exponentiation

I need a way to calculate: (g^u * y^v) mod p in Java. I've found this algorithm for calculating (g^u) mod p: int modulo(int a,int b,int c) { long x=1 long y=a; while(b > 0){ if(b%2 == 1){ x=(x*y)%c; } y = (y*y)%c; // squaring the base b /= 2; } return (int) x%c; } and it works great, but I can't seem to find a way to do this for (g^u * y^v) mod p as my math skills are lackluster. To put it in context, it's for a java implementation of a "reduced" DSA - the verifying part requires this to be solved. Assuming that the two factors will not overflow, I believe you can simplify an expression like

What is the Prolog operator ^ ? Looking at The Prolog Built-in Directive op gives a list of the built-in operators. I see ** is exponentiation /\ is or but what is ^ ? Each of the three current answers are of value and I learned something: Roy for the book false for the examples I accepted the answer by CapelliC because it made clear that ^/2 has multiple meanings depending on context which instantly cleared up my confusion. In Prolog, most symbols can be used 'uninterpreted', at syntactic level, in particular after a op/3 declaration, any atom can be used as operator . Then you can use, for

I have a need to create an integer value to a specific power (that's not the correct term, but basically I need to create 10, 100, 1000, etc.) The "power" will be specified as a function parameter. I came up with a solution but MAN does it feel hacky and wrong. I'd like to learn a better way if there is one, maybe one that isn't string based? Also, eval() is not an option. Here is what I have at this time: function makeMultiplierBase(precision) { var numToParse = '1'; for(var i = 0; i < precision; i++) { numToParse += '0'; } return parseFloat(numToParse); } I also just came up with this non

I know it has been proven NP-complete, and that's ok. I'm currently solving it with branch and bound where I set the initial upper limit at the number of multiplications it would take the normal binary square/multiply algorithm, and it does give the right answers, but I'm not satisfied with the running time (it can take several seconds for numbers around 200). This being an NP-complete problem, I'm not expecting anything spectacular; but there are often tricks to get the Actual Time under control somewhat. Are there faster ways to do this in practice? If so, what are they? This looks like

My problem is to compute (g^x) mod p quickly in JavaScript, where ^ is exponentiation, mod is the modulo operation. All inputs are nonnegative integers, x has about 256 bits, and p is a prime number of 2048 bits, and g may have up to 2048 bits. Most of the software I've found that can do this in JavaScript seems to use the JavaScript BigInt library ( http://www.leemon.com/crypto/BigInt.html ). Doing a single exponentiation of such size with this library takes about 9 seconds on my slow browser (Firefox 3.0 with SpiderMonkey). I'm looking for a solution which is at least 10 times faster. The