 0
w10: 0
w11: 0
w12: 0
w13: 0
w14: 1
w15: 0
w16: 1
w17: 1
w18: 0
w19: 1
w20: 5
w21: 0
w22: 0
w23: 0
w24: 0
w25: 0
w26: 0
w27: 0

License

Licensed under either of

• Apache License, Version 2.0, (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.

Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.