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bcpowmod

(PHP 5, PHP 7)

bcpowmod — Raise an arbitrary precision number to another, reduced by a specified modulus

Descrierea

bcpowmod ( string $num , string $exponent , string $modulus , int|null $scale = null ) : string

Use the fast-exponentiation method to raise num to the power exponent with respect to the modulus modulus.

Parametri

num: The base, as an integral string (i.e. the scale has to be zero).
exponent: The exponent, as an non-negative, integral string (i.e. the scale has to be zero).
modulus: The modulus, as an integral string (i.e. the scale has to be zero).
scale: Acest parametru opțional este utilizat pentru a stabili numărul cifrelor după virgulă din rezultat. Dacă este omis, valoarea implicită va fi cea stabilită global cu funcția bcscale(), sau va fi 0 dacă nu a fost stabilită cu ajutorul acestei funcții.

Valorile întoarse

Returns the result as a string, or false if modulus is 0 or exponent is negative.

Note

Notă:
Because this method uses the modulus operation, numbers which are not positive integers may give unexpected results.

Istoricul schimbărilor

Versiune	Descriere
8.0.0	`scale` is now nullable.

Exemple

The following two statements are functionally identical. The bcpowmod() version however, executes in less time and can accept larger parameters.


<?php
$a = bcpowmod($x, $y, $mod);

$b = bcmod(bcpow($x, $y), $mod);

// $a and $b are equal to each other.

?>

A se vedea și

bcpow() - Raise an arbitrary precision number to another
bcmod() - Get modulus of an arbitrary precision number

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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);
    }
}

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