tested interpolation

destributed-key-generation/src/main/java/FeldmanVerifiableSecretSharing/VerifiableSecretSharing.java

@@ -2,6 +2,7 @@ package FeldmanVerifiableSecretSharing;
 
 import ShamirSecretSharing.SecretSharing;
 import org.bouncycastle.util.Arrays;
+import org.factcenter.qilin.primitives.CyclicGroup;
 import org.factcenter.qilin.primitives.concrete.Zpstar;
 
 import java.math.BigInteger;
@@ -15,9 +16,9 @@ public class VerifiableSecretSharing extends SecretSharing {
     private final BigInteger[] commitments;
     private final BigInteger g;
 
-    public VerifiableSecretSharing(Zpstar zpstar, int t, int n, BigInteger s, Random random) {
-        super(zpstar, t, n, s, random);
-        this.g = BigInteger.ONE; //ToDO zpstar.getGenerator()
+    public VerifiableSecretSharing(CyclicGroup<BigInteger> group, int t, int n, BigInteger s, Random random) {
+        super(group, t, n, s, random);
+        this.g = group.getGenerator();
         this.commitments = generateCommitments();
     }
 
@@ -25,7 +26,7 @@ public class VerifiableSecretSharing extends SecretSharing {
         BigInteger[] coefficients = polynomial.getCoefficients();
         BigInteger[] commitments = new BigInteger[coefficients.length];
         for (int i = 0 ; i < commitments.length;i++){
-            commitments[i] = zpstar.multiply(g,coefficients[i]);
+            commitments[i] = group.multiply(g,coefficients[i]); //(g ^ coeff[i]) % p
         }
         return commitments;
     }
@@ -34,13 +35,14 @@ public class VerifiableSecretSharing extends SecretSharing {
         if(i < 1 || i > n){
             throw new Exception();
         }
-        BigInteger v = BigInteger.ONE;
+        BigInteger v = group.zero();
         int power = 1;
         for (int j = 0 ; j < commitments.length ; j ++){
-            v.multiply(commitments[i].pow(power));
+            v = group.add(v,commitments[i].pow(power));
             power *=i;
         }
-        return zpstar.add(BigInteger.ONE,v);
+
+        return group.add(group.zero(),v);
     }
 
 

destributed-key-generation/src/main/java/ShamirSecretSharing/LagrangePolynomial.java

@@ -0,0 +1,40 @@
+package ShamirSecretSharing;
+
+import java.math.BigInteger;
+
+/**
+ * Created by Tzlil on 1/28/2016.
+ */
+class LagrangePolynomial{
+    public final Polynomial polynomial;
+    public final BigInteger image;
+    public final BigInteger divisor;
+
+    private LagrangePolynomial(Polynomial polynomial, BigInteger image, BigInteger divisor) {
+        this.polynomial = polynomial;
+        this.image = image;
+        this.divisor = divisor;
+    }
+
+    public static LagrangePolynomial[] lagrangePolynomials(Polynomial.Point[] points){
+        LagrangePolynomial[] lagrangePolynomials = new LagrangePolynomial[points.length];
+        Polynomial[] factors = new Polynomial[points.length];
+        for (int i = 0 ; i < factors.length ; i++){
+            factors[i] = new Polynomial(new BigInteger[]{BigInteger.ZERO.subtract(points[i].x),BigInteger.ONE}); // X - Xi
+        }
+        Polynomial product;
+        BigInteger divisor;
+        for(int i = 0; i < points.length; i ++) {
+            product = Polynomial.ONE;
+            divisor = BigInteger.ONE;
+            for (int j = 0; j < points.length; j++) {
+                if (i != j) {
+                    divisor = divisor.multiply(points[i].x.subtract(points[j].x));
+                    product = product.mul(factors[j]);
+                }
+            }
+            lagrangePolynomials[i] = new LagrangePolynomial(product,points[i].y,divisor);
+        }
+        return lagrangePolynomials;
+    }
+}

destributed-key-generation/src/main/java/ShamirSecretSharing/Polynomial.java

@@ -2,6 +2,7 @@ package ShamirSecretSharing;
 
 import org.bouncycastle.util.Arrays;
 import org.factcenter.qilin.primitives.concrete.ECGroup;
+import org.factcenter.qilin.util.Pair;
 
 import java.math.BigInteger;
 
@@ -10,8 +11,8 @@ import java.math.BigInteger;
  */
 public class Polynomial {
 
-    private static final Polynomial ZERO = new Polynomial(new BigInteger[]{BigInteger.ZERO});
-    private static final Polynomial ONE = new Polynomial(new BigInteger[]{BigInteger.ONE});
+    protected static final Polynomial ZERO = new Polynomial(new BigInteger[]{BigInteger.ZERO});
+    protected static final Polynomial ONE = new Polynomial(new BigInteger[]{BigInteger.ONE});
     private final int degree;
     private final BigInteger[] coefficients;
 
@@ -25,36 +26,53 @@ public class Polynomial {
         this.coefficients = polynomial.getCoefficients();
     }
 
+    public boolean isEquals(Polynomial other) {
+        if (this.degree != other.degree)
+            return false;
+        return Arrays.areEqual(this.coefficients,other.coefficients);
+    }
+
+    @Override
+    public String toString() {
+        return "Polynomial{" +
+                "degree=" + degree +
+                ", coefficients=" + java.util.Arrays.toString(coefficients) +
+                '}';
+    }
+
     public BigInteger image(BigInteger x){
         BigInteger result = BigInteger.ZERO;
         BigInteger power = BigInteger.ONE;
         for(int i = 0 ; i <= degree ; i++){
-            result.add(coefficients[i].multiply(power));
-            power.multiply(x);
+            result = result.add(coefficients[i].multiply(power));
+            power = power.multiply(x);
         }
         return result;
     }
 
     public static Polynomial interpolation(Point[] points){
-        Polynomial[] factors = new Polynomial[points.length];
-        for (int i = 0 ; i < factors.length ; i++){
-            factors[i] = new Polynomial(new BigInteger[]{BigInteger.ONE,points[i].x}); // X - Xi
+        LagrangePolynomial[] l = LagrangePolynomial.lagrangePolynomials(points);
+
+        BigInteger product = BigInteger.ONE;
+        for (int i = 0; i < l.length;i++){
+            product = product.multiply(l[i].divisor);
         }
-        Polynomial result = ZERO;
-        BigInteger constant;
-        Polynomial product;
-        for (int i = 0 ; i < points.length; i++){
-            constant = points[i].y;
-            product = ONE;
-            for (int j = 0 ; j < points.length; j ++){
-                if(i != j ) {
-                    constant = constant.divide(points[i].x.subtract(points[j].x));
-                    product = product.mul(factors[j]);
-                }
+
+        BigInteger[] factors = new BigInteger[l.length];
+        for (int i = 0; i < l.length;i++){
+            factors[i] = product.divide(l[i].divisor);
+        }
+
+        int degree = l[0].polynomial.degree;
+        BigInteger[] coefficients = new BigInteger[degree + 1];
+        for (int j = 0; j < coefficients.length;j++){
+            coefficients[j] = BigInteger.ZERO;
+            for (int i = 0; i < l.length; i++){
+                coefficients[j] = coefficients[j].add(l[i].image.multiply(factors[i]).multiply(l[i].polynomial.coefficients[j]));
             }
-            result.add(product.mul(constant));
+            coefficients[j] = coefficients[j].divide(product);
         }
-        return result;
+        return new Polynomial(coefficients);
     }
 
     public Polynomial add(Polynomial other){

destributed-key-generation/src/main/java/ShamirSecretSharing/SecretSharing.java

@@ -1,6 +1,7 @@
 package ShamirSecretSharing;
 
 
+import org.factcenter.qilin.primitives.CyclicGroup;
 import org.factcenter.qilin.primitives.concrete.Zpstar;
 
 import java.math.BigInteger;
@@ -10,13 +11,13 @@ import java.util.Random;
  * Created by Tzlil on 1/27/2016.
  */
 public class SecretSharing {
-    protected final Zpstar zpstar;
+    protected final CyclicGroup<BigInteger> group;
     protected final int t;
     protected final int n;
     protected final Polynomial polynomial;
 
-    public SecretSharing(Zpstar zpstar, int t, int n, BigInteger s, Random random) {
-        this.zpstar = zpstar;
+    public SecretSharing(CyclicGroup<BigInteger> group, int t, int n, BigInteger s, Random random) {
+        this.group = group;
         this.t = t;
         this.n = n;
         this.polynomial = generateRandomPolynomial(s,random);
@@ -25,13 +26,15 @@ public class SecretSharing {
     private Polynomial generateRandomPolynomial(BigInteger s, Random random) {
         BigInteger[] coefficients = new BigInteger[t + 1];
         coefficients[0] = s;
+        BigInteger p = group.orderUpperBound();
+        int bits = p.bitLength();
         for (int i = 1 ; i <= t; i++ ){
-            coefficients[i] = zpstar.sample(random);
+            coefficients[i] = new BigInteger(bits,random).mod(p); // sample from Zp [0,... p-1]
         }
         return new Polynomial(coefficients);
     }
 
-    //ToDo make it safe : permission to call this func + modulo calc
+    //ToDo make it safe : permission to call this func
     public Polynomial.Point getShare(int i) throws Exception {
         if(i < 1 || i > n){
             throw new Exception();

destributed-key-generation/src/test/java/Polynomial/AddTest.java

@@ -0,0 +1,44 @@
+package Polynomial;
+import ShamirSecretSharing.Polynomial;
+import org.junit.Before;
+import org.junit.Test;
+
+import java.math.BigInteger;
+import java.util.Random;
+
+/**
+ * Created by Tzlil on 1/27/2016.
+ */
+public class AddTest {
+
+    Polynomial[] arr1;
+    Polynomial[] arr2;
+    int tests = 1 << 12;
+    int maxDegree = 15;
+    int bits = 128;
+    Random random;
+
+    @Before
+    public void settings(){
+        random = new Random();
+        arr1 = new Polynomial[tests];
+        arr2 = new Polynomial[tests];
+        for (int i = 0; i < arr1.length; i++){
+            arr1[i] = Utils.generateRandomPolynomial(random.nextInt(maxDegree),bits,random);
+            arr2[i] = Utils.generateRandomPolynomial(random.nextInt(maxDegree),bits,random);
+        }
+    }
+
+    public void oneTest(Polynomial p1, Polynomial p2){
+        Polynomial sum = p1.add(p2);
+        BigInteger x = new BigInteger(bits,random);
+        assert(sum.image(x).equals(p1.image(x).add(p2.image(x))));
+    }
+
+    @Test
+    public void addTest(){
+        for (int i = 0 ; i < arr1.length; i ++){
+            oneTest(arr1[i],arr2[i]);
+        }
+    }
+}

destributed-key-generation/src/test/java/Polynomial/InterpolationTest.java

@@ -0,0 +1,61 @@
+package Polynomial;
+
+import ShamirSecretSharing.Polynomial;
+import org.junit.Before;
+import org.junit.Test;
+
+import java.math.BigInteger;
+import java.util.HashSet;
+import java.util.Random;
+import java.util.Set;
+
+/**
+ * Created by Tzlil on 1/27/2016.
+ */
+public class InterpolationTest {
+    Polynomial[] polynomials;
+    int tests = 1 << 10;
+    int maxDegree = 15;
+    int bits = 128;
+    Random random;
+    Polynomial.Point[][] pointsArrays;
+    @Before
+    public void settings(){
+        random = new Random();
+        polynomials = new Polynomial[tests];
+        pointsArrays = new Polynomial.Point[tests][];
+        for (int i = 0; i < polynomials.length; i++){
+            polynomials[i] = Utils.generateRandomPolynomial(random.nextInt(maxDegree),bits,random);
+            pointsArrays[i] = randomPoints(polynomials[i]);
+        }
+    }
+
+    public Polynomial.Point[] randomPoints(Polynomial p){
+        Polynomial.Point[] points = new Polynomial.Point[p.getDegree() + 1];
+        BigInteger x;
+        Boolean b;
+        Set<BigInteger> set = new HashSet();
+        for (int i = 0; i < points.length; i++){
+            x = new BigInteger(bits,random);
+            if(set.contains(x)){
+                i--;
+                continue;
+            }
+            set.add(x);
+            points[i] = new Polynomial.Point(x,p.image(x));
+        }
+        return points;
+    }
+
+    public void oneTest(Polynomial p, Polynomial.Point[] points){
+        Polynomial interpolation = Polynomial.interpolation(points);
+        assert (p.isEquals(interpolation));
+    }
+
+    @Test
+    public void interpolationTest(){
+        for (int i = 0; i < polynomials.length; i ++){
+            oneTest(polynomials[i],pointsArrays[i]);
+        }
+    }
+}

destributed-key-generation/src/test/java/Polynomial/MulByConstTest.java

@@ -0,0 +1,46 @@
+package Polynomial;
+
+import ShamirSecretSharing.Polynomial;
+import org.junit.Before;
+import org.junit.Test;
+
+import java.math.BigInteger;
+import java.util.Random;
+
+/**
+ * Created by Tzlil on 1/27/2016.
+ */
+public class MulByConstTest {
+
+
+    Polynomial[] arr1;
+    BigInteger[] arr2;
+    int tests = 1 << 12;
+    int maxDegree = 15;
+    int bits = 128;
+    Random random;
+
+    @Before
+    public void settings(){
+        random = new Random();
+        arr1 = new Polynomial[tests];
+        arr2 = new BigInteger[tests];
+        for (int i = 0; i < arr1.length; i++){
+            arr1[i] = Utils.generateRandomPolynomial(random.nextInt(maxDegree),bits,random);
+            arr2[i] = new BigInteger(bits,random);
+        }
+    }
+
+    public void oneTest(Polynomial p, BigInteger c){
+        Polynomial product = p.mul(c);
+        BigInteger x = new BigInteger(bits,random);
+        assert(product.image(x).equals(p.image(x).multiply(c)));
+    }
+
+    @Test
+    public void mulByConstTest(){
+        for (int i = 0 ; i < arr1.length; i ++){
+            oneTest(arr1[i],arr2[i]);
+        }
+    }
+}

destributed-key-generation/src/test/java/Polynomial/MulTest.java

@@ -0,0 +1,46 @@
+package Polynomial;
+
+import ShamirSecretSharing.Polynomial;
+import org.junit.Before;
+import org.junit.Test;
+
+import java.math.BigInteger;
+import java.util.Random;
+
+/**
+ * Created by Tzlil on 1/27/2016.
+ */
+public class MulTest {
+
+
+    Polynomial[] arr1;
+    Polynomial[] arr2;
+    int tests = 1 << 12;
+    int maxDegree = 15;
+    int bits = 128;
+    Random random;
+
+    @Before
+    public void settings(){
+        random = new Random();
+        arr1 = new Polynomial[tests];
+        arr2 = new Polynomial[tests];
+        for (int i = 0; i < arr1.length; i++){
+            arr1[i] = Utils.generateRandomPolynomial(random.nextInt(maxDegree),bits,random);
+            arr2[i] = Utils.generateRandomPolynomial(random.nextInt(maxDegree),bits,random);
+        }
+    }
+
+    public void oneTest(Polynomial p1, Polynomial p2){
+        Polynomial product = p1.mul(p2);
+        BigInteger x = new BigInteger(bits,random);
+        assert(product.image(x).equals(p1.image(x).multiply(p2.image(x))));
+    }
+
+    @Test
+    public void mulTest(){
+        for (int i = 0 ; i < arr1.length; i ++){
+            oneTest(arr1[i],arr2[i]);
+        }
+    }
+}

destributed-key-generation/src/test/java/Polynomial/Utils.java

@@ -0,0 +1,21 @@
+package Polynomial;
+
+import ShamirSecretSharing.Polynomial;
+
+import java.math.BigInteger;
+import java.util.Random;
+
+/**
+ * Created by Tzlil on 1/27/2016.
+ */
+public class Utils {
+
+    public static Polynomial generateRandomPolynomial(int degree,int bits,Random random) {
+        BigInteger[] coefficients = new BigInteger[degree + 1];
+
+        for (int i = 0 ; i <= degree; i++ ){
+            coefficients[i] = new BigInteger(bits,random); // sample from Zp [0,... p-1]
+        }
+        return new Polynomial(coefficients);
+    }
+}