Involutive bases algorithm incorporating F5 criterion

Gerdt, Vladimir P.; Hashemi, Amir; M.-Alizadeh, Benyamin

doi:10.1016/j.jsc.2013.08.002

Cited by 9 publications

(10 citation statements)

References 23 publications

(80 reference statements)

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“…Hospital Financial Data Based on Noekeon Algorithm e encryption and decryption structure of Noekeon algorithm are very similar, and each basic module algorithm is matched. [7].…”

Section: Design Of Hybrid Encryption Scheme Ofmentioning

confidence: 99%

Hybrid Encryption Scheme for Hospital Financial Data Based on Noekeon Algorithm

Yao

2021

Security and Communication Networks

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The previous encryption methods of hospital financial data have the problem of overburden. Therefore, a research study on hybrid encryption of hospital financial data based on Noekeon algorithm is proposed. From the basic principles of the Noekeon algorithm and the application and implementation of the Noekeon algorithm, a hybrid encryption scheme for hospital financial data based on the Noekeon algorithm is designed. In order to improve the security of the encryption system, the RSA algorithm is used to encrypt the encrypted content twice. The hybrid algorithm realizes the hybrid encryption of the hospital's financial data. Finally, a hybrid encryption system for hospital financial data based on Noekeon algorithm is designed. Experimental results show that this method has a higher success rate and better comprehensive performance. It not only improves the encryption efficiency of hospital financial data but also enhances the security of hospital financial data, which has greater application value.

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“…Hospital Financial Data Based on Noekeon Algorithm e encryption and decryption structure of Noekeon algorithm are very similar, and each basic module algorithm is matched. [7].…”

Section: Design Of Hybrid Encryption Scheme Ofmentioning

confidence: 99%

Hybrid Encryption Scheme for Hospital Financial Data Based on Noekeon Algorithm

Yao

2021

Security and Communication Networks

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“…involutive bases [54,55] (2013) AP [3] (2009) GVW(HS) [48,49,83] (2011) on solvable algebras [81] (2012) SB [70] (2012) SSG [44] (2012) G2V [46] (2010) GVW(v1) [47] (2010) iG2V [26] (2012)…”

Section: Invariant (Group Action)mentioning

confidence: 99%

“…Moreover, there are first works in using signature-based criteria for computing involutive bases ( [54,55]).…”

Section: Algorithmic Property 83mentioning

confidence: 99%

A survey on signature-based algorithms for computing Gröbner bases

Eder

Faugère

2017

Journal of Symbolic Computation

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This paper is a survey on the area of signature-based Gröbner basis algorithms that was initiated by Faugère's F5 algorithm in 2002. We explain the general ideas behind the usage of signatures. We show how to classify the various known variants by 3 different orderings. For this we give translations between different notations and show that besides notations many approaches are just the same. Moreover, we give a general description of how the idea of signatures is quite natural when performing the reduction process using linear algebra. This survey shall help to outline this field of active research. At the moment the area of signature-based Gröbner basis algorithms is confusing and vast. More and more papers are published proving statements already proven before, and even more publications can be found on "new" variants that boil down to be a known one just with a different notation. In this paper we try to give a rigorous survey on signature-based Gröbner basis theory, including all variants known up to now. We lay an emphasis on understanding and we show how the variants presented over the last years are mostly differ in small parts only. Moreover, we give the reader a vocabulary book at hand which helps to understand how notations, varying for different authors, coincide. Since this is a survey, we do not give proofs if they are long, complex, or do not help in understanding the topic. We always explain the idea behind the proofs and refer to the related publication which includes a complete proof. There the reader is then, with our descriptions and explanations, able to understand the

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“…In this section, by using the algorithm described in Section 3, we show how one can incorporate an involutive version of Hilbert driven strategy to improve this algorithm. compare behavior of InvolutiveBasis and HDQuasiStable algorithms with Gerdt et al [17] and QuasiStable [24] algorithms, respectively (we shall remark that QuasiStable has the same structure as the HDQuasiStable, however to compute Janet bases we use Gerdt's algorithm). For this purpose, we used some well-known examples from computer algebra literature.…”

Section: Hilbert Driven Pommaret Bases Computationsmentioning

confidence: 99%

“…

In this paper, we describe improved algorithms to compute Janet and Pommaret bases. To this end, based on the method proposed by Möller et al [21], we present a more efficient variant of Gerdt's algorithm (than the algorithm presented in [17]) to compute minimal involutive bases. Further, by using the involutive version of Hilbert driven technique, along with the new variant of Gerdt's algorithm, we modify the algorithm, given in [24], to compute a linear change of coordinates for a given homogeneous ideal so that the new ideal (after performing this change) possesses a finite Pommaret basis.

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confidence: 99%

Improved Computation of Involutive Bases

Binaei

Hashemi

Seiler

2016

Computer Algebra in Scientific Computing

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Abstract. In this paper, we describe improved algorithms to compute Janet and Pommaret bases. To this end, based on the method proposed by Möller et al. [21], we present a more efficient variant of Gerdt's algorithm (than the algorithm presented in [17]) to compute minimal involutive bases. Further, by using the involutive version of Hilbert driven technique, along with the new variant of Gerdt's algorithm, we modify the algorithm, given in [24], to compute a linear change of coordinates for a given homogeneous ideal so that the new ideal (after performing this change) possesses a finite Pommaret basis. All the proposed algorithms have been implemented in Maple and their efficiency is discussed via a set of benchmark polynomials.

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Involutive bases algorithm incorporating F5 criterion

Cited by 9 publications

References 23 publications

Hybrid Encryption Scheme for Hospital Financial Data Based on Noekeon Algorithm

Hybrid Encryption Scheme for Hospital Financial Data Based on Noekeon Algorithm

A survey on signature-based algorithms for computing Gröbner bases

Improved Computation of Involutive Bases

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