Biblio

Pairing is carried out by two steps, Miller loop and final exponentiation. In this manuscript, the authors propose an efficient Miller loop for a pairing on the FK12 curve. A Hamming weight and bit-length of loop parameter have a great effect on the computational cost of Miller loop. Optimal-ate pairing is used as the most efficient pairing on the FK12 curve currently. The loop parameter of optimal-ate pairing is 6z+2 where z is the integer to make the FK12 curve parameter. Our method uses z which has a shorter bit-length than the previous optimal-ate pairing as the loop parameter. Usually, z has a low Hamming weight to make final exponentiation efficient. Therefore, the loop parameter in our method has a lower Hamming weight than the loop parameter of the previous one in many cases. The authors evaluate our method by the number of multiplications and execution time. As a result, the proposed algorithm leads to the 3.71% reduction in the number of multiplications and the 3.38% reduction in the execution time.

Embedded electronic devices and sensors such as smartphones, smart watches, medical implants, and Wireless Sensor Nodes (WSN) are making the “Internet of Things” (IoT) a reality. Such devices often require cryptographic services such as authentication, integrity and non-repudiation, which are provided by Public-Key Cryptography (PKC). As these devices are severely resource-constrained, choosing a suitable cryptographic system is challenging. Pairing Based Cryptography (PBC) is among the best candidates to implement PKC in lightweight devices. In this research, we present a fast and energy efficient implementation of PBC based on Barreto-Naehrig (BN) curves and optimal Ate pairing using hardware/software co-design. Our solution consists of a hardware-based Montgomery multiplier, and pairing software running on an ARM Cortex A9 processor in a Zynq-7020 System-on-Chip (SoC). The multiplier is protected against simple power analysis (SPA) and differential power analysis (DPA), and can be instantiated with a variable number of processing elements (PE). Our solution improves performance (in terms of latency) over an open-source software PBC implementation by factors of 2.34 and 2.02, for 256- and 160-bit field sizes, respectively, as measured in the Zynq-7020 SoC.

Recently, various certificate-less signature (CLS) schemes have been developed using bilinear pairing to provide authenticity of message. In 2015, Jia-Lun Tsai proposed a certificate-less pairing based short signature scheme using elliptic curve cryptography (ECC) and prove its security under random oracle. However, it is shown that the scheme is inappropriate for its practical use as there is no message-signature dependency present during signature generation and verification. Thus, the scheme is vulnerable. To overcome these attacks, this paper aims to present a variant of Jia-Lun Tsai's short signature scheme. Our scheme is secured under the hardness of collusion attack algorithm with k traitors (k–-CAA). The performance analysis demonstrates that proposed scheme is efficient than other related signature schemes.