Modular arithmetic using low order redundant bases

N-digit, radix-α bases are proposed for VLSI implementation of redundant arithmetic, mod m, where <α/sup N/> _m = ±1, <α/sup j/> _m≠±1, for 0 < j < N and m is prime. These bases simplify arithmetic overflow and are well suited to redundant arithmetic. The representations provide competitive, multiplierless T-point number theoretic transforms, mod m, where Tl N or Tl 2N.