bcpowmod

(PHP 5, PHP 7, PHP 8)

bcpowmod — Effettua l'elevamento a potenza, applicando quindi il modulo

Descrizione

bcpowmod(
    string $x,
    string $y,
    string $modulo,
    int $precisione = ?
): string

Utilizza il metodo di esponenziazione veloce per elevare x alla potenza y rispetto al modulo modulo. Il parametro opzionale precisione può essere utilizzato per impostare il numero di cifre dopo il punto decimale.

Nota:
Dal momento che questo metodo utilizza l'operatore modulo, numeri non naturali possono dare risultati inattesi. Un numero naturale è un qualsiasi numero positivo intero diverso da zero.

Esempi

Le seguenti istruzioni sono funzionalmente identiche. La versione bcpowmod(), comunque, esegue in meno tempo e può accettare parametri più grandi.

<?php
$a = bcpowmod($x, $y, $mod);

$b = bcmod(bcpow($x, $y), $mod);

// $a e $b sono uguali. 

?>

Vedere anche:

bcpow() e bcmod().

add a note

User Contributed Notes 3 notes

down

ewilde aht bsmdevelopment dawt com ¶

19 years ago


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);
  }

down

-3

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."

down

-5

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);
    }
}

add a note