Diminished-1 modulo 2n+1 squarer design

Squarers modulo M are useful design blocks for digital signal processors that internally use a residue number system and for implementing the exponentiators required in cryptographic algorithms. In these applications, some of the most commonly used moduli are those of the form 2ⁿ+1. To avoid using (n+1)-bit circuits, the diminished-1 number system can be effectively used in modulo 2ⁿ+1 arithmetic applications. In the paper, for the first time in the open literature, the authors formally derive modulo 2ⁿ+1 squarers that adopt the diminished-1 number system. The resulting implementations are built using only full-and half-adders and a final diminished-1 adder and can therefore be pipelined straightforwardly.