88 lines
2.2 KiB
Java
88 lines
2.2 KiB
Java
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/**
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*
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*/
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package zutil.algo;
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import java.math.BigInteger;
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/**
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* The algorithm solves the discreet log equation x^2 = n mod p
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*
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* @author Ziver
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* @see http://en.wikipedia.org/wiki/Shanks-Tonelli_algorithm
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*/
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public class ShanksTonelliAlgo {
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public static BigInteger calc(BigInteger n, BigInteger p){
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BigInteger nOrg = n;
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BigInteger S = null, V, R, U, X;
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BigInteger ONE = BigInteger.ONE;
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BigInteger TWO = BigInteger.valueOf( 2 );
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BigInteger Q = p.add( ONE ).divide( TWO );
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switch( p.mod( BigInteger.valueOf(4) ).intValue() ){
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case 3:
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S = n.pow( Q.divide( TWO ).intValue() ).mod( p );
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break;
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case 1:
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S = ONE;
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n = n.subtract( ONE );
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while (n.divide( p ).compareTo( ONE ) == 0) {
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S = S.add( ONE );
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//n = (n-2s+1) mod p
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n = n.subtract( TWO.multiply( S ) ).add( ONE ).mod( p );
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if (n.compareTo( BigInteger.ZERO ) == 0){
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return S;
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}
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}
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Q = Q.divide( TWO );
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V = ONE;
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R = S;
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U = ONE;
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while (Q.compareTo( BigInteger.ZERO ) > 0) {
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X = R.pow(2).subtract( n.multiply( U.pow(2) ) ).mod( p );
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U = TWO.multiply( R ).multiply( U ).mod( p );
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R = X;
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if ( Q.testBit(0) ){
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X = S.multiply( R ).subtract( n.multiply(V).multiply(U) ).mod( p );
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V = V.multiply(R).add( S.multiply(U) ).mod( p );
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S = X;
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}
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Q = Q.divide( TWO );
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}
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}
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if( S != null && S.multiply( S ).mod( p ).compareTo( nOrg ) != 0 ){
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return null;
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}
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return S;
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/*
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//p-1 = Q*2^S
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BigInteger S = null, Q = null, R = null, V = null, W = null;
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//Q = ( 2^S )/( 1-p );
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p-1 = ( 2^S )/( 1-p ) * 2^S;
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// R = n^( (Q+1)/2 ) mod p
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R = n.pow( Q.add(BigInteger.ONE).divide(BigInteger.valueOf(2)).intValue() ).mod( p );
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// V = W^Q mod p
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V = W.pow( Q.intValue() ).mod( p );
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for(int i=S.intValue(); true ;){
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while( true ){
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i--;
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// 1 = ( ( R^2 * n^-1 )^2^i ) mod p
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if( ( R.pow(2).multiply( n.pow(-1) ) ).pow( (int)Math.pow(2, i) ).mod( p ).compareTo( BigInteger.ONE ) == 0 )
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break;
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}
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if(i == 0) return R;
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//R = ( RV^(2^(S-i-1)) ) mod p
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else R = ( R.multiply( V.pow( (int)Math.pow( 2, S.intValue()-i-1) ) )).mod( p );
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}
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*/
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}
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}
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