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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 257904, 16 pages
Research Article

Pseudorandom Bit Sequence Generator for Stream Cipher Based on Elliptic Curves

Department of Electronics and Communication Engineering, National Institute of Technology, Calicut, Kerala 673 601, India

Received 1 April 2015; Revised 17 August 2015; Accepted 24 August 2015

Academic Editor: David Bigaud

Copyright © 2015 Jilna Payingat and Deepthi P. Pattathil. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a pseudorandom sequence generator for stream ciphers based on elliptic curves (EC). A detailed analysis of various EC based random number generators available in the literature is done and a new method is proposed such that it addresses the drawbacks of these schemes. Statistical analysis of the proposed method is carried out using the NIST (National Institute of Standards and Technology) test suite and it is seen that the sequence exhibits good randomness properties. The linear complexity analysis shows that the system has a linear complexity equal to the period of the sequence which is highly desirable. The statistical complexity and security against known plain text attack are also analysed. A comparison of the proposed method with other EC based schemes is done in terms of throughput, periodicity, and security, and the proposed method outperforms the methods in the literature. For resource constrained applications where a highly secure key exchange is essential, the proposed method provides a good option for encryption by time sharing the point multiplication unit for EC based key exchange. The algorithm and architecture for implementation are developed in such a way that the hardware consumed in addition to point multiplication unit is much less.