Ding's conjectured difference sets from x(x+1) polynomials

Let $m\geq 4$ and, for $f\in\operatorname{GF}(2^m)[x]$, define

$$D_f=\{f(x(x+1)):x\in\operatorname{GF}(2^m)\}\setminus\{0\}.$$

Ding's second difference-set conjecture. For the following three polynomials, with the indicated parity conditions,

$$f(x)=x+x^{2^{(m+1)/2}-1}+x^{2^m-2^{(m+1)/2}+1}\quad(m\text{ odd}),$$ $$f(x)=x+x^{(2^m+1)/3}+x^{(2^{m+1}-1)/3}\quad(m\text{ odd}),$$ $$f(x)=x+x^{2^{(m+2)/2}-1}+x^{2^m-2^{m/2}+1}\quad(m\text{ even}),$$

$D_f$ is a difference set in $(\operatorname{GF}(2^m)^*,\times)$ with Singer parameters

$$(2^m-1,\,2^{m-1}-1,\,2^{m-2}-1).$$

The claim is another list of conjectured cyclic difference sets attributed in the source to Chapter 4 of Ding's book.