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Bug fix and some other things

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Ziver Koc 2009-03-31 17:56:23 +00:00
parent 9297bea93d
commit 7cb0fdb435
4 changed files with 129 additions and 37 deletions
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87
src/zutil/algo/ShanksTonelliAlgo.java Normal file
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@ -0,0 +1,87 @@
/**
*
*/
package zutil.algo;
import java.math.BigInteger;
/**
* The algorithm solves the discreet log equation x^2 = n mod p
*
* @author Ziver
* @see http://en.wikipedia.org/wiki/Shanks-Tonelli_algorithm
*/
public class ShanksTonelliAlgo {
public static BigInteger calc(BigInteger n, BigInteger p){
BigInteger nOrg = n;
BigInteger S = null, V, R, U, X;
BigInteger ONE = BigInteger.ONE;
BigInteger TWO = BigInteger.valueOf( 2 );
BigInteger Q = p.add( ONE ).divide( TWO );
switch( p.mod( BigInteger.valueOf(4) ).intValue() ){
case 3:
S = n.pow( Q.divide( TWO ).intValue() ).mod( p );
break;
case 1:
S = ONE;
n = n.subtract( ONE );
while (n.divide( p ).compareTo( ONE ) == 0) {
S = S.add( ONE );
//n = (n-2s+1) mod p
n = n.subtract( TWO.multiply( S ) ).add( ONE ).mod( p );
if (n.compareTo( BigInteger.ZERO ) == 0){
return S;
}
}
Q = Q.divide( TWO );
V = ONE;
R = S;
U = ONE;
while (Q.compareTo( BigInteger.ZERO ) > 0) {
X = R.pow(2).subtract( n.multiply( U.pow(2) ) ).mod( p );
U = TWO.multiply( R ).multiply( U ).mod( p );
R = X;
if ( Q.testBit(0) ){
X = S.multiply( R ).subtract( n.multiply(V).multiply(U) ).mod( p );
V = V.multiply(R).add( S.multiply(U) ).mod( p );
S = X;
}
Q = Q.divide( TWO );
}
}
if( S != null && S.multiply( S ).mod( p ).compareTo( nOrg ) != 0 ){
return null;
}
return S;
/*
//p-1 = Q*2^S
BigInteger S = null, Q = null, R = null, V = null, W = null;
//Q = ( 2^S )/( 1-p );
p-1 = ( 2^S )/( 1-p ) * 2^S;
// R = n^( (Q+1)/2 ) mod p
R = n.pow( Q.add(BigInteger.ONE).divide(BigInteger.valueOf(2)).intValue() ).mod( p );
// V = W^Q mod p
V = W.pow( Q.intValue() ).mod( p );
for(int i=S.intValue(); true ;){
while( true ){
i--;
// 1 = ( ( R^2 * n^-1 )^2^i ) mod p
if( ( R.pow(2).multiply( n.pow(-1) ) ).pow( (int)Math.pow(2, i) ).mod( p ).compareTo( BigInteger.ONE ) == 0 )
break;
}
if(i == 0) return R;
//R = ( RV^(2^(S-i-1)) ) mod p
else R = ( R.multiply( V.pow( (int)Math.pow( 2, S.intValue()-i-1) ) )).mod( p );
}
*/
}
}

1
src/zutil/algo/WienersAlgo.java
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@ -46,6 +46,7 @@ public class WienersAlgo {
d1 = g.multiply( d1 ).add( d0 );
d0 = t;
// (d1*e-1) % c1 == 0
n1 = d1.multiply( e ).subtract( BigInteger.ONE );
if( n1.mod( c1 ).equals( BigInteger.ZERO ) ){
n1 = n1.divide( c1 );