A Novel Polynomial basis and Fast Fourier Transform for Finite Fields

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• Yunghsiang Han, Dongguan University of Technology, China
• Tuesday 23 July 2019, 11:00-12:00
• Room 503, EEE Department.

If you have a question about this talk, please contact Cong Ling.

Finding an n-point Fast Fourier Transform (FFT) algorithm over an arbitrary finite field with additive and multiplicative complexity O(n log(n)) has been a long standing open problem in the coding area. It has been known for a long time that a better FFT algorithm can improve the encoding and decoding complexity of Reed-Solomon (RS) codes, one of the most popular codes in the world. Even though an FFT algorithm over a complexity field with additive and multiplicative complexity O(n log(n)) was invented decades ago, it remains unknown whether such an algorithm exists over finite fields. In this talk, we present the first FFT algorithm over finite fields with additive and multiplicative complexity O(n log(n)). A new basis of polynomial over finite fields is invented and then apply it to the FFT over finite fields. The proposed polynomial basis allows that n-point FFT can be computed in O(n log(n)) finite field operations with extremely small leading constant. Based on this novel FFT algorithm, we then develop the encoding algorithms for the (n = 2r, k) Reed-Solomon codes. Thanks to the efficiency of transform based on the polynomial basis, the encoding can be completed in O(n log2(k)) or O(n log2(n−k) finite field operations. As the complexity of leading factor is small, the algorithms are advantageous in practical applications such as encoding/decoding of Reed-Solomon codes and polynomial multiplications in cryptography.

Biography: Yunghsiang S. Han received B.Sc. and M.Sc. degrees in electrical engineering from the National Tsing Hua University, Taiwan, in 1984 and 1986, respectively, and a Ph.D. degree from the School of Computer and Information Science, Syracuse University, NY, in 1993. He was with Hua Fan College of Humanities and Technology, National Chi Nan University, and National Taipei University, Taiwan. From August 2010 to January 2017, he was with the Department of Electrical Engineering at National Taiwan University of Science and Technology. Now he is with the School of Electrical Engineering & Intelligentization at Dongguan University of Technology, China. He is also a Chair Professor at National Taipei University from February 2015. Dr. Han’s research interests are in error-control coding, wireless networks, and security. Dr. Han has conducting state-of-the-art research in the area of decoding error-correcting codes for more than twenty years. He first developed a sequential-type algorithm based on Algorithm A* from artificial intelligence. At the time, this algorithm drew a lot of attention since it was the most efficient maximum-likelihood decoding algorithm for binary linear block codes. Dr. Han has also successfully applied coding theory in the area of wireless sensor networks. He has published several highly cited works on wireless sensor networks such as random key pre-distribution schemes. He also serves as the editors of several international journals. Dr. Han was the winner of the Syracuse University Doctoral Prize in 1994 and a Fellow of IEEE . One of his papers won the prestigious 2013 ACM CCS Test-of-Time Award in cybersecurity to recognize its significant impact on the security area over ten years.

This talk is part of the COMMSP Seminar series.

This talk is included in these lists:

• COMMSP & CP list
• COMMSP Seminar
• Room 503, EEE Department
• SAP Talks

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