backward-compatible triple encryption

I was asked to encrypt a message by applying backward-compatible triple encryption using the 8-bit key $k = (k_1, k_2)$ where $k_1≠k_2$.

I'm a little confused because I thought all 3 keys had to be independent for it to be backward-compatible with DES, unless by backward-compatible they were referring to something else? Thanks.

• You probably mean 8-byte key, right? – Maarten Bodewes Nov 16 '16 at 15:10

What they may be referring to is the DES weak keys. There are keys $k_1$ and $k_2$ for DES where $E_{k_1}(E_{k_2}(X)) = X$. So if you'd use triple encryption $E_{k_1}(E_{k_2}(E_{k_1}(X)))$ then you would get $E_{k_1}(X)$ if you'd use weak keys.
Alternatively, they may just mean that you currently have to use triple-DES and that you achieve backwards compatibility in case $k_1 = k_2$.