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 um número de precisão arbitrária para outro, reduzido por um módulo especificado
Descrição
bcpowmod
( string
$left_operand
, string $right_operand
, string $modulus
, int $scale = 0
) : string
Utiliza o método de exponenciação rápida para elevar
left_operand para a potência
right_operand levando em conta o módulo
modulus.
Parâmetros
-
left_operand -
O operando da esquerda, do tipo string.
-
right_operand -
O operando da direita, do tipo string.
-
modulus -
O módulo, do tipo string.
-
scale -
Este parâmetro opcional é utilizado para configurar o número de dígitos na parte fracionária do resultado. Se omitido será utilizada a escala padrão globalmente configurada com a função bcscale(), com padrão de fábrica em
0se não configurado.
Valor Retornado
Retorna um string com resultado ou null se modulus
for 0.
Notas
Nota:
Por que esse método usa a operação de módulo, números não positivos podem gerar resultados inesperados.
Exemplos
As seguintes instruções têm funcionalidades idênticas. A versão bcpowmod(), no entanto, executa em menos tempo e pode aceitar parâmetros maiores.
<?php
$a = bcpowmod($x, $y, $mod);
$b = bcmod(bcpow($x, $y), $mod);
// $a e $b são iguais.
?>
add a note
User Contributed Notes 3 notes
ewilde aht bsmdevelopment dawt com ¶
18 years ago
laysoft at gmail dot com ¶
17 years ago
I found a better way to emulate bcpowmod on PHP 4, which works with very big numbers too:
function powmod($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);
}
}
rrasss at gmail dot com ¶
17 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."
