PHPのお勉強！

PHP TOP
PHP 8.4.2 Released!

    bcpowmod

    (PHP 5, PHP 7, PHP 8)

    bcpowmod — 任意精度数値のべき乗の、指定した数値による剰余

    説明

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

    modulus で割った余りを求めることを考慮して、 num の exponent 乗を高速に計算します。

    パラメータ

    num

    基数を表す整数の文字列。 (つまり、scale は 0 でなければいけません)

    exponent

    指数を表す、負でない、整数の文字列。 (つまり、scale は 0 でなければいけません)

    modulus

    法を表す、整数の文字列。 (つまり、scale は 0 でなければいけません)

    scale
    This parameter is used to set the number of digits after the decimal place in the result. If null, it will default to the default scale set with bcscale(), or fallback to the value of the bcmath.scale INI directive.

    戻り値

    結果を文字列で返します。

    エラー / 例外

    This function throws a ValueError in the following cases:

    • num, exponent or modulus is not a well-formed BCMath numeric string
    • num, exponent or modulus has a fractional part
    • exponent is a negative value
    • scale is outside the valid range

    This function throws a DivisionByZeroError exception if modulus is 0.

    変更履歴

    バージョン 説明
    8.0.0 scale は、nullable になりました。
    8.0.0 Now throws a ValueError instead of returning false if exponent is a negative value.
    8.0.0 Dividing by 0 now throws a DivisionByZeroError exception instead of returning false.

    例

    以下の 2 つの文は機能的に同じです。しかし bcpowmod() バージョンのほうが実行時間が早いうえ、 より大きな値の計算が可能です。

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

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

    // $a と $b は同じ値になります

    ?>

    注意

    注意:

    このメソッドでは剰余計算を行っているので、 正の整数以外を指定すると予期せぬ結果となります。

    参考

    • bcpow() - 任意精度数値をべき乗する
    • bcmod() - 2 つの任意精度数値の剰余を取得する

    Found A Problem?

    Learn How To Improve This Page • Submit a Pull Request • Report a Bug
    ＋add a note

    User Contributed Notes 3 notes

    up
    2
    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);
    }
    up
    -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."
    up
    -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
    To Top