Ignoring the philosophical and export issues, I'd suggest that you'd be better off encrypting the data in the table directly.
You need to obfuscate the decryption key(s) in your code. Typically, this means breaking them into pieces and encoding the strings in hex and using functions to assemble the pieces of the key together.
For the algorithm, I'd use a trusted implementation of AES for whatever language you're using.
Maybe this one for C#:
http://msdn.microsoft.com/en-us/magazine/cc164055.aspx
Finally, you need to be aware of the limitations of the approach. Namely, the decryption key is a weak link, it will be available in memory at run-time in clear text. (At a minimum) It has to be so that you can use it. The implementation of your encryption scheme is another weakness--any flaws there are flaws in your code too. As several other people have pointed out your client-server communications are suspect too.
You should remember that your executable can be examined in a hex editor where cleartext strings will leap out of the random junk that is your compiled code. And that many languages (like C# for example) can be reverse-compiled and all that will be missing are the comments.
All that said, encrypting your data will raise the bar for cheating a bit. How much depends on how careful you are; but even so a determined adversary will still break your encryption and cheat. Furthermore, they will probably write a tool to make it easy if your game is popular; leaving you with an arms-race scenario at that point.
Regarding a checksum value, you can compute a checksum based on the sum of the values in a row assuming that you have enough numeric values in your database to do so. Or, for an bunch of boolean values you can store them in a varbinary field and use the bitwise exclusive operator ^ to compare them--you should end up with 0s.
For example,
for numeric columns,
2|3|5|7| with a checksum column | 17 |
for booleans,
0|1|0|1| with a checksum column | 0101 |
If you do this, you can even add a summary row at the end that sums your checksums. Although this can be problematic if you are constantly adding new records. You can also convert strings to their ANSI/UNICODE components and sum these too.
Then when you want to check the checksum simple do a select like so:
Select *
FROM OrigTable
right outer join
(select pk, (col1 + col2 + col3) as OnTheFlyChecksum, PreComputedChecksum from OrigTable) OT on OrigTable.pk = OT.pk
where OT.OnTheFlyChecksum = OT.PreComputedChecksum