  We ask whether two or more images of arithmetic may inhabit the same space
via different encodings. The answers have significance for a class of processor
design that does all its computation in an encrypted form, without ever
performing any decryption or encryption itself. Against the possibility of
algebraic attacks against the arithmetic in a `crypto-processor' (KPU) we
propose a defence called `ABC encryption' and show how this kind of encryption
makes it impossible for observations of the arithmetic to be used by an
attacker to discover the actual values. We also show how to construct such
encrypted arithmetics.
