Today we continue to read up on security zones. A security zone is nothing more than a network segment with protected ingress. We said that the external facing security zones are typically prevented from talking to one another. Each is a separate VLAN and no routing is allowed between them. These edge switches typically trunk to an L2 aggregation switch. Aggregating external traffic allows implementation of single point packet, session and network behaviour monitoring. The L2 switch trunks to a L3 Q Switch. An Intrusion Prevention system may be placed on this trunk. Q Switches provide dynamic port configuration.  This allows  a switch to configure port as an access port or a trunk port.They dynamic trunking protocol automatically creates trunk port between Q switches. A DTP can be compromised if the there are two VLAN tags in the packet. This concept is similar to VPN. When an attacker sends a packet with two VLAN tags, the first Q-switch strips the packet one tag and send it out to the other switch which treats it as a regular packet and forwards to all appropriate ports. The double tagging must be disabled to mitigate this. This is also another reason why don't have the edge switches talk to one another.  A private VLAN extends this restriction further by configuring the ports in a way where none of the ports in the VLAN set can communicate with each other. For example, database servers are put in a private VLAN because they don't need to communicate with each other. Finally access is only one of the instruments for control. ACLs, separation of duties, least privilege and need to know are all applied to improve security.
Some examples of securing packet traffic with advanced techniques can be seen as in the case of IP Packet security with IPSEC protocols that authenticate and encrypt IP Packets. The IPSEC protocol uses the concept of security association in order to secure the IP. A security association is a bundle of algorithms and parameters (such as keys) that is used to authenticate and encrypt a particular flow in one direction. A flow is usually denoted as a five tuple <src address, src port, destination address, destination port, protocol> While TLS and SSH operate in the upper layers of the Application which involve data and transport, only IPSec works on Internet layer. The link layer is secured by 802.1x, Point to Point protocols PPP and Point to Point Tunneling protocols.

Is Partitioning a good idea ?
In computing industry, there is a widespread understanding that partitioning is best done only when it is absolutely necessary. In other words we don't involve any partitioning of resources because such planning doesn't always scale to future needs and often is more binding with lot more work to undo if business needs change.
take ulimits for example and almost everyone will understand it is more onerous than it does good. Some operating systems do not provide this option.
Take disk partitioning and we only find ourselves shooting in the foot when we partition up front and discover that we have improperly managed resources.  A large unfragmented disk does not cause such symptoms.
Even Solaris introduced partitions for different flavors and soon applications would start failing in one partition because they didn't have enough resources on this as they earlier had on the undivided host.
Quotas often cause resource starvation and non-deterministic behavior of otherwise sound applications. Soft limits complicate the matter even further.
Containers are useful when they are elastic.

#coding exercise
Write a function that takes two parameters n and k and returns the binomial coefficient C(n, k)
int C(int n, int k)
{
if ( k == 0 || k == n) return 1;
return C(n-1,k-1) + C(n-1,k);
}

Given a boolean expression with the following symbols
'T' - true
'F' - false and logical operators
& - AND
| - OR
^  - XOR
Count the number of ways we can paranthesize the expression so that the value remains true.
We have to do this operator by operator basis:
Let T(i,j) represent the number of ways to paranthesize the symbols between i and j ( such that the subexpression between i and j evaluates to true
Let F(i,j) represent the number of ways to paranthesize the symbols between i and j ( both inclusive) such that the subexpression between i and j evaluates to false.

Total(i,j) = T(i,j) + F(i,j)
T(i,j) = sum k from I to j-1 [ T (i,k) × T (k+1,j)  for the AND operation
Total(i,k) x Total (k+1,j) - F (i,k) × F (k+1, j) for the OR operation
T (i,k) × F (k+1, j)  + F (i,k) x T (k+1, j) for the XOR operation



The reverse holds for F(i,j)