A unified signed-digit adder for high-radix modular exponentiation on GF(p) and GF(2p)

Addition on GF(p) and GF(2p) differs only in terms of the propagation of the carry. The unification of carry propagation and carry-less operations can provide higher performance using less hardware resources. Modular multiplication is a basic kernel computation for RSA and ECC, which is realized using repeated additions. Modular exponentiation, which uses modular multiplication, requires high radix values so as to provide the necessary security level for modern secure applications. The proposed arithmetic unit can support high radix modular exponentiation on both fields using a signed-digit number adder, which provides a balance between carry propagation and carry-less operations. The proposed design is optimized for Xilinx Virtex 5 devices.