Number theoretic transforms with modulus 22q- 2q+ 1

Number theoretic transforms using the modulus , which require no multiplications, are introduced. These transforms have 50% greater sequence lengths for a given wordlength than Fermat transforms, and there is greater flexibility in the choice of wordlength. Furthermore, arithmetic modulo is not significantly more complex than arithmetic modulo a Fermat number. Complex number theoretic transforms using these moduli are also discussed and techniques for using them to convolve real data are described.