There is no such thing as a sigle-sided "certified" cable.
Here's the deal in a nutshell... Genuine Apple cables (and certified 3rd party cables) have a small chip in them with a small set of code. They will work unless defective. Period.
Then there are 3rd party cables that are not certified. They all fall into a couple of categories:
1. Cables that use a hacked chip that reasonably duplicates the anticipated data iOS is looking for when cable is connected, thus it works (I apparently have a couple of these non-certifed cables that work just fine).
2. Cables that use a hacked chip that doesn't reflect the correct info/code for iOS to recognize it - these cables will not work, or MIGHT work after dismissing the warning message (rare).
3. Cables that have a chip (or not) that essentially does nothing - these may have worked ok prior to iOS7, but now do not. - this is the most common super-cheap cable on eBay. Some are very poorly made, regardless of the presence of a chip or not).
I submit - if you have a genuine Apple (or certified/licensed) cable, and it still is not recognized - either the cable is broken/defective in some way, or your phone has a hardware issue.
But don't forget - there are knock-off cables out there that CLAIM to be certified/licensed that are not.
My own experience - I purchased my iPhone 5S at an AT&T store. I wanted an extra cable to keep in my truck. They sold me oen of their own AT&T branded cables. It works (in fact, it is plugge dup to my phone and my MacBook Pro right now). It was rather expensive for a cable - but I believe it is an officially licensed/certified cable.
I bought two cheap cables from a seller on eBay that claimed (in fact, the eBay item page is still live, and still claims to be compatible) - $2.20 each. Neither works at all under any circumstances - turn cable over, try in different power sources, etc. They just flat-out do not work.
I ordered a genuine Apple cable from a seller on eBay - it is a legit cable, so it works just fine.
I ordered a pair of 3rd party cables (no menton in the ad or the limited packaging, consising of a little plastic bag) of being certified - no Apple logos, no nothing. These are very long and ribbon shaped. I love them, as they give me a lot more working room - and they work - doesn't matter which direction the plug is turned. No issues at all. I suspect these cables fit into #1 above. $5.99 for two cables, shipped.
Might Apple release yet another iOS update that causes my working 3rd Party cables to quit... maybe. But for now, I'm not too frustrated.