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/ViaThinkSoft Distributed/src/de/viathinksoft/immortable/internal/Endzeitpunkt.java
0,0 → 1,39
package de.viathinksoft.immortable.internal;
 
import java.math.BigInteger;
 
public class Endzeitpunkt {
 
// Allgemeine Daten zum Test (GenX)
private static final BigInteger TEST_BEGINN = new BigInteger("1291006160");
 
// Der alte Algorithmus (r19)
// private static final int ABSCHNITT_STEP = 3;
// private static final BigInteger ABSCHNITT_BEGINN = new BigInteger("789");
// private static final BigInteger ABFALL_MEDIAN = new BigInteger("199");
 
// Der neue Algorithmus (r20)
private static final int ABSCHNITT_STEP = 29;
private static final BigInteger ABSCHNITT_BEGINN = new BigInteger("94923");
private static final BigInteger ABFALL_MEDIAN = new BigInteger("30");
 
private static BigInteger f(int u) {
BigInteger res = ABSCHNITT_BEGINN;
for (int i = ABSCHNITT_STEP + 1; i <= u; i++) {
res = res.add(ABFALL_MEDIAN.multiply(BigInteger.valueOf(i)));
}
return res;
}
 
private static BigInteger u(int u) {
return f(u).add(TEST_BEGINN);
}
 
public static void main(String[] args) {
int max_step = Integer.MAX_VALUE / 100000;
 
System.out.println("End time for step: " + max_step);
System.out.println(u(max_step));
}
 
}
/ViaThinkSoft Distributed/src/de/viathinksoft/immortable/gen2/math/MathUtils2.java
0,0 → 1,176
package de.viathinksoft.immortable.gen2.math;
 
import java.math.BigInteger;
 
public class MathUtils2 {
public static BigInteger length(BigInteger x) throws Exception {
// TODO: größer als MAX_INTEGER erlauben!
BigInteger z = new BigInteger(""+x.toString().length());
if (z.signum() == -1) {
throw new Exception("Integer overflow! (BigInteger-Length)");
}
return z;
}
public static BigInteger pow(BigInteger base, BigInteger exponent) {
if (exponent.signum() == -1) {
throw new ArithmeticException("Negative exponent");
}
 
BigInteger i = new BigInteger("0");
BigInteger res = new BigInteger("1");
while (i.compareTo(exponent) != 0) {
i = i.add(BigInteger.ONE);
res = res.multiply(base);
}
return res;
}
 
/**
* Division with remainder method - based on the original Java<br>
* 'divideAndRemainder' method<br>
* returns an object of results (of type BigInteger):<br>
* -> the division result (q=a/b)<br>
* result[1] -> the remainder (r=a-q*b)<br>
* If b==0 then result will be 0. No ArithmeticException!
*
* @param a
* @param b
* @return
* @see http://tupac.euv-frankfurt-o.de/www/kryptos/demos/Demos.java
**/
public static DivisionAndRemainderResult divRem(BigInteger a, BigInteger b) {
// if (b==0) {
// -> divideAndRemainder() throws ArithmeticException when b==0
if (b.signum() == 0) {
return new DivisionAndRemainderResult(BigInteger.ZERO,
BigInteger.ZERO);
}
 
BigInteger[] x = a.divideAndRemainder(b);
return new DivisionAndRemainderResult(x[0], x[1]);
}
 
/**
*
* @param a
* @param b
* @return
* @see http://www.arndt-bruenner.de/mathe/scripts/chineRestsatz.js
*/
private static BigInteger[] extGGT(BigInteger a, BigInteger b) {
if (b.signum() == 0) {
return new BigInteger[] { BigInteger.ONE, BigInteger.ZERO };
}
 
BigInteger rem = divRem(a, b).getRemainder();
if (rem.signum() == 0) {
return new BigInteger[] { BigInteger.ZERO, BigInteger.ONE };
}
 
BigInteger[] c = extGGT(b, rem);
BigInteger x = c[0];
BigInteger y = c[1];
 
return new BigInteger[] { y, x.subtract(y.multiply(a.divide(b))) };
}
 
/**
* Erweiterter euklidscher Algorithmus
*
* @param a
* @param b
* @return Erzeugt Objekt mit mit gcd=ggT(a,b) und gcd=alpha*a+beta*b
* @see http://www.arndt-bruenner.de/mathe/scripts/chineRestsatz.js
*/
private static ExtEuclResult erwGGT(BigInteger a, BigInteger b) {
BigInteger aa = new BigInteger("1");
BigInteger bb = new BigInteger("1");
 
if (a.signum() == -1) {
aa = new BigInteger("-1");
a = a.negate();
}
 
if (b.signum() == -1) {
bb = new BigInteger("-1");
b = b.negate();
}
 
BigInteger[] c = extGGT(a, b);
BigInteger g = a.gcd(b);
 
return new ExtEuclResult(c[0].multiply(aa), c[1].multiply(bb), g);
}
 
/**
* Allgemeines Lösen zweier Kongruenzen (Chinesischer Restsatz)
*
* @param a
* @param n
* @param b
* @param m
* @return
* @throws CRTNotSolveableException
* @throws RemainderNotSmallerThanModulusException
* @see http://de.wikipedia.org/wiki/Chinesischer_Restsatz#Direktes_L.C3.B6sen_von_simultanen_Kongruenzen_ganzer_Zahlen
*/
public static BigInteger chineseRemainder(BigInteger a, BigInteger n,
BigInteger b, BigInteger m) throws CRTException {
// Frage: Ist es notwendig, dass wir divRem() verwenden, das von a%0==0 ausgeht?
if (a.signum() == -1) {
a = a.negate();
}
if (b.signum() == -1) {
b = b.negate();
}
if (n.signum() == -1) {
n = n.negate();
}
if (m.signum() == -1) {
m = m.negate();
}
if ((a.compareTo(n) >= 0) || (b.compareTo(m) >= 0)) {
throw new RemainderNotSmallerThanModulusException();
}
 
// d = ggT(n,m)
BigInteger d = n.gcd(m);
 
// a === b (mod d) erfüllt?
if (!divRem(a, d).getRemainder().equals(divRem(b, d).getRemainder())) {
throw new CRTNotSolveableException();
}
 
// ggT(n,m) = yn + zm
BigInteger y = erwGGT(n, m).getAlpha();
 
// x = a - y*n*((a-b)/d) mod (n*m/d)
BigInteger N = n.multiply(m).divide(d);
BigInteger x = divRem(
a.subtract(y.multiply(n).multiply(a.subtract(b).divide(d))), N)
.getRemainder();
x = a.subtract(y.multiply(n).multiply(a.subtract(b).divide(d)));
 
while (x.signum() == -1) {
x = x.add(N);
}
 
return x;
}
 
private MathUtils2() {
}
 
}
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/ViaThinkSoft Distributed/src/de/viathinksoft/immortable/gen2/math/CoPrimeExpectedException.java
0,0 → 1,7
package de.viathinksoft.immortable.gen2.math;
 
public class CoPrimeExpectedException extends CRTException {
 
private static final long serialVersionUID = 8804691690532130114L;
 
}
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/ViaThinkSoft Distributed/src/de/viathinksoft/immortable/gen2/math/CRTNotSolveableException.java
0,0 → 1,7
package de.viathinksoft.immortable.gen2.math;
 
public class CRTNotSolveableException extends CRTException {
 
private static final long serialVersionUID = -2550866943316039887L;
 
}
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/ViaThinkSoft Distributed/src/de/viathinksoft/immortable/gen2/math/CRTException.java
0,0 → 1,7
package de.viathinksoft.immortable.gen2.math;
 
public class CRTException extends Exception {
 
private static final long serialVersionUID = 1040331240918766268L;
 
}
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/ViaThinkSoft Distributed/src/de/viathinksoft/immortable/gen2/math/ExtEuclResult.java
0,0 → 1,30
package de.viathinksoft.immortable.gen2.math;
 
import java.math.BigInteger;
 
public class ExtEuclResult {
private BigInteger alpha; // inverse
private BigInteger beta;
private BigInteger gcd; // ggT
 
public ExtEuclResult(BigInteger alpha, BigInteger beta, BigInteger gcd) {
super();
this.alpha = alpha;
this.beta = beta;
this.gcd = gcd;
}
public BigInteger getAlpha() {
return alpha;
}
public BigInteger getBeta() {
return beta;
}
public BigInteger getGcd() {
return gcd;
}
 
}
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/ViaThinkSoft Distributed/src/de/viathinksoft/immortable/gen2/math/MathUtils.java
0,0 → 1,140
package de.viathinksoft.immortable.gen2.math;
 
import java.math.BigInteger;
 
public class MathUtils {
 
/**
* Division with remainder method - based on the original Java<br>
* 'divideAndRemainder' method<br>
* returns an object of results (of type BigInteger):<br>
* -> the division result (q=a/b)<br>
* result[1] -> the remainder (r=a-q*b)
*
* @param a
* @param b
* @return
* @see http://tupac.euv-frankfurt-o.de/www/kryptos/demos/Demos.java
**/
 
public static DivisionAndRemainderResult divRem(BigInteger a, BigInteger b) {
// if (b==0) {
// -> divideAndRemainder() throws ArithmeticException when b==0
if ((b.compareTo(BigInteger.ZERO)) == 0) {
return new DivisionAndRemainderResult(BigInteger.ZERO,
BigInteger.ZERO);
}
 
BigInteger[] x = a.divideAndRemainder(b);
return new DivisionAndRemainderResult(x[0], x[1]);
}
 
/**
* The Extended Euclidean Algorithm
*
* @param a
* @param gcd
* @return Object of "alpha" (inverse), "beta" and gcd (of type BigInteger).
* @see http://tupac.euv-frankfurt-o.de/www/kryptos/demos/Demos.java
*/
 
public static ExtEuclResult extEucl(BigInteger a, BigInteger gcd) {
 
// Coefficients
BigInteger alpha_0 = new BigInteger("1");
BigInteger alpha_1 = new BigInteger("0");
BigInteger beta_0 = new BigInteger("0");
BigInteger beta_1 = new BigInteger("1");
BigInteger alpha = new BigInteger("0");
BigInteger beta = new BigInteger("1");
 
if (gcd.compareTo(BigInteger.ZERO) == 0) {
alpha = BigInteger.ONE;
beta = BigInteger.ZERO;
gcd = a;
} else if (a.compareTo(BigInteger.ZERO) != 0) {
DivisionAndRemainderResult qr = divRem(a, gcd);
 
while (qr.getRemainder().compareTo(BigInteger.ZERO) != 0) {
alpha = alpha_0.subtract(qr.getDivisionResult().multiply(
alpha_1));
beta = beta_0.subtract(qr.getDivisionResult().multiply(beta_1));
 
alpha_0 = alpha_1;
beta_0 = beta_1;
 
alpha_1 = alpha;
beta_1 = beta;
 
a = gcd;
gcd = qr.getRemainder();
qr = divRem(a, gcd);
}
}
 
return new ExtEuclResult(alpha, beta, gcd);
}
 
/**
* Determinates wheter p and q are coprimes or not.
*
* @param p
* @param q
* @return
*/
public static boolean isCoprime(BigInteger p, BigInteger q) {
return p.gcd(q).compareTo(BigInteger.ONE) == 0;
}
 
/**
* Solves the simultaneous congruences by means of the CR-Theorem:<br>
* M = Mp mod P and M = Mq mod Q<br>
* M = (Mq*Yp*P + Mp*Yq*Q) mod N<br>
* (Yp, Yq -> Ext.Eucl: Yp*P + Yq*Q = 1)
*
* @param Mp
* @param P
* @param Mq
* @param Q
* @return
* @throws CoPrimeExpectedException
* @see http://tupac.euv-frankfurt-o.de/www/kryptos/demos/Rsa.java
*/
 
public static BigInteger chineseRemainder(BigInteger Mp, BigInteger P, BigInteger Mq,
BigInteger Q) throws CoPrimeExpectedException {
 
if (!isCoprime(P, Q)) {
throw new CoPrimeExpectedException();
}
 
// 1) yiMi = 1 mod mi -> computing Inverses yi (extended
// Euclides):
// yp*P = 1 mod Q -> yp (inverse)
// yq*Q = 1 mod P -> yq (inverse)
 
BigInteger yq = extEucl(Q, P).getAlpha();
BigInteger yp = extEucl(P, Q).getAlpha();
 
// 2) collecting 'M = (Mp*yq*Q + Mq*yp*P) mod N':
 
BigInteger psum = Mp.multiply(yq).multiply(Q);
BigInteger qsum = Mq.multiply(yp).multiply(P);
BigInteger sum = psum.add(qsum);
 
// computing 'sum mod m'
BigInteger N = P.multiply(Q); // common modulus
BigInteger M = divRem(sum, N).getRemainder();
 
// if remainder (a/b) is negative (cause 'a' negative) then:
if (M.compareTo(BigInteger.ZERO) < 0) {
M = M.add(N);
}
 
return M;
}
private MathUtils() {
}
 
}
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/ViaThinkSoft Distributed/src/de/viathinksoft/immortable/gen2/math/RemainderNotSmallerThanModulusException.java
0,0 → 1,7
package de.viathinksoft.immortable.gen2.math;
 
public class RemainderNotSmallerThanModulusException extends CRTException {
 
private static final long serialVersionUID = -1361245285354281472L;
 
}
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/ViaThinkSoft Distributed/src/de/viathinksoft/immortable/gen2/math/DivisionAndRemainderResult.java
0,0 → 1,25
package de.viathinksoft.immortable.gen2.math;
 
import java.math.BigInteger;
 
public class DivisionAndRemainderResult {
private BigInteger divisionResult;
private BigInteger remainder;
 
public DivisionAndRemainderResult(BigInteger divisionResult,
BigInteger remainder) {
super();
this.divisionResult = divisionResult;
this.remainder = remainder;
}
 
public BigInteger getDivisionResult() {
return divisionResult;
}
 
public BigInteger getRemainder() {
return remainder;
}
 
}
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