The optimal split method of large integer multiplication for smart low-end devices on P2P ubiquitous networks

Abstract

This paper proposes an optimal method for large integer multiplication when implementing modern cryptographic applications on Peer-to-Peer ubiquitous networks. P2P ubiquitous networks are usually composed of smart low-end devices, which operate on the limited battery power. To maximize the lifetime of P2P networks, the power consumption rate of each node must be quite careful, and an efficient and energy-saving large integer multiplication makes the cryptographic protocols possible to be executed on such nodes. The proposed method first recursively bisections multiplier and multiplicand in threshold times. Subsequently, classical multiplication calculates the products of the split multiplier and multiplicand blocks. Finally, the products of the blocks are gradually integrated to obtain the product of the large integers. This study demonstrates that the n-times recursive-balanced-2-way split method, where n is the floor of log2(0.13515 × s), obtains the optimal performance in multiplying two s-words based on classical multiplication. The experiment results show that modular exponentiation combined with other modular multiplication methods uses 1.28×–2.10× the computational cost required in the proposed method. The energy consumption of software is closely related to the execution time. The proposed scheme is an energy-saving method to maximize the lifetime of P2P ubiquitous networks when implementing security protocols in smart low-end devices on P2P networks. It is suitable for realizing robust security protocol on smart low-end devices, in which the framework is based on modular exponentiation and modular multiplication. Smart low-end devices based on the proposed method perform security protocols in satisfying the security recommendations of NIST.