Is Norton Security available in 32-bit and 64-bit versions?
No. Norton security is available only as a 32-bit application. Although, it does have 32-bit and 64-bit drivers depending upon the operating system platform it is installed on. But currently, Symantec's developers are only creating x64 binaries of required, for the rest they use x86 binaries. The reason behind this is that there is no advantage of using x64 binaries when x86 binaries works well. The application which benefits from x64 are the applications with more than 3GB memory utilization requirements and the apps like Norton security and Norton Security Backup) are not included in this category.
Norton Security will have to carry both versions of required DLLs in order to support both 32-bit and 64-bit environments.