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Concurrent Error Detection in a Polynomial Basis Multiplier over GF(2m)

Chiou-Yng Lee, Che Wun Chiou, Jim-Min Lin
2006 Journal of electronic testing  
Employing the re-computing shifted operand concept, this study presents a semi-systolic array polynomial basis multiplier with concurrent error detection with minimal area overhead.  ...  Hence, a multiplier with concurrent error detection ability is urgently necessary to avert attacks.  ...  Acknowledgments The authors would like to thank anonymous referees and the editor for carefully reading the paper and for their great help in improving the paper.  ... 
doi:10.1007/s10836-006-7446-9 fatcat:wlkmh7x2gva6xd5zj7lasfa3hq

A semi-systolic Montgomery multiplier over GF(2m)

Kee-Won Kim, Jun-Cheol Jeon
2015 IEICE Electronics Express  
In this study, we present an efficient finite field arithmetic architecture based on systolic array for multiplication which is a core algorithm for division and exponentiation operations.  ...  The proposed multiplier saves at least 40% area complexity as compared to the corresponding existing structures.  ...  Also they proposed the semisystolic polynomial basis multipliers with concurrent error detection and correction capability.  ... 
doi:10.1587/elex.12.20150769 fatcat:bjjifc7cargehixnvzvw4x7c2y

Multiple Bit Error Tolerant Galois Field Architectures Over GF (2m)

Mahesh Poolakkaparambil, Jimson Mathew, Abusaleh Jabir
2012 Electronics  
The experimental results show that the proposed dynamic error detection and correction architecture results in 50% reduction in critical path delay by dynamically bypassing the error correction logic when  ...  As a benchmark test case, the finite field multiplier circuit is considered as the functional block which can be the target for major attacks.  ...  . , α m−1 } forms elements of the polynomial basis (PB) over a certain primitive polynomial. Any element AGF(2 m ) is represented using the elements in PB.  ... 
doi:10.3390/electronics1010003 fatcat:7naqh75l4ve7hc23j4rnjbjlvi

A low latency semi-systolic multiplier over GF(2m)

Kee-Won Kim, Seung-Hoon Kim
2013 IEICE Electronics Express  
A low latency semi-systolic multiplier over GF (2 m ) Kee-Won Kim 1a) and Seung-Hoon Kim 2b) Abstract: A finite field multiplier is commonly used in implementations of cryptosystems and error correcting  ...  In this paper, we present a low latency semi-systolic multiplier over GF (2 m ). We propose a finite field multiplication algorithm to reduce latency based on parallel computation.  ...  Acknowledgments The present research was conducted by the research fund of Dankook University in 2012.  ... 
doi:10.1587/elex.10.20130354 fatcat:ee6j7l5d4bcqjbvmdtmp2w5ndq

Reduced complexity polynomial multiplier architecture for finite fields GF(2m)

Se-Hyu Choi, Keon-Jik Lee
2017 IEICE Electronics Express  
This letter presents a low-complexity semi-systolic array implementation for polynomial multiplication over GF(2 m ).  ...  Compared to related multipliers, the proposed scheme yields significantly lower AT complexity.  ...  [4] proposed a semi-systolic multiplier with concurrent error detection. Huang et al. [5] proposed a semi-systolic multiplier to reduce both time and space complexities.  ... 
doi:10.1587/elex.14.20160797 fatcat:az3h3ph6nvhcpfvnm2ywayqk2u

Low complexity semi–systolic multiplication architecture over GF(2m)

Se-Hyu Choi, Keon-Jik Lee
2014 IEICE Electronics Express  
This paper presents a semi-systolic Montgomery multiplier based on the redundant basis representation of the finite field elements.  ...  We also propose a serial systolic Montgomery multiplier that can be applied well in space-limited hardware. Furthermore, a simple inversion based on the proposed scheme is presented.  ...  [4] proposed a semi-systolic Montgomery multiplier (MM) with concurrent error detection capability.  ... 
doi:10.1587/elex.11.20140713 fatcat:3uywqzz6njahddr7ejxxepptmm

Concurrent Error Detection in Finite-Field Arithmetic Operations Using Pipelined and Systolic Architectures

Siavash Bayat-Sarmadi, M.A. Hasan
2009 IEEE transactions on computers  
detection capability of the scheme for the single and multiple stuck-at faults in a polynomial basis multiplier are 99.08% and 100%, respectively.  ...  Index Terms Finite field operations, concurrent error detection (CED), concurrent error correction (CEC), polynomial basis, dual basis, normal basis, pipelined architectures, systolic arrays.  ...  In this section, we use RESO method to concurrently detect errors in arithmetic operations over the field GF (2 m ).  ... 
doi:10.1109/tc.2009.62 fatcat:nbas6igye5es7nqr4dttt7bboi

Concurrent Error Detection in Montgomery Multiplication over Binary Extension Fields

Arash Hariri, Arash Reyhani-Masoleh
2011 IEEE transactions on computers  
Here, we use a parity-based concurrent error detection approach to increase the reliability of different Montgomery multipliers available in the literature.  ...  In this paper, we consider the finite field multiplication used in elliptic curve cryptography and design concurrent error detection circuits.  ...  This work was supported in part by an NSERC Discovery grant awarded to Arash Reyhani-Masoleh.  ... 
doi:10.1109/tc.2010.258 fatcat:d5ehkapwefgrtimtnzgbvjrq7e

Concurrent Error Detection in Multiplexer-Based Multipliers for Normal Basis of GF(2 m ) Using Double Parity Prediction Scheme

Chiou-Yng Lee, Che Wun Chiou, Jim-Min Lin
2009 Journal of Signal Processing Systems  
To obtain reliable cryptographic applications, a novel concurrent error detection (CED) architecture to detect erroneous outputs in multiplexer-based normal basis (NB) multiplier over GF (2 m ) using the  ...  By using the structure of the proposed CED NB multiplier, a CED scalable multiplier over composite fields with 100% error detection rate is also presented.  ...  We can utility our proposed CED NB multiplier in Fig. 7 to realize the concurrent error detection in the sub-field multiplication over GF(2 n ).  ... 
doi:10.1007/s11265-009-0361-4 fatcat:r5ek7txpgfab3b4ymcosxcikxq

Low complexity design of bit parallel polynomial basis systolic multiplier using irreducible polynomials

Sakshi Devi, Rita Mahajan, Deepak Bagai
2021 Egyptian Informatics Journal  
In this paper, a modular multiplication algorithm is used to propose a bit parallel polynomial basis systolic multiplier which has achieved 89% less and 17% less area-delay product than the best existing  ...  Several high-speed systolic bit parallel multipliers with low area complexity have been proposed in the literature.  ...  The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.  ... 
doi:10.1016/j.eij.2021.07.003 fatcat:pucjwe6t5zhw5p2f3qbaq7zaba

Concurrent All-Cell Error Detection in Semi-Systolic Multiplier Using Linear Codes

Wangjie Qiu, Xiao Zhang, Haoyang Li, Zhao Wang, Yao Zhang, Zhiming Zheng
2013 Applied Mathematics & Information Sciences  
In this paper, it is purposed to propose a concurrent all-cell error detection semi-systolic polynomial basis multiplier based on coding theory which can realize high-speed calculation and high efficient  ...  Finally, based on the all-cell error model, the proposed multiplier is only with 2.088% extra time overhead and 4.978% extra area overhead, and its probability of concurrent error detection reaches to  ...  Acknowledgement The authors are grateful to the anonymous referee for a careful checking of the details and for helpful comments that improved this paper.  ... 
doi:10.12785/amis/070312 fatcat:tsrbb5r6trhbnhddlj7oguu3eu

Efficient Semi-Systolic Finite Field Multiplier Using Redundant Basis

Hyun-Ho Lee, Kee-Won Kim
2016 Zenodo  
The arithmetic operations over GF(2m) have been extensively used in error correcting codes and public-key cryptography schemes.  ...  In this paper, we present a parallel computation algorithm that operates Montgomery multiplication over finite field using redundant basis.  ...  [14] proposed a semi-systolic polynomial basis multiplier over GF (2 m they proposed the semi-systolic polynomial basis multipliers with concurrent error detection and correction capability.  ... 
doi:10.5281/zenodo.1126729 fatcat:g4urrpmuwjcqzixpyg67cxk6ru

New systolic array architecture for finite field division

Atef Ibrahim, Hamed Elsimary, Fayez Gebali
2018 IEICE Electronics Express  
This paper proposes a new systolic array architecture to perform division operations over GF(2 m ) based on the modified Stein's algorithm.  ...  This approach starts by obtaining the dependency graph for the intended algorithm and assigning a time value to each node in the dependency graph using a scheduling function and ends by projecting several  ...  architectures for multiplicative inversion and division over GF (2 m Polynomial division over finite fields is extensively used in several applications such as data coding, error detection, digital  ... 
doi:10.1587/elex.15.20180255 fatcat:mig37t6bejdpvf5aun52f26do4

NREPO: Normal basis Recomputing with Permuted Operands

Xiaofei Guo, Debdeep Mukhopadhyay, Chenglu Jin, Ramesh Karri
2014 2014 IEEE International Symposium on Hardware-Oriented Security and Trust (HOST)  
Concurrent Error Detection (CED) can be used to detect these faults. We present NREPO, a CED which does not require redundant computational resources in the design.  ...  We integrate NREPO in a low-cost Advanced Encryption Standard (AES) implementation with 8-bit datapath.  ...  Then {v e , v} is a normal basis of GF (2 2m ).  ... 
doi:10.1109/hst.2014.6855581 dblp:conf/host/GuoMJK14 fatcat:l64tlrqud5gyjefj7xz242jyoa

Symmetry and Classification of Multipartite Entangled States [article]

Adam Burchardt
2022 arXiv   pre-print
Finally, we present a novel approach for the general problem of verification of the equivalence between any pair of arbitrary quantum states based on a single polynomial entanglement measure.  ...  This dissertation covers various aspects of the quantification of entanglement in multipartite states and the role of symmetry in such systems.  ...  Same as before, each polynomial ax + b might be associated with the natural number 3a + b ∈ Z 9 , which defines quantum state |ψ GF(9) via Eq. (4.6) written in the computational basis.  ... 
arXiv:2204.13441v1 fatcat:flnzkmeeqbcbpcpp43iui5ceuq
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