The Experts below are selected from a list of 58491 Experts worldwide ranked by ideXlab platform
Marc Moreno Maza - One of the best experts on this subject based on the ideXlab platform.
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ISSAC - Big Prime Field FFT on Multi-core Processors
Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, 2019Co-Authors: Svyatoslav Covanov, Davood Mohajerani, Marc Moreno Maza, Linxiao WangAbstract:We report on a multi-threaded implementation of Fast Fourier Transforms over generalized Fermat Prime Fields. This work extends a previous study realized on graphics processing units to multi-core processors. In this new context, we overcome the less fine control of hardware resources by successively using FFT in support of the multiplication in those Fields. We obtain favorable speedup factors (up to 6.9x on a 6-core, 12 threads node, and 4.3x on a 4-core, 8 threads node) of our parallel implementation compared to the serial implementation for the overall application thanks to the low memory footprint and the sharp control of arithmetic instructions of our implementation of generalized Fermat Prime Fields.
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big Prime Field fft on the gpu
International Symposium on Symbolic and Algebraic Computation, 2017Co-Authors: Liangyu Chen, Svyatoslav Covanov, Davood Mohajerani, Marc Moreno MazaAbstract:We consider Prime Fields of large characteristic, typically fitting on $k$ machine words, where k is a power of 2. When the characteristic of these Fields is restricted to a subclass of the generalized Fermat numbers, we show that arithmetic operations in such Fields offer attractive performance, both in terms of algebraic complexity and parallelism. In particular, these operations can be vectorized, leading to efficient implementation of fast Fourier transforms on graphics processing units.
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ISSAC - Big Prime Field FFT on the GPU
Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, 2017Co-Authors: Liangyu Chen, Svyatoslav Covanov, Davood Mohajerani, Marc Moreno MazaAbstract:We consider Prime Fields of large characteristic, typically fitting on $k$ machine words, where k is a power of 2. When the characteristic of these Fields is restricted to a subclass of the generalized Fermat numbers, we show that arithmetic operations in such Fields offer attractive performance, both in terms of algebraic complexity and parallelism. In particular, these operations can be vectorized, leading to efficient implementation of fast Fourier transforms on graphics processing units.
A. V. Bessalov - One of the best experts on this subject based on the ideXlab platform.
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Supersingular Twisted Edwards Curves Over Prime Fields. I. Supersingular Twisted Edwards Curves with j-Invariants Equal to Zero and 12^3
Cybernetics and Systems Analysis, 2019Co-Authors: A. V. Bessalov, L. V. KovalchukAbstract:An analysis of existence conditions of supersingular twisted Edwards curves over a Prime Field is given. Theorems on the conditions of existence of supersingular curves with j -invariants equal to zero and 12^3 in different classes of curves are formulated and proved. Based on these results, concrete parameters for some supersingular curves are obtained. A generalization of the results obtained earlier using an isomorphism of curves in Weierstrass and Edwards forms is given.
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Exact Number of Elliptic Curves in the Canonical Form, Which are Isomorphic to Edwards Curves Over Prime Field
Cybernetics and Systems Analysis, 2015Co-Authors: A. V. Bessalov, L. V. KovalchukAbstract:The necessary and sufficient conditions for the parameters of the curve in the canonical form with two points of order 4 are found. Two lemmas about the properties of quadratic residues are proved, using the Gauss scheme for quadratic residues and non-residues. Based on this lemmas, the exact formulas are derived for the number of elliptic curves with non-zero parameters a and b and two points of order 4 that are isomorphic to Edwards curves over the Prime Field. It is proved that for large Fields the share of such curves is close to 1/4.
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Interrelation of families of points of high order on the Edwards curve over a Prime Field
Problems of Information Transmission, 2015Co-Authors: A. V. Bessalov, O. V. TsygankovaAbstract:We propose a modification of the addition law on the Edwards curve over a Prime Field. We prove three theorems on properties of coordinates of high-order points and on a degenerate pair of twisted curves. We propose an algorithm for reconstructing all unknown points kP of the Edwards curve when only 1/8 of the points are known.
Yeong Min Jang - One of the best experts on this subject based on the ideXlab platform.
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fpga implementation of high speed area efficient processor for elliptic curve point multiplication over Prime Field
IEEE Access, 2019Co-Authors: Md Mainul Islam, Md Selim Hossain, Moh Khalid Hasan, Md Shahjalal, Yeong Min JangAbstract:Developing a high-speed elliptic curve cryptographic (ECC) processor that performs fast point multiplication with low hardware utilization is a crucial demand in the Fields of cryptography and network security. This paper presents Field-programmable gate array (FPGA) implementation of a high-speed, low-area, side-channel attacks (SCAs) resistant ECC processor over a Prime Field. The processor supports 256-bit point multiplication on recently recommended twisted Edwards curve, namely, Edwards25519, which is used for a high-security digital signature scheme called Edwards curve digital signature algorithm (EdDSA). The paper proposes novel hardware architectures for point addition and point doubling operations on the twisted Edwards curve, where the processor takes only 516 and 1029 clock cycles to perform each point addition and point doubling, respectively. For a 256-bit key, the proposed ECC processor performs single point multiplication in 1.48 ms, running at a maximum clock frequency of 177.7 MHz in a cycle count of 262 650 with a throughput of 173.2 kbps, utilizing only 8873 slices on the Xilinx Virtex-7 FPGA platform, where the points are represented in projective coordinates. The implemented design is time-area-efficient as it offers fast scalar multiplication with low hardware utilization without compromising the security level.
L. V. Kovalchuk - One of the best experts on this subject based on the ideXlab platform.
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Supersingular Twisted Edwards Curves Over Prime Fields. I. Supersingular Twisted Edwards Curves with j-Invariants Equal to Zero and 12^3
Cybernetics and Systems Analysis, 2019Co-Authors: A. V. Bessalov, L. V. KovalchukAbstract:An analysis of existence conditions of supersingular twisted Edwards curves over a Prime Field is given. Theorems on the conditions of existence of supersingular curves with j -invariants equal to zero and 12^3 in different classes of curves are formulated and proved. Based on these results, concrete parameters for some supersingular curves are obtained. A generalization of the results obtained earlier using an isomorphism of curves in Weierstrass and Edwards forms is given.
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Exact Number of Elliptic Curves in the Canonical Form, Which are Isomorphic to Edwards Curves Over Prime Field
Cybernetics and Systems Analysis, 2015Co-Authors: A. V. Bessalov, L. V. KovalchukAbstract:The necessary and sufficient conditions for the parameters of the curve in the canonical form with two points of order 4 are found. Two lemmas about the properties of quadratic residues are proved, using the Gauss scheme for quadratic residues and non-residues. Based on this lemmas, the exact formulas are derived for the number of elliptic curves with non-zero parameters a and b and two points of order 4 that are isomorphic to Edwards curves over the Prime Field. It is proved that for large Fields the share of such curves is close to 1/4.
Svyatoslav Covanov - One of the best experts on this subject based on the ideXlab platform.
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Big Prime Field FFT on Multi-core Processors
2019Co-Authors: Svyatoslav Covanov, Davood Mohajerani, Marc Moreno Maza, Linxiao WangAbstract:We report on a multi-threaded implementation of Fast Fourier Transforms over generalized Fermat Prime Fields. This work extends a previous study realized on graphics processing units to multi-core processors. In this new context, we overcome the less fine control of hardware resources by successively using FFT in support of the multiplication in those Fields. We obtain favorable speedup factors (up to 6.9x on a 6-core, 12 threads node, and 4.3x on a 4-core, 8 threads node) of our parallel implementation compared to the serial implementation for the overall application thanks to the low memory footprint and the sharp control of arithmetic instructions of our implementation of generalized Fermat Prime Fields.
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ISSAC - Big Prime Field FFT on Multi-core Processors
Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, 2019Co-Authors: Svyatoslav Covanov, Davood Mohajerani, Marc Moreno Maza, Linxiao WangAbstract:We report on a multi-threaded implementation of Fast Fourier Transforms over generalized Fermat Prime Fields. This work extends a previous study realized on graphics processing units to multi-core processors. In this new context, we overcome the less fine control of hardware resources by successively using FFT in support of the multiplication in those Fields. We obtain favorable speedup factors (up to 6.9x on a 6-core, 12 threads node, and 4.3x on a 4-core, 8 threads node) of our parallel implementation compared to the serial implementation for the overall application thanks to the low memory footprint and the sharp control of arithmetic instructions of our implementation of generalized Fermat Prime Fields.
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big Prime Field fft on the gpu
International Symposium on Symbolic and Algebraic Computation, 2017Co-Authors: Liangyu Chen, Svyatoslav Covanov, Davood Mohajerani, Marc Moreno MazaAbstract:We consider Prime Fields of large characteristic, typically fitting on $k$ machine words, where k is a power of 2. When the characteristic of these Fields is restricted to a subclass of the generalized Fermat numbers, we show that arithmetic operations in such Fields offer attractive performance, both in terms of algebraic complexity and parallelism. In particular, these operations can be vectorized, leading to efficient implementation of fast Fourier transforms on graphics processing units.
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ISSAC - Big Prime Field FFT on the GPU
Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, 2017Co-Authors: Liangyu Chen, Svyatoslav Covanov, Davood Mohajerani, Marc Moreno MazaAbstract:We consider Prime Fields of large characteristic, typically fitting on $k$ machine words, where k is a power of 2. When the characteristic of these Fields is restricted to a subclass of the generalized Fermat numbers, we show that arithmetic operations in such Fields offer attractive performance, both in terms of algebraic complexity and parallelism. In particular, these operations can be vectorized, leading to efficient implementation of fast Fourier transforms on graphics processing units.
