Scalar multiplication over higher degree rational point groups is often regarded as the bottleneck for faster pairing based cryptography. This paper has presented a skew Frobenius mapping technique in the sub-field isomorphic sextic twisted curve of Kachisa-Schaefer-Scott (KSS) pairing friendly curve of embedding degree 18 in the context of Ate based pairing. Utilizing the skew Frobenius map along with multi-scalar multiplication procedure, an efficient scalar multiplication method for KSS curve is proposed in the paper. In addition to the theoretic proposal, this paper has also presented a comparative simulation of the proposed approach with plain binary method, sliding window method and non-adjacent form (NAF) for scalar multiplication. The simulation shows that the proposed method is about 60 times faster than plain implementation of other compared methods.

The authors have proposed a multi-value sequence called an NTU sequence which is generated by a trace function and the Legendre symbol over a finite field. Most of the properties for NTU sequence such as period, linear complexity, autocorrelation, and cross-correlation have been theoretically shown in our previous work. However, the distribution of digit patterns, which is one of the most important features for security applications, has not been shown yet. In this paper, the distribution has been formulated with a theoretic proof by focusing on the number of 0's contained in the digit pattern.

Generalized Minimum Distance (GMD) decoding is a well-known soft-decision decoding for linear codes. Previous research on GMD decoding focused mainly on unquantized AWGN channels with BPSK signaling for binary linear codes. In this paper, a study on the design of a 4-level uniform quantizer for GMD decoding is given. In addition, an extended version of a GMD decoding algorithm for a 4-level quantizer is proposed, and the effectiveness of the proposed decoding is shown by simulation.