Efficient modulo 2 n ±1 squarers

Modulo 2 n ±1 squarers are useful components for designing special purpose digital signal processors that internally use a residue number system and for implementing the modulo exponentiators and multiplicative inverses required in cryptographic algorithms. In this paper we propose, in a unified way, architectures for their design that are based on the radix-4 modified Booth encoding. For the modulo 2 n +1 case, both the normal and the diminished-one representations are considered. Experimental results show that the proposed squarers offer significant savings in the implementation area over previous proposals that can reach up to 38% for sufficiently large operand widths, while in many cases a small improvement in execution delay can also be achieved.