With Radio Frequency Identification (RFID) tags posed to replaced Universal Product Codes, serious security and information privacy issues have arisen. Attempts have been made to provide a means of authentication between tags and readers, and simultaneously meet computing and memory specifications for the lowest ranges of RFID tags. This talk will discuss a proposed mutual authentication scheme that requires 32 bits of read/write memory, 62 bits of read-only memory and can be deployed using as few as 224 logic gates. We also propose a stream cipher with the same memory

constraints and magnitude of logic gates. The underlying idea behind these schemes is a notion that we call the abstractions of integer arithmetic.