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As I mentioned in 5, ICMP traffic is not stateful by default on the appliances ICMP messages by default are permitted when traveling from a higher-security-level interface to a lower-level one However, ICMP traffic is denied by default from a lowersecurity-level interface to a higher-level one, even if it is an ICMP message response to a user s ICMP query Typically you should allow the following ICMP message types into your network to help provide some basic management and troubleshooting abilities for your internal devices: echo reply, source quench, unreachable, and time exceeded For external devices to test connectivity to your network, you might also want to permit the ICMP echo message, but I would definitely restrict what ICMP messages Internet users can generate and what destinations in your network can receive these messages To allow ICMP traffic to travel from a lower-level to a higher-level interface, you need to enable one of two things: Stateful processing of ICMP An ACL entry or entries for the ICMP messages

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functional dependencies If we are to check updates ef ciently, we should design relational-database schemas that allow update validation without the computation of joins To decide whether joins must be computed to check an update, we need to determine what functional dependencies can be tested by checking each relation individually Let F be a set of functional dependencies on a schema R, and let R1 , R2 , , Rn be a decomposition of R The restriction of F to Ri is the set Fi of all functional dependencies in F + that include only attributes of Ri Since all functional dependencies in a restriction involve attributes of only one relation schema, it is possible to test such a dependency for satisfaction by checking only one relation Note that the de nition of restriction uses all dependencies in F + , not just those in F For instance, suppose F = {A B, B C}, and we have a decomposition into AC and AB The restriction of F to AC is then A C, since A C is in F + , even though it is not in F The set of restrictions F1 , F2 , , Fn is the set of dependencies that can be checked ef ciently We now must ask whether testing only the restrictions is suf cient Let F = F1 F2 Fn F is a set of functional dependencies on schema R, but, in general, F = F However, even if F = F , it may be that F + = F + If the latter is true, then every dependency in F is logically implied by F , and, if we verify that F is satis ed, we have veri ed that F is satis ed We say that a decomposition having the property F + = F + is a dependency-preserving decomposition Figure 712 shows an algorithm for testing dependency preservation The input is a set D = {R1 , R2 , , Rn } of decomposed relation schemas, and a set F of functional dependencies This algorithm is expensive since it requires computation of F + ; we will describe another algorithm that is more ef cient after giving an example of testing for dependency preservation We can now show that our decomposition of Lending-schema is dependency preserving Instead of applying the algorithm of Figure 712, we consider an easier alternative: We consider each member of the set F of functional dependencies that we compute F + ; for each schema Ri in D do begin Fi : = the restriction of F + to Ri ; end F := for each restriction Fi do begin F = F Fi end compute F + ; if (F + = F + ) then return (true) else return (false); Figure 712 Testing for dependency preservation.

NOTE If address translation is required, you also need a matching translation policy for the ICMP traffic Starting in version 70 of the OS, you can enable stateful processing of ICMP traffic using the Cisco Modular Policy Framework (MPF), discussed in s 10 and 11 However, as you will see in these chapters, enabling stateful processing of ICMP traffic has its own set of problems And stateful processing of ICMP is only new as of version 70 of the appliances; in prior versions, you had to use the second option: ACLs I ll use the network shown previously in Figure 6-3 to illustrate what an ACL to allow returning ICMP traffic to your users would look like I ll build upon the Listing 6-7 example that I covered in the previous section Here s an example of the configuration to allow returning ICMP traffic:

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