a124d003cf
Add a mapping function which converts sequential integers to a sequence in which most of the digits change each time, but without significantly increasing the length. Change-Id: I1011a96894fbf0b92d20a96149e68014f53e3c3c
97 lines
3 KiB
PHP
97 lines
3 KiB
PHP
<?php
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namespace MediaWiki\User\TempUser;
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/**
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* A mapping which converts sequential input into an output sequence that looks
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* pseudo-random, but preserves the base-10 length of the input number.
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*
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* Take a sequence generated by multiplying the previous element of the
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* sequence by a fixed number "g", then applying the modulus "p":
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*
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* X(0) = 1
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* X(i) = ( g X(i-1) ) mod p
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*
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* If g is a primitive root modulo p, then this sequence will cover all values
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* from 1 to p-1 before it repeats. X(i) is a modular exponential function
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* (g^i mod p) and algorithms are available to calculate it efficiently.
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*
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* Loosely speaking, we choose a sequence based on the number of digits N in the
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* input, with the period being approximately 10^N, so that the number of digits
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* in the output will be approximately the same.
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*
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* More precisely, after offsetting the subsequent sequences to avoid colliding
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* with the previous sequences, the period ends up being about 0.9 * 10^N
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*
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* The modulo p is always a prime number because that makes the maths easier.
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* We use a value for g close to p/sqrt(3) since that seems to stir the digits
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* better than the largest or smallest primitive root.
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*
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* @internal
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*/
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class ScrambleMapping implements SerialMapping {
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/**
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* Appropriately sized prime moduli and their associated largest primitive
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* root. Generated with this GP/PARI script:
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* s=0; \
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* for(q = 2, 10, \
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* p=precprime(10^q - s); \
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* s = s + p; \
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* forstep(i = floor(p/sqrt(3)), 1, -1, \
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* if(znorder(Mod(i, p)) == p-1, \
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* print("[ ", i, ", ", p, " ],"); \
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* break )))
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*/
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private const GENERATORS = [
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[ 56, 97 ],
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[ 511, 887 ],
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[ 5203, 9013 ],
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[ 51947, 90001 ],
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[ 519612, 900001 ],
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[ 5196144, 8999993 ],
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[ 51961523, 89999999 ],
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[ 519615218, 899999963 ],
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[ 5196152444, 9000000043 ],
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];
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/** @var int */
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private $offset;
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/** @var bool */
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private $hasGmp;
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/** @var bool */
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private $hasBcm;
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public function __construct( $config ) {
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$this->offset = $config['offset'] ?? 0;
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$this->hasGmp = extension_loaded( 'gmp' );
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$this->hasBcm = extension_loaded( 'bcmath' );
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if ( !$this->hasGmp && !$this->hasBcm ) {
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throw new \MWException( __CLASS__ . ' requires the bcmath or gmp extension' );
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}
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}
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public function getSerialIdForIndex( int $index ): string {
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if ( $index <= 0 ) {
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return (string)$index;
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}
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$offset = $this->offset;
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foreach ( self::GENERATORS as [ $g, $p ] ) {
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if ( $index - $offset < $p ) {
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return (string)( $offset + $this->powmod( $g, $index - $offset, $p ) );
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}
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$offset += $p - 1;
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}
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throw new \MWException( __METHOD__ . ": The index $index is too large" );
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}
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private function powmod( $num, $exponent, $modulus ) {
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if ( $this->hasGmp ) {
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return \gmp_intval( \gmp_powm( $num, $exponent, $modulus ) );
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} elseif ( $this->hasBcm ) {
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return (int)\bcpowmod( (string)$num, (string)$exponent, (string)$modulus );
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} else {
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throw new \MWException( __CLASS__ . ' requires the bcmath or gmp extension' );
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}
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}
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}
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