The common notion is that in order to gain muscle you must be a "calorie surplus", and in order to burn fat/lose weight you must be a in a "calorie deficit. However the cyclic-ketogenic diet claims that it allows muscle building AND fat loss? How is this possible and what is the mechanism behind it? Since surely you cannot be in a surplus and deficit at the same time?
I don't think there's very much reliable empirical evidence available on the subject. Every mention of this diet that I've seen tends to be either hyperbolic, anecdotal, or very clearly tainted by conflict-of-interest. Wikipedia's page on the subject, for example, uses as its main reference a book which advocates said diet. It's possible that the author is a verified expert who's diligently studied the matter and scrupulously documented all his sources, but my default reaction is extreme skepticism. For what it's worth, ketogenic diets have been used in the treatment of epilepsy for decades, and the medical consensus appears to be that they're generally safe. That said, there's some evidence that ketogenic diets will, if anything, impair performance during anaerobic activities due to more rapid glycogen depletion (q.v., http://www.ncbi.nlm.nih.gov/pmc/articles/PMC524027/), though aerobic performance should not be detrimentally impacted. Given that muscle-building gains are largely dependent on anaerobic types of exercise, and that greater intensity and increased repetition to failure are generally correlated with greater gains, I would expect negative results, if anything.
As far as the hypothetical mechanism for these diets, the idea is that if the body is deprived of carbohydrates it is forced to begin to metabolize fat into fatty acids through lipolysis. Those fatty acids are then further metabolized into ketone bodies (hence, the name of the diet). Whether this actually results in improved fat loss vs. carb-containing diets while holding caloric intake constant isn't known with any certainty.
I know someone who recently used the cyclic ketogenic diet to get good results. Based on his experience, and some of the other experiences I've read who used the approach, it's important to set your expectations appropriately.
Ketosis is itself a contentious subject with researchers on both sides of the argument having studies to back up their arguments. Unfortunately, most studies use readily available sedentary people, and rarely any demographic that would match my own. I will also say that ketosis is not for everyone. I did well with it, but I have friends who didn't. I recommend a trial run without any exercise to see how you adjust. The principles behind ketosis are fairly simple and straightforward:
All ketogenic diets share a common trait: medium to high protein intake. The higher protein intake is necessary to provide the gluconeogenisis process a source of protein other than your muscles and organs. Additionally, if you are lifting weights, the higher protein intake is needed to repair your muscles and supply the necessary amino acids. Building muscle does take a lot of energy, but thankfully the body can use fat as a source of energy.
Ketosis based diets will completely deplete the glycogen stores in your muscles and organs by design. This has a negative impact on performance. Unchecked, high intensity exercise like weight lifting can increase the demands of energy enough where ketosis alone isn't enough to supply the energy requirements. This is a bad thing. The cyclic ketogenic diet replenishes the glycogen stores once a week. This gives you most of the week to burn fat, while keeping your energy up to meet the demands of exercise.
There have been several studies to show that there is a direct correlation between your body's maximum ability and its weight. As you lose weight, you can expect a loss of your maximum strength. Part of this is due to any cut causing a loss of lean mass as well as fat mass. That doesn't mean you are losing muscle, it very well could be some of the energy support systems that feed the muscle. However, this loss of absolute strength is relatively small compared to your fat loss. Once you reach your goal, you can rebuild that max strength.
The high fat content during the week in the cyclic ketogenic diet is sufficient to fuel your training. However, the body does do better with a periodic refeed when you are training hard.