this check is not good enough: https://github.com/zksecurity/noname/blob/main/src/stdlib/native/int/lib.no#L17

fn Uint8.new(val: Field) -> Uint8 {
    let bit_len = 8;

    bits::check_field_size(bit_len);

why? Because when we multiply:

fn Uint8.mul(self, rhs: Uint8) -> Uint8 {
    return Uint8.new(self.inner * rhs.inner);
}

we might return a value of 16 bits here. If our field modulus is 16 bits (or lower), then the multiplication might wrap around

so we need to check that the field modulus is 17 bits at least so it can contain the result of that multiplication

so I think it should be bits::assert_circuit_field_strictly_larger_than(bit_len * 2)