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Digg bcpowmod
Raise an arbitrary precision number to another, reduced by a specified modulus
(PHP 5)
Use the fast-exponentiation method to raise left_operand to the power right_operand with respect to the modulus modulus. Parameters
Notes
Note:
Because this method uses the modulus operation, non-natural numbers may give unexpected results. A natural number is any positive non-zero integer. ExamplesThe following two statements are functionally identical. The bcpowmod() version however, executes in less time and can accept larger parameters. <?phpCode Examples / Notes » bcpowmodewilde aht bsmdevelopment dawt com
Versions of PHP prior to 5 do not have bcpowmod in their repertoire. This routine simulates this function using bcdiv, bcmod and bcmul. It is useful to have bcpowmod available because it is commonly used to implement the RSA algorithm. The function bcpowmod(v, e, m) is supposedly equivalent to bcmod(bcpow(v, e), m). However, for the large numbers used as keys in the RSA algorithm, the bcpow function generates a number so big as to overflow it. For any exponent greater than a few tens of thousands, bcpow overflows and returns 1. This routine will iterate through a loop squaring the result, modulo the modulus, for every one-bit in the exponent. The exponent is shifted right by one bit for each iteration. When it has been reduced to zero, the calculation ends. This method may be slower than bcpowmod but at least it works. function PowModSim($Value, $Exponent, $Modulus) { // Check if simulation is even necessary. if (function_exists("bcpowmod")) return (bcpowmod($Value, $Exponent, $Modulus)); // Loop until the exponent is reduced to zero. $Result = "1"; while (TRUE) { if (bcmod($Exponent, 2) == "1") $Result = bcmod(bcmul($Result, $Value), $Modulus); if (($Exponent = bcdiv($Exponent, 2)) == "0") break; $Value = bcmod(bcmul($Value, $Value), $Modulus); } return ($Result); } william
The author's statement: "A natural number is any positive non-zero integer." should be, imo, something like: "In this context only positive non-zero integers are considered to be natural numbers." http://mathworld.wolfram.com/NaturalNumber.html http://planetmath.org/encyclopedia/NaturalNumber.html http://en.wikipedia.org/wiki/Natural_number laysoft
I found a better way to emulate bcpowmod on PHP 4, which works with very big numbers too: function powmod($m,$e,$n) { if (intval(PHP_VERSION)>4) { return(bcpowmod($m,$e,$n)); } else { $r=""; while ($e!="0") { $t=bcmod($e,"4096"); $r=substr("000000000000".decbin(intval($t)),-12).$r; $e=bcdiv($e,"4096"); } $r=preg_replace("!^0+!","",$r); if ($r=="") $r="0"; $m=bcmod($m,$n); $erb=strrev($r); $q="1"; $a[0]=$m; for ($i=1;$i<strlen($erb);$i++) { $a[$i]=bcmod(bcmul($a[$i-1],$a[$i-1]),$n); } for ($i=0;$i<strlen($erb);$i++) { if ($erb[$i]=="1") { $q=bcmod(bcmul($q,$a[$i]),$n); } } return($q); } } rrasss
However, if you read his full note, you see this paragraph: "The function bcpowmod(v, e, m) is supposedly equivalent to bcmod(bcpow(v, e), m). However, for the large numbers used as keys in the RSA algorithm, the bcpow function generates a number so big as to overflow it. For any exponent greater than a few tens of thousands, bcpow overflows and returns 1." So you still can, and should (over bcmod(bcpow(v, e), m) ), use his function if you are using larger exponents, "any exponent greater than a few tens of thousand." |
