M-ary parallel modular exponentiation: Software vs. hardware

Most of cryptographic systems are based on modular exponentiation. It is performed using successive modular multiplications. One way of improving the throughput of a cryptographic system implementation is reducing the number of the required modular multiplications. Existing methods attempt to reduce this number by partitioning the exponent in constant or variable size windows. In this paper, in the purpose of further accelerating the computation of modular exponentiation, a concurrent novel approach is proposed along with the corresponding software and hardware implementations.