Parallel Extended Basic Operations for Conic Curves Cryptography over Ring Zn

Li, Yongnan; Xiao, Limin; Chen, Siming; Tian, Hongyun; Ruan, Li; Bin-bin, YU

doi:10.1109/ispaw.2011.16

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…Therefore, it is important to design highspeed parallel algorithms for both encryption and decryption. We have done some works regarding the parallel algorithms for conic curves cryptosystem over finite field Fp and ring Zn [6][7][8][9][10][11]. Finite field GF (2 n ) is one of the common used mathematical sets for constructing cryptosystems including elliptic curves cryptography [12,13] and conic curves cryptography.…”

Section: Introductionmentioning

confidence: 99%

Parallelization of Point Operations on Conic Curves over Finite Field GF(2n)

Li¹,

Xiao²

2014

IJGDC

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Section: Introductionmentioning

confidence: 99%

Parallelization of Point Operations on Conic Curves over Finite Field GF(2n)

Li¹,

Xiao²

2014

IJGDC

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“…There are many scientists dedicated to simplifying and accelerating the operation of Chinese remainder theorem to reduce the computation complexities in these applications. These works about parallelization of Chinese remainder theorem are mainly focused on fault-tolerant technology [2,3], binary reverse converter [4][5][6], distributed key distribution scheme [7,8] and fast encryption/decryption of cryptographic algorithm [9][10][11]. However, there is less deep study on more general parallel algorithms concerning multiple-precision integers for Chinese remainder theorem.…”

Section: Introductionmentioning

confidence: 99%

Fast Parallel Garner Algorithm for Chinese Remainder Theorem

Xiao

Liang

et al. 2012

Lecture Notes in Computer Science

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Abstract. This paper presents a fast parallel garner algorithm for Chinese remainder theorem. The variables in garner algorithm are divided into public parameters that are constants for fixed module and private parameters that represent random input integers. We design the parallel garner algorithm by analyzing the data dependencies of these arithmetic operations for computing public variables and private variables. Time complexities and speedup ratios of the parallel algorithm and the sequential algorithm are calculated to make the quantitative comparison based on our previous work about some fundamental parallel algorithms. The performance evaluation shows high efficiency of the proposed parallel algorithm compared to the sequential one.

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“…Work in [9] introduces two types of parallel pointmultiplications in conic curves cryptosystem over ring Zn and finite field Fp. We propose parallel algorithms of two extended operations of point-addition and point-double on conic curves over ring Zn in [10]. Performance of three parallel point-multiplications for conic curves cryptosystem over ring Zn is compared in [11].…”

Section: Introductionmentioning

confidence: 99%

High Performance Point-Multiplication for Conic Curves Cryptosystem Based on Standard NAF Algorithm and Chinese Remainder Theorem

Xiao

Wang

et al. 2011

2011 International Conference on Information Science and Applications

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This paper presents parallel point-multiplication on conic curves based on standard NAF algorithm and Chinese Remainder Theorem. All analysis of parallel methodologies should take advantage of the basic parallel algorithms of conic curves cryptosystem in our previous works. We employ standard NAF algorithm to parallel the point-multiplication over finite field Fp by adopting the pipeline technique to compute point-addition and point-double respectively. The expression of point-addition over ring Zn is deduced to declare that the parallel methodology over finite field Fp could be used over ring Zn. The operation of pointmultiplication over ring Zn is paralleled by partitioning the operation into two different finite fields based on Chinese Remainder Theorem and then combining the two temporary parameters to get the final result. After that, a quantitative performance contrast is made between sequential algorithm and parallel algorithm to show our approaches allow speeding up the point-multiplication on conic curves and reduce the time complexity. Additionally, the parallel method of paralleling point-multiplication over ring Zn introduced in this paper is also more efficient than an old parallel algorithm we proposed before.

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Parallel Extended Basic Operations for Conic Curves Cryptography over Ring Zn

Cited by 5 publications

References 10 publications

Parallelization of Point Operations on Conic Curves over Finite Field GF(2n)

Parallelization of Point Operations on Conic Curves over Finite Field GF(2n)

Fast Parallel Garner Algorithm for Chinese Remainder Theorem

High Performance Point-Multiplication for Conic Curves Cryptosystem Based on Standard NAF Algorithm and Chinese Remainder Theorem

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