# Zero Knowledge SNARKs

This crate provides functionality for creating and using zero knowledge proofs. The implementation is based on groth16.

# Usage

The main functions of the alrotihm are the `setup`, `prove` and `verify` functions in the `groth16` module. Intermediate representations can be generated from .zk files, which are written in a DSL that represents an arithmetic circuit.

## Language

The language for representing arithmetic circuits is quite basic and is written in a lisp-esque style that uses parenthesised prefix notation. The following is an example program for a circuit that computes a quadratic polynomial `y = ax^2 + bx + c`:

``````(in x a b c)
(out y)
(verify x y)

(program
(= t1
(* x a))
(= t2
(* x (+ t1 b)))
(= y
(* 1 (+ t2 c))))
``````

The order must always follow `in`, `out`, `verify` and then `program`. Currently parentheses are 'sticky' in that there must not be any whitespace between them and their interior tokens. The keywords are as follows:

• `in` precedes the list of input wires to the circuit, excluding the constant unity wire.
• `out` precedes the list of output wires from the circuit.
• `verify` precedes the list of wires that the verifier will check by providing them as input in the verification process.
• `program` precedes the list of multiplication subcircuits that constitute the entire arithmetic circuit. The multiplication subcircuits model a single multiplication gate that has fan in two, where the two inputs can be a linear combination of any number of circuit inputs and previous internal wires. They use the following keywords.
• `=` is the assignment operator, which takes two arguments. The first is the variable that is being assigned to, and represents the output wire of the multiplication gate. The second is the expression being assigned, and represents the linear combination of input wires.
• `*` is the multiplication operator, which is used both for the multiplication gate and also to represent the constant scaling in the linear combination inputs to the multiplication gate. It takes only two arguments; when used for a multiplication gate the order does not matter, but for constant scaling the constant must be the first argument.
• `+` is the addition operator, and as stated before can have an arbitrary number of arguments. Each argument can either be a variable, or a scaled variable (i.e. it can either look like `x`, or, for example, like `(* 5 x)`).

# Examples

As an example, consider the simple arithmetic expression `x = 4ab + c + 6`. We want to verify the wires `x` and `b`. The program file can look like the following:

``````(in a b c)
(out x)
(verify b x)

(program
(= temp
(* a b))
(= x
(* 1 (+ (* 4 temp) c 6))))
``````

Suppose that the prover wants to prove that they know values `a` and `c` for which the circuit is satisfied when the verifier inputs `b = 2` and `x = 34`. For our example we will use the satisfying assignments `a = 3` and `c = 4`. The following code is an example of the setup, prove and verify process.

```extern crate zksnark;

use zksnark::groth16;
use zksnark::groth16::{Proof, SigmaG1, SigmaG2, QAP};
use zksnark::groth16::circuit::{ASTParser, TryParse};
use zksnark::groth16::fr::FrLocal;
use zksnark::groth16::coefficient_poly::CoefficientPoly;

// x = 4ab + c + 6
let qap: QAP<CoefficientPoly<FrLocal>> =
ASTParser::try_parse(code)
.unwrap()
.into();

// The assignments are the inputs to the circuit in the order they
// appear in the file
let assignments = &[
3.into(), // a
2.into(), // b
4.into(), // c
];
let weights = groth16::weights(code, assignments).unwrap();

let (sigmag1, sigmag2) = groth16::setup(&qap);

let proof = groth16::prove(&qap, (&sigmag1, &sigmag2), &weights);

assert!(groth16::verify(
&qap,
(sigmag1, sigmag2),
&vec![FrLocal::from(2), FrLocal::from(34)],
proof
));Run```

## Modules

 field Defines the `Field` trait along with other utility functions for working with fields. groth16 Implementaiton of groth16 along with a basic language for representing arithmetic circuits.