Efficiency of two decoders based on hash techniques and syndrome calculation over a Rayleigh channel

The explosive growth of connected devices demands high quality and reliability in data transmission and storage. Error correction codes (ECCs) contribute to this in ways that are not very apparent to the end user, yet indispensable and effective at the most basic level of transmission. This paper presents an investigation of the performance and analysis of two decoders that are based on hash techniques and syndrome calculation over a Rayleigh channel. These decoders under study consist of two main features: a reduced complexity compared to other competitors and good error correction performance over an additive white gaussian noise (AWGN) channel. When applied to decode some linear block codes such as Bose, Ray-Chaudhuri, and Hocquenghem (BCH) and quadratic residue (QR) codes over a Rayleigh channel, the experiment and comparison results of these decoders have shown their efficiency in terms of guaranteed performance measured in bit error rate (BER). For example, the coding gain obtained by syndrome decoding and hash techniques (SDHT) when it is applied to decode BCH (31, 11, 11) equals 34.5 dB, i.e., a reduction rate of 75% compared to the case where the exchange is carried out without coding and decoding process

An efficient combination between Berlekamp-Massey and Hartmann Rudolph algorithms to decode BCH codes

In digital communication and storage systems, the exchange of data is achieved using a communication channel which is not completely reliable. Therefore, detection and correction of possible errors are required by adding redundant bits to information data. Several algebraic and heuristic decoders were designed to detect and correct errors. The Hartmann Rudolph (HR) algorithm enables to decode a sequence symbol by symbol. The HR algorithm has a high complexity, that's why we suggest using it partially with the algebraic hard decision decoder Berlekamp-Massey (BM). In this work, we propose a concatenation of Partial Hartmann Rudolph (PHR) algorithm and Berlekamp-Massey decoder to decode BCH (Bose-Chaudhuri-Hocquenghem) codes. Very satisfying results are obtained. For example, we have used only 0.54% of the dual space size for the BCH code (63,39,9) while maintaining very good decoding quality. To judge our results, we compare them with other decoders

Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications

Coding; Communications; Engineering; Networks; Information Theory; Algorithm

Some Applications of Coding Theory in Cryptography

viii+80hlm.;24c

THRIVE: Threshold Homomorphic encryption based secure and privacy preserving bIometric VErification system

In this paper, we propose a new biometric verification and template protection system which we call the THRIVE system. The system includes novel enrollment and authentication protocols based on threshold homomorphic cryptosystem where the private key is shared between a user and the verifier. In the THRIVE system, only encrypted binary biometric templates are stored in the database and verification is performed via homomorphically randomized templates, thus, original templates are never revealed during the authentication stage. The THRIVE system is designed for the malicious model where the cheating party may arbitrarily deviate from the protocol specification. Since threshold homomorphic encryption scheme is used, a malicious database owner cannot perform decryption on encrypted templates of the users in the database. Therefore, security of the THRIVE system is enhanced using a two-factor authentication scheme involving the user's private key and the biometric data. We prove security and privacy preservation capability of the proposed system in the simulation-based model with no assumption. The proposed system is suitable for applications where the user does not want to reveal her biometrics to the verifier in plain form but she needs to proof her physical presence by using biometrics. The system can be used with any biometric modality and biometric feature extraction scheme whose output templates can be binarized. The overall connection time for the proposed THRIVE system is estimated to be 336 ms on average for 256-bit biohash vectors on a desktop PC running with quad-core 3.2 GHz CPUs at 10 Mbit/s up/down link connection speed. Consequently, the proposed system can be efficiently used in real life applications

Cryptanalysis of McEliece Cryptosystem Based on Algebraic Geometry Codes and their subcodes

We give polynomial time attacks on the McEliece public key cryptosystem based either on algebraic geometry (AG) codes or on small codimensional subcodes of AG codes. These attacks consist in the blind reconstruction either of an Error Correcting Pair (ECP), or an Error Correcting Array (ECA) from the single data of an arbitrary generator matrix of a code. An ECP provides a decoding algorithm that corrects up to $\frac{d^*-1-g}{2}$ errors, where $d^*$ denotes the designed distance and $g$ denotes the genus of the corresponding curve, while with an ECA the decoding algorithm corrects up to $\frac{d^*-1}{2}$ errors. Roughly speaking, for a public code of length $n$ over $\mathbb F_q$, these attacks run in $O(n^4\log (n))$ operations in $\mathbb F_q$ for the reconstruction of an ECP and $O(n^5)$ operations for the reconstruction of an ECA. A probabilistic shortcut allows to reduce the complexities respectively to $O(n^{3+\varepsilon} \log (n))$ and $O(n^{4+\varepsilon})$. Compared to the previous known attack due to Faure and Minder, our attack is efficient on codes from curves of arbitrary genus. Furthermore, we investigate how far these methods apply to subcodes of AG codes.Comment: A part of the material of this article has been published at the conferences ISIT 2014 with title "A polynomial time attack against AG code based PKC" and 4ICMCTA with title "Crypt. of PKC that use subcodes of AG codes". This long version includes detailed proofs and new results: the proceedings articles only considered the reconstruction of ECP while we discuss here the reconstruction of EC