NSRegularExpression should solve your issue.
In order to use it, you will need to understand Regex first. In your case, you can use value=[\\w]+[^.]+ as your regex pattern.
The following code will give you a [String] object contains value=allCharacterBeforeFirstPeriod
let regex = try NSRegularExpression(pattern: "value=[\\w]+[^.]+", options: [])
let nsStr = str as NSString
let array = regex.matchesInString(str, options: [], range: NSMakeRange(0, nsStr.length))
let results = array.map({ nsStr.substringWithRange($0.range) })
And then if you only need the value after value=, you can use another map function to do it:
results.map({ $0.stringByReplacingOccurrencesOfString("value=", withString: "") })
I have tested the code with a 10,000 characters String. It finishes in ~0.3 sec