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);
}
bcpowmod
(PHP 5, PHP 7, PHP 8)
bcpowmod — Eleva un número de precisión arbitraria a otro, reducido por un módulo especificado
Descripción
bcpowmod(
string
string
string
int
): string
string
$left_operand = "",string
$right_operand = "",string
$modulus = "",int
$scale = int): string
Usa el método de exponenciación rápida para aumentar el
left_operand a la potencia
right_operand con respecto al módulo
modulus.
Parámetros
-
left_operand -
El left operand, como una cadena.
-
right_operand -
El right operand, como una cadena.
-
modulus -
El modulus, como una cadena.
-
scale -
Este parámetro opcional es usado para establecer el número de dígitos después del punto decimal en el resultado. Si se omite, su valor será el de la escala establecida globalmente con la función bcscale(), o se recurrirá a
0si este valor no ha sido establecido.
Valores devueltos
Devuelve el resultado como una cadena, o null si modulus
es 0.
Notas
Nota:
Debido a que este método utiliza la operación módulo, podrían obtenerse resultados inesperados en números enteros no positivos.
Ejemplos
Los siguientes dos comandos son funcionalmente idénticos. La version bcpowmod() sin embargo, se ejecuta en menos tiempo y admite mas parametros.
<?php
$a = bcpowmod($x, $y, $mod);
$b = bcmod(bcpow($x, $y), $mod);
// $a and $b are equal to each other.
?>
add a note
User Contributed Notes 3 notes
ewilde aht bsmdevelopment dawt com ¶
19 years ago
rrasss at gmail dot com ¶
18 years ago
However, if you read his full note, you see this paragraph:
"The function bcpowmod(v, e, m) is supposedly equivalent to bcmod(bcpow(v, e), m). However, for the large numbers used as keys in the RSA algorithm, the bcpow function generates a number so big as to overflow it. For any exponent greater than a few tens of thousands, bcpow overflows and returns 1."
So you still can, and should (over bcmod(bcpow(v, e), m) ), use his function if you are using larger exponents, "any exponent greater than a few tens of thousand."
laysoft at gmail dot com ¶
17 years ago
I found a better way to emulate bcpowmod on PHP 4, which works with very big numbers too:
function powmod($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);
}
}
