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、 numexponent 乗を高速に計算します。

パラメータ

num

exponent

modulus

scale

このオプションパラメータを使用して、結果の小数点以下の桁数を指定します。省略した場合は、bcscale() 関数でグローバルに設定した桁数をデフォルトとして使用します。それも設定されていない場合は 0 を使用します。

変更履歴

バージョン 説明
8.0.0 scale は、nullable になりました。

例

<?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

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

ewilde aht bsmdevelopment dawt com
16 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);
}
-2
laysoft at gmail dot com
14 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=\$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);
}
}
-2
rrasss at gmail dot com
15 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." 