Soft-Decision Low-Complexity Chase Decoders for the RS(255,239) Code

[EN] In this work, we present a new architecture for soft-decision Reed-Solomon (RS) Low-Complexity Chase (LCC) decoding. The proposed architecture is scalable and can be used for a high number of test vectors. We propose a novel Multiplicity Assignment stage that sorts and stores only the location of the errors inside the symbols and the powers of a that identify the positions of the symbols in the frame. Novel schematics for the Syndrome Update and Symbol Modification blocks that are adapted to the proposed sorting stage are also presented. We also propose novel solutions for the problems that arise when a high number of test vectors is processed. We implemented three decoders: a h = 4 LCC decoder and two decoders that only decode 31 and 60 test vectors of true h = 5 and h = 6 LCC decoders, respectively. For example, our h = 4 decoder requires 29% less look-up tables in Virtex-V Field Programmable Gate Array (FPGA) devices than the best soft-decision RS decoder published to date, while has a 0.07 dB coding gain over that decoder.This research was funded by the Spanish Ministerio de Economia y Competitividad and FEDER grant number TEC2015-70858-C2-2-RTorres Carot, V.; Valls Coquillat, J.; Canet Subiela, MJ.; García Herrero, FM. (2019). Soft-Decision Low-Complexity Chase Decoders for the RS(255,239) Code. Electronics. 8(1):1-13. https://doi.org/10.3390/electronics8010010S11381Cideciyan, R., Gustlin, M., Li, M., Wang, J., & Wang, Z. (2013). Next generation backplane and copper cable challenges. IEEE Communications Magazine, 51(12), 130-136. doi:10.1109/mcom.2013.6685768Koetter, R., & Vardy, A. (2003). Algebraic soft-decision decoding of reed-solomon codes. IEEE Transactions on Information Theory, 49(11), 2809-2825. doi:10.1109/tit.2003.819332Sudan, M. (1997). Decoding of Reed Solomon Codes beyond the Error-Correction Bound. Journal of Complexity, 13(1), 180-193. doi:10.1006/jcom.1997.0439Guruswami, V., & Sudan, M. (1999). Improved decoding of Reed-Solomon and algebraic-geometry codes. IEEE Transactions on Information Theory, 45(6), 1757-1767. doi:10.1109/18.782097Jiang, J., & Narayanan, K. R. (2008). Algebraic Soft-Decision Decoding of Reed–Solomon Codes Using Bit-Level Soft Information. IEEE Transactions on Information Theory, 54(9), 3907-3928. doi:10.1109/tit.2008.928238Jiangli Zhu, Xinmiao Zhang, & Zhongfeng Wang. (2009). Backward Interpolation Architecture for Algebraic Soft-Decision Reed–Solomon Decoding. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 17(11), 1602-1615. doi:10.1109/tvlsi.2008.2005575Jiangli Zhu, & Xinmiao Zhang. (2008). Efficient VLSI Architecture for Soft-Decision Decoding of Reed–Solomon Codes. IEEE Transactions on Circuits and Systems I: Regular Papers, 55(10), 3050-3062. doi:10.1109/tcsi.2008.923169Zhongfeng Wang, & Jun Ma. (2006). High-Speed Interpolation Architecture for Soft-Decision Decoding of Reed–Solomon Codes. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 14(9), 937-950. doi:10.1109/tvlsi.2006.884046Zhang, X. (2006). Reduced Complexity Interpolation Architecture for Soft-Decision Reed–Solomon Decoding. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 14(10), 1156-1161. doi:10.1109/tvlsi.2006.884177Xinmiao Zhang, & Parhi, K. K. (2005). Fast factorization architecture in soft-decision Reed-Solomon decoding. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 13(4), 413-426. doi:10.1109/tvlsi.2004.842914Bellorado, J., & Kavcic, A. (2010). Low-Complexity Soft-Decoding Algorithms for Reed–Solomon Codes—Part I: An Algebraic Soft-In Hard-Out Chase Decoder. IEEE Transactions on Information Theory, 56(3), 945-959. doi:10.1109/tit.2009.2039073García-Herrero, F., Valls, J., & Meher, P. K. (2011). High-Speed RS(255, 239) Decoder Based on LCC Decoding. Circuits, Systems, and Signal Processing, 30(6), 1643-1669. doi:10.1007/s00034-011-9327-4Zhang, W., Wang, H., & Pan, B. (2013). Reduced-Complexity LCC Reed–Solomon Decoder Based on Unified Syndrome Computation. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 21(5), 974-978. doi:10.1109/tvlsi.2012.2197030Peng, X., Zhang, W., Ji, W., Liang, Z., & Liu, Y. (2015). Reduced-Complexity Multiplicity Assignment Algorithm and Architecture for Low-Complexity Chase Decoder of Reed-Solomon Codes. IEEE Communications Letters, 19(11), 1865-1868. doi:10.1109/lcomm.2015.2477495Lin, Y.-M., Hsu, C.-H., Chang, H.-C., & Lee, C.-Y. (2014). A 2.56 Gb/s Soft RS (255, 239) Decoder Chip for Optical Communication Systems. 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On the implementation of modified fuzzy vault for biometric encryption

Abstract—Biometrics, such as irises and fingerprints, enable se-cure and non-repudiable authentication. Fuzzy vault is a scheme that can monolithically bind secret to biometric templates. Moreover, the modified fuzzy vault (MFV) leads to less entropy loss and requires less memory for storing the sketches. This paper proposes a novel low-complexity scheme to compute the monic polynomial for the sketch during the enrollment process of the MFV. An innovative interpolation method is also developed to reduce the computation complexity and latency of the verification process. Efficient hardware implementation architectures are developed in this paper for the proposed schemes and their complexities are analyzed in detail. I

A Test Vector Generation Method Based on Symbol Error Probabilities for Low-Complexity Chase Soft-Decision Reed-Solomon Decoding

© 2019 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] This paper presents a low-complexity chase (LCC) decoder for Reed-Solomon (RS) codes, which uses a novel method for the selection of test vectors that is based on the analysis of the symbol error probabilities derived from simulations. Our results show that the same performance as the classical LCC is achieved with a lower number of test vectors. For example, the amount of test vectors is reduced by half and by 1/16 for the RS(255,239) and RS(255,129) codes, respectively. We provide an evidence that the proposed method is suitable for RS codes with different rates and Galois fields. In order to demonstrate that the proposed method results in a reduction of the complexity of the decoder, we also present a hardware architecture for an RS(255,239) decoder that uses 16 test vectors. This decoder achieves a coding gain of 0.56 dB at the frame error rate that is equal to 10(-6) compared with hard-decision decoding, which is higher than that of an eta = 5 LCC. The implementation results in ASIC show that a throughput of 3.6 Gb/s can be reached in a 90-nm process and 29.1XORs are required. The implementation results in Virtex-7 FPGA devices show that the decoder reaches 2.5 Gb/s and requires 5085 LUTs.This work was supported by the Spanish Ministerio de Economia y Competitividad and FEDER under Grant TEC2015-70858-C2-2-R. This paper was recommended by Associate Editor M. Boukadoum.Valls Coquillat, J.; Torres Carot, V.; Canet Subiela, MJ.; García-Herrero, FM. (2019). A Test Vector Generation Method Based on Symbol Error Probabilities for Low-Complexity Chase Soft-Decision Reed-Solomon Decoding. IEEE Transactions on Circuits and Systems I Regular Papers. 66(6):2198-2207. https://doi.org/10.1109/TCSI.2018.2882876S2198220766

Decryption Failure Attacks on Post-Quantum Cryptography

This dissertation discusses mainly new cryptanalytical results related to issues of securely implementing the next generation of asymmetric cryptography, or Public-Key Cryptography (PKC).PKC, as it has been deployed until today, depends heavily on the integer factorization and the discrete logarithm problems.Unfortunately, it has been well-known since the mid-90s, that these mathematical problems can be solved due to Peter Shor's algorithm for quantum computers, which achieves the answers in polynomial time.The recently accelerated pace of R&D towards quantum computers, eventually of sufficient size and power to threaten cryptography, has led the crypto research community towards a major shift of focus.A project towards standardization of Post-quantum Cryptography (PQC) was launched by the US-based standardization organization, NIST. PQC is the name given to algorithms designed for running on classical hardware/software whilst being resistant to attacks from quantum computers.PQC is well suited for replacing the current asymmetric schemes.A primary motivation for the project is to guide publicly available research toward the singular goal of finding weaknesses in the proposed next generation of PKC.For public key encryption (PKE) or digital signature (DS) schemes to be considered secure they must be shown to rely heavily on well-known mathematical problems with theoretical proofs of security under established models, such as indistinguishability under chosen ciphertext attack (IND-CCA).Also, they must withstand serious attack attempts by well-renowned cryptographers both concerning theoretical security and the actual software/hardware instantiations.It is well-known that security models, such as IND-CCA, are not designed to capture the intricacies of inner-state leakages.Such leakages are named side-channels, which is currently a major topic of interest in the NIST PQC project.This dissertation focuses on two things, in general:1) how does the low but non-zero probability of decryption failures affect the cryptanalysis of these new PQC candidates?And 2) how might side-channel vulnerabilities inadvertently be introduced when going from theory to the practice of software/hardware implementations?Of main concern are PQC algorithms based on lattice theory and coding theory.The primary contributions are the discovery of novel decryption failure side-channel attacks, improvements on existing attacks, an alternative implementation to a part of a PQC scheme, and some more theoretical cryptanalytical results