An Efficient (n,k) Information Dispersal Algorithm Based on Fermat Number Transforms

• Published in: IEEE transactions on information forensics and security Vol. 8; no. 8; pp. 1371 - 1383
• Main Authors: LIN, Sian-Jheng, CHUNG, Wei-Ho
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Arithmetic; Coding, codes; Complexity theory; Computer information security; Computer science; control theory; systems; Computer systems performance. Reliability; Decoding; Digital; Encoding; Erasure codes; Exact sciences and technology; fast Fourier transforms; Galois fields; information dispersal algorithm (IDA); Information, signal and communications theory; Memory and file management (including protection and security); Memory organisation. Data processing; Polynomials; Reed-Solomon codes; Shadows; Signal and communications theory; Software; Telecommunications and information theory; Theoretical computing; Transforms; Vectors; Reed Solomon code; fast Fourier transforms; Fast Fourier transformation; Galois algebra; Shadow; Decoding; Galois fields; Distributed memory; Reed-Solomon codes; information dispersal algorithm (IDA); Coding; Algorithm complexity; Erasure codes; Error correcting code; Arithmetic operation; Fault tolerant system
• ISSN: 1556-6013; 1556-6021
• DOI: 10.1109/TIFS.2013.2270892

The (n,k) information dispersal algorithm (IDA) is a coding technique converting a digital source file into n small digital files (shadows), and the receipt of any k out of the n shadows can losslessly reconstruct the source file. This paper presents an encoding and two decoding algorithms of (n,k) IDA via the fast Fermat number transform (FNT). The proposed encoding algorithm requires O(nlog k) arithmetic operations, and the two decoding algorithms have complexities O(nlog k) and O(klog 2 k) for a reasonably large file. As compared with existing work, the proposed algorithms generate significant improvement in the throughput in the low code rate k/n ≤ 1/2 settings.