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/*******************************************************************************
* Copyright (c) 2017 Politecnico di Torino and others.
*
* All rights reserved. This program and the accompanying materials
* are made available under the terms of the Apache License, Version 2.0
* which accompanies this distribution, and is available at
* http://www.apache.org/licenses/LICENSE-2.0
*******************************************************************************/
package mcnet.components;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import com.microsoft.z3.BoolExpr;
import com.microsoft.z3.Constructor;
import com.microsoft.z3.Context;
import com.microsoft.z3.DatatypeExpr;
import com.microsoft.z3.DatatypeSort;
import com.microsoft.z3.EnumSort;
import com.microsoft.z3.Expr;
import com.microsoft.z3.FuncDecl;
import com.microsoft.z3.IntExpr;
import com.microsoft.z3.Solver;
import com.microsoft.z3.Sort;
import mcnet.netobjs.DumbNode;
/**
* Basic fields and other things required for model checking.
*
*/
public class NetContext extends Core{
List<BoolExpr> constraints;
List<Core> policies;
public HashMap<String,NetworkObject> nm; //list of nodes, callable by node name
public HashMap<String,DatatypeExpr> am; // list of addresses, callable by address name
public HashMap<String,FuncDecl> pf;
Context ctx;
public EnumSort node,address;
public FuncDecl src_port,dest_port,nodeHasAddr,addrToNode,send,recv;
public DatatypeSort packet;
/* Constants definition
- used in the packet proto field */
public final int HTTP_REQUEST = 1;
public final int HTTP_RESPONSE = 2;
public final int POP3_REQUEST = 3;
public final int POP3_RESPONSE = 4;
/**
* Context for all of the rest that follows. Every network needs one of these
* @param ctx
* @param args
*/
public NetContext(Context ctx,Object[]... args ){
super(ctx,args);
}
@Override
protected void init(Context ctx, Object[]... args) {
this.ctx = ctx;
nm = new HashMap<String,NetworkObject>(); //list of nodes, callable by node name
am = new HashMap<String,DatatypeExpr>(); // list of addresses, callable by address name
pf= new HashMap<String,FuncDecl>() ;
mkTypes((String[])args[0],(String[])args[1]);
constraints = new ArrayList<BoolExpr>();
policies = new ArrayList<Core>();
baseCondition();
}
/**
* A policy is a collection of shared algorithms or functions used by multiple components
* (for instance compression or DPI policies etc).
* @param policy
*/
public void AddPolicy (NetworkObject policy){
policies.add(policy);
}
@Override
protected void addConstraints(Solver solver) {
BoolExpr[] constr = new BoolExpr[constraints.size()];
solver.add(constraints.toArray(constr));
for (Core policy : policies){
policy.addConstraints(solver);
}
}
private void mkTypes (String[] nodes, String[] addresses){
//Nodes in a network
node = ctx.mkEnumSort("Node", nodes);
for(int i=0;i<node.getConsts().length;i++){
DatatypeExpr fd = (DatatypeExpr)node.getConst(i);
DumbNode dn =new DumbNode(ctx,new Object[]{fd});
nm.put(fd.toString(),dn);
}
//Addresses for this network
String[] new_addr = new String[addresses.length+1];
for(int k=0;k<addresses.length;k++)
new_addr[k] = addresses[k];
new_addr[new_addr.length-1] = "null";
address = ctx.mkEnumSort("Address", new_addr);
for(int i=0;i<address.getConsts().length;i++){
DatatypeExpr fd = (DatatypeExpr)address.getConst(i);
am.put(fd.toString(),fd);
}
// Type for packets, contains (some of these are currently represented as relations):
// - src: Source address
// - dest: Destination address
// - origin: Node where the data originated. (Node)
// - body: Packet contents. (Integer)
// - seq: Sequence number for packets. (Integer)
// - options: A representation for IP options. (Integer)
String[] fieldNames = new String[]{
"src","dest","inner_src","inner_dest","origin","orig_body","body","seq","proto","emailFrom","url","options","encrypted"};
Sort[] srt = new Sort[]{
address,address,address,address,node,ctx.mkIntSort(),ctx.mkIntSort(),ctx.mkIntSort(),
ctx.mkIntSort(),ctx.mkIntSort(),ctx.mkIntSort(),ctx.mkIntSort(),ctx.mkBoolSort()};
Constructor packetcon = ctx.mkConstructor("packet", "is_packet", fieldNames, srt, null);
packet = ctx.mkDatatypeSort("packet", new Constructor[] {packetcon});
for(int i=0;i<fieldNames.length;i++){
pf.put(fieldNames[i], packet.getAccessors()[0][i]); // pf to get packet's function declarations by name
}
src_port = ctx.mkFuncDecl("sport", packet, ctx.mkIntSort());
dest_port = ctx.mkFuncDecl("dport", packet, ctx.mkIntSort());
// Some commonly used relations
// nodeHasAddr: node -> address -> boolean
nodeHasAddr = ctx.mkFuncDecl("nodeHasAddr", new Sort[]{node, address},ctx.mkBoolSort());
// addrToNode: address -> node
addrToNode = ctx.mkFuncDecl("addrToNode", address, node);
// Send and receive both have the form:
// source-> destination -> packet-> int-> bool
// send: node -> node -> packet-> int-> bool
send = ctx.mkFuncDecl("send", new Sort[]{ node, node, packet, ctx.mkIntSort()},ctx.mkBoolSort());
// recv: node -> node -> packet-> int-> bool
recv = ctx.mkFuncDecl("recv", new Sort[]{ node, node, packet, ctx.mkIntSort()},ctx.mkBoolSort());
}
/**
* Set up base conditions for the network
*/
private void baseCondition(){
// Basic constraints for the overall model
Expr n_0 = ctx.mkConst("ctx_base_n_0", node);
Expr n_1 = ctx.mkConst("ctx_base_n_1", node);
Expr n_2 = ctx.mkConst("ctx_base_n_2", node);
Expr p_0 = ctx.mkConst("ctx_base_p_0", packet);
Expr p_1 = ctx.mkConst("ctx_base_p_1", packet);
IntExpr t_0 = ctx.mkIntConst("ctx_base_t_0");
IntExpr t_1 = ctx.mkIntConst("ctx_base_t_1");
// Constraint1 send(n_0, n_1, p_0, t_0) -> n_0 != n_1
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies((BoolExpr)send.apply(n_0, n_1, p_0, t_0),ctx.mkNot(ctx.mkEq( n_0, n_1))),1,null,null,null,null));
// Constraint2 recv(n_0, n_1, p_0, t_0) -> n_0 != n_1
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies((BoolExpr)recv.apply(n_0, n_1, p_0, t_0),ctx.mkNot(ctx.mkEq( n_0, n_1))),1,null,null,null,null));
// Constraint3 send(n_0, n_1, p_0, t_0) -> p_0.src != p_0.dest
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies((BoolExpr)send.apply(n_0, n_1, p_0, t_0),
ctx.mkNot(ctx.mkEq( pf.get("src").apply(p_0), pf.get("dest").apply(p_0)))),1,null,null,null,null));
// Constraint4 recv(n_0, n_1, p_0, t_0) -> p_0.src != p_0.dest
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies((BoolExpr)recv.apply(n_0, n_1, p_0, t_0),
ctx.mkNot(ctx.mkEq(pf.get("src").apply(p_0),pf.get("dest").apply(p_0)))),1,null,null,null,null));
// Constraint5 recv(n_0, n_1, p, t_0) -> send(n_0, n_1, p, t_1) && t_1 < t_0
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies((BoolExpr)recv.apply(n_0, n_1, p_0, t_0),
ctx.mkExists(new Expr[]{t_1},
ctx.mkAnd((BoolExpr)send.apply(n_0, n_1, p_0, t_1),
ctx.mkLt(t_1, t_0)),1,null,null,null,null)),1,null,null,null,null));
// Constraint6 send(n_0, n_1, p, t_0) -> p.src_port > 0 && p.dest_port < MAX_PORT
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies((BoolExpr)send.apply(n_0, n_1, p_0, t_0),
ctx.mkAnd( ctx.mkGe((IntExpr)src_port.apply(p_0),(IntExpr)ctx.mkInt(0)),
ctx.mkLt((IntExpr)src_port.apply(p_0),(IntExpr) ctx.mkInt(MAX_PORT)))),1,null,null,null,null));
// Constraint7 recv(n_0, n_1, p, t_0) -> p.src_port > 0 && p.dest_port < MAX_PORT
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies((BoolExpr)recv.apply(n_0, n_1, p_0, t_0),
ctx.mkAnd( ctx.mkGe((IntExpr)dest_port.apply(p_0),(IntExpr)ctx.mkInt(0)),
ctx.mkLt((IntExpr)dest_port.apply(p_0),(IntExpr) ctx.mkInt(MAX_PORT)))),1,null,null,null,null));
// Constraint8 recv(n_0, n_1, p_0, t_0) -> t_0 > 0
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies((BoolExpr)recv.apply(n_0, n_1, p_0, t_0),
ctx.mkGt(t_0,ctx.mkInt(0))),1,null,null,null,null));
// Constraint9 send(n_0, n_1, p_0, t_0) -> t_0 > 0
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies((BoolExpr)send.apply(n_0, n_1, p_0, t_0),
ctx.mkGt(t_0,ctx.mkInt(0))),1,null,null,null,null));
// Extra constriants for supporting the VPN gateway
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies(
ctx.mkAnd((BoolExpr)send.apply(n_0, n_1, p_0, t_0),
ctx.mkNot(ctx.mkEq(this.pf.get("inner_src").apply(p_0), this.am.get("null")))),
ctx.mkNot(ctx.mkEq(this.pf.get("inner_src").apply(p_0), this.pf.get("inner_dest").apply(p_0)))),1,null,null,null,null));
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies(
ctx.mkAnd((BoolExpr)send.apply(n_0, n_1, p_0, t_0),
ctx.mkEq(this.pf.get("inner_src").apply(p_0), this.am.get("null"))),
ctx.mkEq(this.pf.get("inner_src").apply(p_0), this.pf.get("inner_dest").apply(p_0))),1,null,null,null,null));
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies(
ctx.mkAnd((BoolExpr)send.apply(n_0, n_1, p_0, t_0),
ctx.mkEq(this.pf.get("inner_dest").apply(p_0), this.am.get("null"))),
ctx.mkEq(this.pf.get("inner_src").apply(p_0), this.pf.get("inner_dest").apply(p_0))),1,null,null,null,null));
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies(
ctx.mkAnd((BoolExpr)recv.apply(n_0, n_1, p_0, t_0),
ctx.mkNot(ctx.mkEq(this.pf.get("inner_src").apply(p_0), this.am.get("null")))),
ctx.mkNot(ctx.mkEq(this.pf.get("inner_src").apply(p_0), this.pf.get("inner_dest").apply(p_0)))),1,null,null,null,null));
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies(
ctx.mkAnd((BoolExpr)recv.apply(n_0, n_1, p_0, t_0),
ctx.mkEq(this.pf.get("inner_src").apply(p_0), this.am.get("null"))),
ctx.mkEq(this.pf.get("inner_src").apply(p_0), this.pf.get("inner_dest").apply(p_0))),1,null,null,null,null));
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0},
ctx.mkImplies(
ctx.mkAnd((BoolExpr)recv.apply(n_0, n_1, p_0, t_0),
ctx.mkEq(this.pf.get("inner_dest").apply(p_0), this.am.get("null"))),
ctx.mkEq(this.pf.get("inner_src").apply(p_0), this.pf.get("inner_dest").apply(p_0))),1,null,null,null,null));
constraints.add(
ctx.mkForall(new Expr[]{n_0, n_1, p_0, t_0, n_2, p_1, t_1},
ctx.mkImplies(
ctx.mkAnd(
ctx.mkLt(t_1, t_0),
(BoolExpr)send.apply(n_0, n_1, p_0, t_0),
(BoolExpr)this.pf.get("encrypted").apply(p_1),
(BoolExpr)recv.apply(n_2, n_0, p_1, t_1),
(BoolExpr)this.pf.get("encrypted").apply(p_0)),
ctx.mkAnd(
ctx.mkEq(this.pf.get("inner_src").apply(p_1), this.pf.get("inner_src").apply(p_0)),
ctx.mkEq(this.pf.get("inner_dest").apply(p_1), this.pf.get("inner_dest").apply(p_0)),
ctx.mkEq(this.pf.get("origin").apply(p_1), this.pf.get("origin").apply(p_0)),
ctx.mkEq(this.pf.get("orig_body").apply(p_1), this.pf.get("orig_body").apply(p_0)),
ctx.mkEq(this.pf.get("body").apply(p_1), this.pf.get("body").apply(p_0)),
ctx.mkEq(this.pf.get("seq").apply(p_1), this.pf.get("seq").apply(p_0)),
ctx.mkEq(this.pf.get("proto").apply(p_1), this.pf.get("proto").apply(p_0)),
ctx.mkEq(this.pf.get("emailFrom").apply(p_1), this.pf.get("emailFrom").apply(p_0)),
ctx.mkEq(this.pf.get("url").apply(p_1), this.pf.get("url").apply(p_0)),
ctx.mkEq(this.pf.get("options").apply(p_1), this.pf.get("options").apply(p_0)))),1,null,null,null,null)
);
}
/**
* Two packets have equal headers
* @param p1
* @param p2
* @return
*/
public BoolExpr PacketsHeadersEqual(Expr p1, Expr p2){
return ctx.mkAnd(new BoolExpr[]{
ctx.mkEq(pf.get("src").apply(p1), pf.get("src").apply(p2)),
ctx.mkEq(pf.get("dest").apply(p1), pf.get("dest").apply(p2)),
ctx.mkEq(pf.get("origin").apply(p1), pf.get("origin").apply(p2)),
ctx.mkEq(pf.get("seq").apply(p1), pf.get("seq").apply(p2)),
ctx.mkEq(src_port.apply(p1), src_port.apply(p2)),
ctx.mkEq(dest_port.apply(p1), dest_port.apply(p2)),
ctx.mkEq(pf.get("options").apply(p1), pf.get("options").apply(p2))});
}
/**
* Two packets have equal bodies
* @param p1
* @param p2
* @return
*/
public BoolExpr PacketContentEqual(Expr p1, Expr p2){
return ctx.mkEq(pf.get("body").apply(p1), pf.get("body").apply(p2));
}
/* seems to be useless
*
public Function failurePredicate (NetContext context)
{
return (NetworkObject node) -> ctx.mkNot(context.failed (node.z3Node));
}*/
public BoolExpr destAddrPredicate (Expr p, DatatypeExpr address){
return ctx.mkEq(pf.get("dest").apply(p),address);
}
public BoolExpr srcAddrPredicate (Expr p, DatatypeExpr address){
return ctx.mkEq(pf.get("src").apply(p),address);
}
}
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