In this paper, the authors apply two modular exponentiation algorithms such as left-to-right binary method and Montgomery powering ladder algorithm on Raspberry Pi and evaluate their security against Side-channel attack.

The security of Internet of Things (IoT) devices is one of the most important problems to be addressed by the cryptographers and security engineers. The processing ability of IoT devices is limited, therefore light-weight and secure cryptographic tools are necessary for security of them. This paper shows the implementation of 256-bit Elliptic Curve Cryptography (ECC) on an 8-bit microcontroller. The proposed implementation applies towering technique for extension field of degree 32 with a certain 8-bit prime characteristic instead of the 256-bit prime characteristic. It enables to execute 256-bit ECC operations without complicated multiple-precision arithmetic on small computers like 8-bit microcontrollers. This approach efficiently realizes the scalability of the ECC encryption strength. In addition, the authors use a twisted Montgomery curve with a Montgomery ladder technique which enables fast calculations without inversions referring to Curve25519. It is considered resistant to the Side Channel Attack (SCA) since it applies the Montgomery ladder technique for scalar multiplication (SCM). This ECC implementation on Arduino UNO, an 8-bit microcontroller board, can be utilized for a key agreement protocol among IoT devices.

Pairing based cryptography is considered as the next generation of security for which it attracts many researcher to work on faster and efficient pairing to make it practical. Among the several challenges of efficient pairing; efficient scalar multiplication of rational point defined over extension field of degree k ≥ 12 is important. However, there exists isomorphic rational point group defined over relatively lower degree extension field. Exploiting such property, this paper has showed a mapping technique between isomorphic rational point groups in the context of Ate-based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curve of embedding degree k = 18. In the case of KSS curve, there exists sub-field sextic twisted curve that includes sextic twisted isomorphic rational point group defined over F_p3. This paper has showed the mapping procedure from certain F_p18 rational point group to its sub-field isomorphic rational point group in F_p3 and vice versa. This paper has also showed that scalar multiplication is about 20 times faster after applying the proposed mapping which in-turns resembles that the impact of this mapping will greatly enhance the pairing operation in KSS curve.