Use an UnsafeMutablePointer. I'd imagine UInt8 is probably closest to Java's byte, so you can allocate space for 20 of those and initialize them to0 like so...
let ptr = UnsafeMutablePointer<UInt8>.alloc(20)
ptr.initialize(0)
Edit: Thanks to vacawama
You can also use a Swift array and the & operator to convert it to a pointer, which is syntactically a bit nicer...
var arr = [UInt8](count: 20, repeatedValue: 0)
doSomething(&arr)
These two methods are functionally equivalent as & will convert the array to an UnsafeMutablePointer under the hood.
Note: Notice that I used the var keyword to define the array in the second example, so that the & operator converts it to UnsafeMutablePointer instead of UnsafePointer. Otherwise, you will get a cryptic compiler error if you attempt to mutate the memory
Bytetype in Swift 2.2. There isUInt8though ... What exactly did you do with sizeofValue?