A New Fast Modular Arithmetic Method in Public Key Cryptography

Modular arithmetic is a fundamental operation and plays an important role in public key cryptosystem. A new method and its theory evidence on the basis of modular arithmetic with large integer modulus-changeable modulus algorithm is proposed to improve the speed of the modular arithmetic in the presented paper. For changeable modulus algorithm, when modular computation of modulo n is difficult, it can be realized by computation of modulo n-1 and n-2 on the perquisite of easy modular computations of modulo n-1 and modulo n-2. The conclusion is that the new method is better than the direct method by computing the modular arithmetic operation with large modulus. Especially, when computations of modulo n-1 and modulo n-2 are easy and computation of modulo n is difficult, this new method will be faster and has more advantages than other algorithms on modular arithmetic. Lastly, it is suggested that the proposed method be applied in public key cryptography based on modular multiplication and modular exponentiation with large integer modulus effectively

Secure and Energy Efficient Design of Multi-Modular Exponential Techniques for Public-Key Cryptosystem

The present paper proposes a secure design of the energy-efficient multi-modular exponential techniques that use store and reward method and store and forward method.Computation of the multi-modular exponentiation can be performed by three novel algorithms:store and reward,store and forward 1-bit(SFW1),and store and forward 2-bit(SFW2).Hardware realizations of the proposed algorithms are analyzed in terms of throughput and energy.The experimental results show the proposed algorithms SFW1 and SFW2 increase the throughput by orders of 3.98% and 4.82%,reducing the power by 5.32% and 6.15% and saving the energy in the order of 3.95% and 4.75%,respectively.The proposed techniques can prevent possible side-channel attacks and timing attacks as a consequence of an inbuilt confusion mechanism.Xilinx Vivado-21 on Virtex-7 evaluation board and integrated computer application for recognizing user services(ICARUS)Verilog simulation and synthesis tools are used for field programmable gate array(FPGA)for hardware realization.The hardware compatibility of proposed algorithms has also been checked using Cadence for application specific integrated circuit(ASIC).