Design of Reversible Finite Field Arithmetic Circuits with Error Detection

Motivated by the potential of reversible computing, we present a systematic method for the designing reversible arithmetic circuits for finite field or Galois fields of form GF(2m). It is shown that an adder over GF(2m) can be designed with m garbage bits and that of a PB multiplier with 2m garbage bits. To tackle the problem of errors in computation, we also extend the circuit with error detection feature. Gate count and technology oriented cost metrics are used for evaluation. The expression for the upper bound for gate size is also derived for special primitive polynomials. Our technique, when compared with existing CAD tool gives the same gate size and quantum cost.