This does not contain any provable code yet

[mitschabaude]

The current pattern of using o1js' Gadgets.ForeignField is wrong: you're converting Field3 to/from bigint in every operation. This will fail in provable code -- bigint operations are not provable, and you can't read out JS values of provable types like Field3 in a circuit.

To make an operation provable, you need to build a circuit, not just do normal JS operations. We have a lot of methods for building circuits, like Gadgets.ForeignField.{add(),mul()} and of course all the lower-level methods on Field to operate on the individual limbs of a Field3.

[onurinanc]

What about the following pattern:

const bn254_prime = Field3.from(21888242871839275222246405745257275088696311157297823662689037894645226208583n);

export default class Fq{
    value: Field3;
    modulus: Field3;

    constructor(value: Field3) {
        this.modulus = bn254_prime;
        this.value = value;
    }

    add(x: Fq) {
        return new Fq(
            ForeignField.add(this.value, x.value, Field3.toBigint(this.modulus))
        );
    }

    sub(x: Fq) {
        return new Fq(
            ForeignField.sub(this.value, x.value, Field3.toBigint(this.modulus))
        );
    }

Now, I'm aiming to use toBigInt operation inside the ForeignField arithmetic which is required inside the Gadget.ForeingField

Is it provable inside o1js now?

[mitschabaude]

I wouldn't say so!

• If this.modulus is variable, then you can't convert it to a bigint in the circuit
• If it's a constant, then this works, but on the other hand in that case why not represent it as bigint all the time

[onurinanc]

Got it.

So, this is going to work:

const bn254_prime = 21888242871839275222246405745257275088696311157297823662689037894645226208583n;

export default class Fq{
    value: Field3;

    constructor(value: Field3) {
        this.value = value;
    }

    add(x: Fq) {
        return new Fq(
            ForeignField.add(this.value, x.value, bn254_prime)
        );
    }

    sub(x: Fq) {
        return new Fq(
            ForeignField.sub(this.value, x.value, bn254_prime)
        );
    }

[mitschabaude]

yes 👍🏻