diff --git a/Crypto.csproj b/Crypto.csproj
index 08be3e4..946c98f 100644
--- a/Crypto.csproj
+++ b/Crypto.csproj
@@ -32,8 +32,9 @@
   </ItemGroup>
   <ItemGroup>
     <Compile Include="Properties\AssemblyInfo.cs" />
-    <Compile Include="EC\EllipticCurve.cs" />
     <Compile Include="EC\CurvePoint.cs" />
+    <Compile Include="EC\EllipticCurve.cs" />
+    <Compile Include="EC\ProjectiveCurvePoint.cs" />
   </ItemGroup>
   <ItemGroup>
     <Folder Include="EC\" />
@@ -47,6 +48,10 @@
       <Project>{97CA3CA9-98B3-4492-B072-D7A5995B68E9}</Project>
       <Name>sharp.extensions</Name>
     </ProjectReference>
+    <ProjectReference Include="..\sharp-contracts\sharp.contracts.csproj">
+      <Project>{56733EC1-7D97-48D0-AA4C-98EA624A5A21}</Project>
+      <Name>sharp.contracts</Name>
+    </ProjectReference>
   </ItemGroup>
   <Import Project="$(MSBuildBinPath)\Microsoft.CSharp.targets" />
 </Project>
\ No newline at end of file
diff --git a/EC/CurvePoint.cs b/EC/CurvePoint.cs
index 62b8974..d32c28f 100644
--- a/EC/CurvePoint.cs
+++ b/EC/CurvePoint.cs
@@ -1,4 +1,4 @@
-using System;
+using System;
 using BigInt;
 using System.Text;
 using System.Runtime.CompilerServices;
@@ -7,56 +7,115 @@ namespace Crypto.EC
 {
 	public class CurvePoint
 	{
-		public CurvePoint(EllipticCurve curve,UInteger x,UInteger y){
+		public static readonly CurvePoint INFINITY = new CurvePoint();
+
+		public CurvePoint(EllipticCurve curve,Integer x,Integer y){
 			Curve = curve;
 			X = x;
 			Y = y;
 		}
 
-		public string toHexString(){
+		private CurvePoint(){
+			this.Curve = null;
+			this.X = 0;
+			this.Y = 0;
+		}
+
+		public string toHexString()
+		{
 			StringBuilder sb = new StringBuilder();
-			sb.Append(X.toHexString());
+			sb.Append(((UInteger)X).toHexString());
 			sb.Append(".");
-			sb.Append(Y.toHexString());
+			sb.Append(((UInteger)Y).toHexString());
 			return sb.ToString();
 		}
 
+		public override string ToString()
+		{
+			if ((object)this == (object)INFINITY){
+				return String.Format("[CurvePoint INFINITY]");
+			}
+			return String.Format("[CurvePoint X={0} Y={1}]",X.ToString(),Y.ToString());
+		}
+
 		public EllipticCurve Curve { get; private set; }
-		public UInteger X { get; private set; }
-		public UInteger Y { get; private set; }
+		public Integer X { get; private set; }
+		public Integer Y { get; private set; }
 
 		public bool isOnCurve(){
 			return this.Curve.isOnCurve(this);
 		}
 
+		public bool isInfinity(){
+			return ((object)this == (object)INFINITY);
+		}
+
+		public CurvePoint Negated(){
+			return new CurvePoint(Curve, X, Curve.Fp.AdditiveInverse(Y));
+		}
+
 		public static CurvePoint operator +(CurvePoint p1, CurvePoint p2)
 		{
-			return p1.Curve.Add(p1,p2);
+			if ((object)p1 == (object)INFINITY){
+				return p2;
+			}
+			if ((object)p2 == (object)INFINITY){
+				return p1;
+			}
+
+			return p1.Curve.Add(p1, p2);
 		}
-		public static CurvePoint operator *(CurvePoint p1, UInteger n)
+
+		public static CurvePoint operator -(CurvePoint p1, CurvePoint p2)
 		{
-			if (p1.Y == UInteger.ZERO){
-				throw new NotImplementedException("Eternity point not implemented");
+			if ((object)p1 == (object)INFINITY){
+				return p2;
+			}
+			if ((object)p2 == (object)INFINITY){
+				return p1;
+			}
+			return p1.Curve.Add(p1, p2.Negated());
+		}
+
+		public static CurvePoint operator *(CurvePoint p1, Integer n)
+		{
+			if ((object)p1 == (object)INFINITY){
+				return INFINITY;
+			}
+
+			if (p1.Y == Integer.ZERO){
+				return INFINITY;
+			}
+
+			if (n.isZero()){
+				throw new NotImplementedException("CurevPoint * 0");
 			}
 
 			CurvePoint result = null;
 			CurvePoint p = p1;
 
 			int i;
+			int bitwidth = n.Log2();
 
-			for (i = 0; i < 256; i++)
+			if (bitwidth < 0){
+				bitwidth = -bitwidth;
+			}
+
+			for (i = 0; i < bitwidth; i++)
 			{
-				if (n[i]){
-					result = p;
+				if (n[i])
 					break;
-				}
+				
 				p += p;
 			}
-			for (; i < 256; i++)
+
+			result = p;
+
+			for (i++; i <= bitwidth; i++)
 			{
 				p += p;
 				if (n[i]){
-					result += p;
+					result = p + result;
 				}
 			}
 
diff --git a/EC/EllipticCurve.cs b/EC/EllipticCurve.cs
index 55c5636..8336e14 100644
--- a/EC/EllipticCurve.cs
+++ b/EC/EllipticCurve.cs
@@ -7,15 +7,15 @@ namespace Crypto.EC
 {
 	public class EllipticCurve
 	{
-		public UInteger a { get; private set; }
-		public UInteger b { get; private set; }
-		public UInteger n { get; private set; }
+		public Integer a { get; private set; }
+		public Integer b { get; private set; }
+		public Integer n { get; private set; }
 		public int h  { get; private set; }
 
 		public CurvePoint G  { get; private set; }
 		public IntField Fp { get; private set; }
 
-		public EllipticCurve(UInteger p,UInteger a,UInteger b,UInteger xG,UInteger yG,UInteger n,int h)
+		public EllipticCurve(Integer p,Integer a,Integer b,Integer xG,Integer yG,Integer n,int h)
 		{
 			this.Fp = new IntField(p);
 			this.a = a;
@@ -29,38 +29,38 @@ namespace Crypto.EC
 			}
 		}
 
-		public UInteger Y2(UInteger x){
+		public Integer Y2(Integer x){
 			
-			UInteger yy = x;
+			Integer yy = x;
 
-			Console.WriteLine("Y(x):           X = {0}",x.toHexString());
-			Console.WriteLine("Y(x):         x^2 = {0}",yy.Pow(2).toHexString());
+			//Console.WriteLine("Y(x):           X = {0}",x.toHexString());
+			//Console.WriteLine("Y(x):         x^2 = {0}",yy.Pow(2).toHexString());
 
 			yy = yy.Pow(3);
 
-			Console.WriteLine("Y(x):         x^3 = {0}",yy.toHexString());
+			//Console.WriteLine("Y(x):         x^3 = {0}",yy.toHexString());
 
 			yy += (a * x);
 
-			Console.WriteLine("Y(x):    x^3 + ax = {0}",yy.toHexString());
+			//Console.WriteLine("Y(x):    x^3 + ax = {0}",yy.toHexString());
 
 			yy += b;
 
-			Console.WriteLine("Y(x) x^3 + ax + b = {0}",yy.toHexString());
+			//Console.WriteLine("Y(x) x^3 + ax + b = {0}",yy.toHexString());
 
-			yy %= this.Fp.FieldModulo;
+			yy %= (Integer)this.Fp.FieldModulo;
 
-			Console.WriteLine("Y(x) mod p        = {0}",yy.toHexString());
+			//Console.WriteLine("Y(x) mod p        = {0}",yy.toHexString());
 
 			return yy;
 		}
 
 		public bool isOnCurve(CurvePoint p){
-			UInteger py2 = this.Fp.Fit(p.Y.Pow(2));
-			UInteger pcy2 = Y2(p.X);
+			Integer py2 = this.Fp.Fit(p.Y.Pow(2));
+			Integer pcy2 = Y2(p.X);
 
-			Console.WriteLine("CHECK A: {0}",py2.toHexString());
-			Console.WriteLine("CHECK B: {0}",pcy2.toHexString());
+			//Console.WriteLine("CHECK A: {0}",py2.toHexString());
+			//Console.WriteLine("CHECK B: {0}",pcy2.toHexString());
 
 			return (py2 == pcy2);
 		}
@@ -69,57 +69,39 @@ namespace Crypto.EC
 		{
 			if (((object)p1 == null) || ((object)p2 == null))
 			{
-				throw new ArgumentException("CurvePoints to be added must not be null");
+				throw new ArgumentException("SignedCurvePoints to be added must not be null");
 			}
 
 			if (p1.Curve != p2.Curve)
 			{
-				throw new ArgumentException("Curvepoints to be added must belong to the same curve!");
+				throw new ArgumentException("SignedCurvePoints to be added must belong to the same curve!");
 			}
 
-			if (p1 == p2)
-			{
-//				UInteger inv2y = Euclid.inverse(this.Fp.Fit(p1.Y << 1),this.Fp.FieldModulo);
-				UInteger inv2y = Euclid.inverse((p1.Y * 2),this.Fp.FieldModulo);
-				UInteger s = Fp.Fit(p1.X.Pow(3)) * 3;
-				s += p1.Curve.a;
-				s *= inv2y;
-
-					//(((p1.X.Pow(2) * 3) + p1.Curve.a) / (p1.Y << 1));
-
-				UInteger xR = (s.Pow(2) - (p1.X * 2));
-				UInteger yR = ((s * (p1.X - xR)) - p1.Y);
-
-				xR = this.Fp.Fit(xR);
-				yR = this.Fp.Fit(yR);
-
-				return new CurvePoint(p1.Curve, xR, yR);
+			if ((p1 != p2) && (p1.X == p2.X)){
+				return CurvePoint.INFINITY;
 			}
 
-			if (p1.X == p2.X)
-			{
-				throw new NotImplementedException("Eternity point not implemented");
-			}
-			else
-			{
-				UInteger s = (((p1.Y - p2.Y) / (p1.X - p2.X)));
-				UInteger xR = (s.Pow(2) - p1.X - p2.X);
-				UInteger yR = ((s * (p1.X - xR)) - p1.Y);
+			Integer lambda,divlambda;
 
-				xR = this.Fp.Fit(xR);
-				yR = this.Fp.Fit(yR);
-
-				return new CurvePoint(p1.Curve, xR, yR);
+			if (p1 == p2){
+				lambda = Fp.Fit(3 * p1.X.Pow(2) + a);
+				divlambda = Fp.Fit(2 * p1.Y);
+			} else {
+				lambda = Fp.Fit(p2.Y - p1.Y);
+				divlambda = Fp.Fit(p2.X - p1.X);
 			}
 
-			throw new NotImplementedException("Point addition not yet implemented");
+			lambda = lambda * Euclid.inverse(divlambda, Fp.FieldModulo);
+
+			Integer xR = (lambda.Pow(2) - p1.X - p2.X);
+			Integer yR = (lambda * (p1.X - xR)) - p1.Y;
+
+			xR = Fp.Fit(xR);
+			yR = Fp.Fit(yR);
+
+			return new CurvePoint(this, xR, yR);
 		}
 
-/*		public CurvePoint getPoint(T x){
-			x = new T(x, this.Fp);
-			return new CurvePoint(this,x,Y(x));
-		}
-*/
 		public override string ToString()
 		{
 			StringBuilder sb = new StringBuilder();
@@ -134,20 +116,20 @@ namespace Crypto.EC
 		}
 
 		public static EllipticCurve createSecp256k1(){
-			UInteger p = (UInteger.ONE << 256);
-			p -= UInteger.ONE;
-			p -= (UInteger.ONE << 32);
-			p -= (UInteger.ONE << 9);
-			p -= (UInteger.ONE << 8);
-			p -= (UInteger.ONE << 7);
-			p -= (UInteger.ONE << 6);
-			p -= (UInteger.ONE << 4);
+			Integer p = (Integer.ONE << 256);
+			p -= Integer.ONE;
+			p -= (Integer.ONE << 32);
+			p -= (Integer.ONE << 9);
+			p -= (Integer.ONE << 8);
+			p -= (Integer.ONE << 7);
+			p -= (Integer.ONE << 6);
+			p -= (Integer.ONE << 4);
 
-			UInteger xG = UInteger.fromHexString("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798");
-			UInteger yG = UInteger.fromHexString("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8");
+			Integer xG = Integer.fromHexString("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798");
+			Integer yG = Integer.fromHexString("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8");
 
-			UInteger n  = UInteger.fromHexString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141");
-			return new EllipticCurve(p, new UInteger(0), new UInteger(7), xG, yG, n, 1);
+			Integer n  = Integer.fromHexString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141");
+			return new EllipticCurve(p, new Integer(0), new Integer(7), xG, yG, n, 1);
 		}
 	}
 }
diff --git a/EC/ProjectiveCurvePoint.cs b/EC/ProjectiveCurvePoint.cs
new file mode 100644
index 0000000..160ffac
--- /dev/null
+++ b/EC/ProjectiveCurvePoint.cs
@@ -0,0 +1,198 @@
+using System;
+using BigInt;
+using System.CodeDom;
+using sharp.contracts;
+namespace Crypto.EC
+{
+	public class ProjectiveCurvePoint
+	{
+		public static readonly ProjectiveCurvePoint INFINITY = new ProjectiveCurvePoint(null,1,0,0);
+
+		public Integer X { get; set; }
+		public Integer Y { get; set; }
+		public Integer Z { get; set; }
+
+		public EllipticCurve Curve { get; private set; }
+
+		public ProjectiveCurvePoint(CurvePoint p)
+		{
+			this.Curve = p.Curve;
+			this.X = p.X;
+			this.Y = p.Y;
+			this.Z = 1;
+		}
+
+		public ProjectiveCurvePoint(EllipticCurve curve,Integer x,Integer y,Integer z)
+		{
+			this.Curve = curve;
+			this.X = x;
+			this.Y = y;
+			this.Z = z;
+		}
+
+		public CurvePoint toCurvePoint(){
+			if (Z.isZero()){
+				return CurvePoint.INFINITY;
+			}
+			Integer iz = Euclid.inverse(Z, Curve.Fp.FieldModulo);
+
+			Integer nx = Curve.Fp.Fit(X * iz);
+			Integer ny = Curve.Fp.Fit(Y * iz);
+
+			return new CurvePoint(Curve, nx, ny);
+		}
+
+		public override bool Equals(object obj)
+		{
+			ProjectiveCurvePoint p = INFINITY;
+
+			return new BooleanConditional()
+				.requires(obj != null)
+				.requires(GetType().IsInstanceOfType(obj))
+				.does( () => { p = (ProjectiveCurvePoint)obj; } )
+				.requires(this.Curve == p.Curve)
+				.requires(this.X == p.X)
+				.requires(this.Y == p.Y)
+				.requires(this.Z == p.Z)
+				.isSuccess();
+		}
+
+		public ProjectiveCurvePoint doubled()
+		{
+			Integer s = Curve.Fp.Fit(Y * Z);
+			Integer B = Curve.Fp.Fit(X * Y * s);
+			Integer w = Curve.Fp.Fit(
+				(Curve.a * Z.Pow(2)) +
+				(X.Pow(2) * 3)
+			);
+			Integer h = Curve.Fp.Fit(w.Pow(2) - (B * 8));
+
+			Integer xd = h * s * 2;
+			Integer yd = (
+				(w * ((B * 4) - h)) - 
+				(Y.Pow(2) * s.Pow(2) * 8)
+			);
+			Integer zd = s.Pow(3) * 8;
+
+			xd = Curve.Fp.Fit(xd);
+			yd = Curve.Fp.Fit(yd);
+			zd = Curve.Fp.Fit(zd);
+
+			return new ProjectiveCurvePoint(Curve,xd,yd,zd);
+		}
+
+		public ProjectiveCurvePoint add(ProjectiveCurvePoint p){
+			Integer u = Curve.Fp.Fit( (p.Y * Z) - (Y * p.Z) );
+			Integer v = Curve.Fp.Fit( (p.X * Z) - (X * p.Z) );
+			Integer A = Curve.Fp.Fit(
+				(Z * p.Z * u.Pow(2)) - v.Pow(3) - (v.Pow(2) * X * p.Z * 2)
+			);
+
+			Integer xd = v * A;
+			Integer yd = (
+				(u * ((X * p.Z * v.Pow(2)) - A)) -
+				(v.Pow(3) * Y * p.Z)
+			);
+			Integer zd = Z * p.Z * v.Pow(3);
+
+			xd = Curve.Fp.Fit(xd);
+			yd = Curve.Fp.Fit(yd);
+			zd = Curve.Fp.Fit(zd);
+
+			if (zd == 0){
+				return INFINITY;
+			}
+
+			return new ProjectiveCurvePoint(Curve, xd, yd, zd);
+		}
+
+		public ProjectiveCurvePoint Negated(){
+			return new ProjectiveCurvePoint(Curve, X, Curve.Fp.AdditiveInverse(Y), Z);
+		}
+			
+
+		public override string ToString()
+		{
+			return string.Format("[ProjectiveCurvePoint: Curve=... X={1} Y={2} Z={3}]", Curve,X,Y,Z);
+		}
+
+		public static implicit operator ProjectiveCurvePoint(CurvePoint p){
+			return new ProjectiveCurvePoint(p);
+		}
+
+		public static ProjectiveCurvePoint operator +(ProjectiveCurvePoint p1, ProjectiveCurvePoint p2)
+		{
+			if ((object)p1 == INFINITY){
+				return p2;
+			} else if ((object)p2 == INFINITY){
+				return p1;
+			} else if (p1.Equals(p2)){
+				return p1.doubled();
+			} else {
+				return p1.add(p2);
+			}
+		}
+		public static ProjectiveCurvePoint operator -(ProjectiveCurvePoint p1, ProjectiveCurvePoint p2)
+		{
+			if ((object)p1 == INFINITY)
+			{
+				return p2;
+			}
+			else if ((object)p2 == INFINITY)
+			{
+				return p1;
+			}			
+			return p1 + p2.Negated();
+		}
+		public static ProjectiveCurvePoint operator *(ProjectiveCurvePoint p1, Integer n)
+		{
+			if ((object)p1 == (object)INFINITY)
+			{
+				return INFINITY;
+			}
+
+			if (p1.Y == Integer.ZERO)
+			{
+				return INFINITY;
+			}
+
+			if (n.isZero())
+			{
+				throw new NotImplementedException("CurevPoint * 0");
+			}
+
+			ProjectiveCurvePoint result = null;
+			ProjectiveCurvePoint p = p1;
+
+			int i;
+			int bitwidth = n.Log2();
+
+			if (bitwidth < 0)
+			{
+				bitwidth = -bitwidth;
+			}
+
+			for (i = 0; i < bitwidth; i++)
+			{
+				if (n[i])
+					break;
+
+				p += p;
+			}
+
+			result = p;
+
+			for (i++; i <= bitwidth; i++)
+			{
+				p += p;
+				if (n[i])
+				{
+					result = p + result;
+				}
+			}
+
+			return result;
+		}
+
+	}
+}