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Your search keyword '"Farashahi, Reza Rezaeian"' showing total 32 results
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32 results on '"Farashahi, Reza Rezaeian"'

1. Isomorphism classes of Doche-Icart-Kohel Curves over finite fields

Author

Farashahi, Reza Rezaeian and Hosseini, Mehran

Subjects
Mathematics - Algebraic Geometry, Mathematics - Number Theory
Abstract

We give explicit formulas for the number of distinct elliptic curves over a finite field, up to isomorphism, in two families of curves introduced by C.~Doche, T.~Icart and D.~R. Kohel.

Published
2015

2. Injective Encodings to Binary Ordinary Elliptic Curves

Author

Fadavi, Mojtaba, Farashahi, Reza Rezaeian, Sabbaghian, Soheila, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Cid, Carlos, editor, and Jacobson Jr., Michael J., editor

Published
2019
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3. On the Number of Distinct Legendre, Jacobi and Hessian Curves

Author

Farashahi, Reza Rezaeian

Subjects
Mathematics - Algebraic Geometry, Mathematics - Number Theory, 11G05, 11T06, 14H52
Abstract

We give explicit formulas for the number of distinct elliptic curves over a finite field, up to isomorphism, in the families of Legendre, Jacobi, Hessian and generalized Hessian curves., Comment: 25 pages

Published
2011

4. On group structures realized by elliptic curves over a fixed finite field

Author

Farashahi, Reza Rezaeian and Shparlinski, Igor E.

Subjects
Mathematics - Number Theory, Mathematics - Algebraic Geometry, 11G05, 14H52
Abstract

We obtain explicit formulas for the number of non-isomorphic elliptic curves with a given group structure (considered as an abstract abelian group). Moreover, we give explicit formulas for the number of distinct group structures of all elliptic curves over a finite field. We use these formulas to derive some asymptotic estimates and tight upper and lower bounds for various counting functions related to classification of elliptic curves accordingly to their group structure. Finally, we present results of some numerical tests which exhibit several interesting phenomena in the distribution of group structures. We pose getting an explanation to these as an open problem.

Published
2010

5. Differential Addition on Twisted Edwards Curves

Author

Farashahi, Reza Rezaeian, Hosseini, Seyed Gholamhossein, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Pieprzyk, Josef, editor, and Suriadi, Suriadi, editor

Published
2017
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9. Hashing into Hessian Curves

Author

Farashahi, Reza Rezaeian, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Nitaj, Abderrahmane, editor, and Pointcheval, David, editor

Published
2011
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11. Extractors for Jacobians of Binary Genus-2 Hyperelliptic Curves

Author

Farashahi, Reza Rezaeian, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Mu, Yi, editor, Susilo, Willy, editor, and Seberry, Jennifer, editor

Published
2008
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12. The Quadratic Extension Extractor for (Hyper)Elliptic Curves in Odd Characteristic

Author

Farashahi, Reza Rezaeian, Pellikaan, Ruud, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Carlet, Claude, editor, and Sunar, Berk, editor

Published
2007
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13. Efficient Pseudorandom Generators Based on the DDH Assumption

Author

Farashahi, Reza Rezaeian, Schoenmakers, Berry, Sidorenko, Andrey, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Rangan, C. Pandu, editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Okamoto, Tatsuaki, editor, and Wang, Xiaoyun, editor

Published
2007
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14. Extractors for Jacobian of Hyperelliptic Curves of Genus 2 in Odd Characteristic

Author

Farashahi, Reza Rezaeian, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, and Galbraith, Steven D., editor

Published
2007
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20. On the Number of Distinct Legendre, Jacobi,Hessian and Edwards Curves (Extended Abstract)

Author

Farashahi, Reza Rezaeian and Saadi, Assia

Subjects
Legendre curve, Hessian curve, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-IT] Mathematics [math]/Information Theory [math.IT], cryptography, isomorphism, j-invariant, Elliptic curve, Edwards curve, [INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT], Jacobi curve, [INFO.INFO-CR] Computer Science [cs]/Cryptography and Security [cs.CR]
Abstract

We give explicit formulas for the number of distinct elliptic curves over a nite eld, up to isomorphism, in the families of Legendre, Jacobi, Hessian and Edwards curves.

Published
2011

29. Efficient Implementation of Low Time Complexity and Pipelined Bit-Parallel Polynomial Basis Multiplier over Binary Finite Fields.

Author

Rashidi, Bahram, Farashahi, Reza Rezaeian, and Sayedi, Sayed Masoud

Subjects
PARALLEL computers, FINITE fields, MULTIPLIERS (Mathematical analysis)
Abstract

This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF(2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. The second structure only even powers of the polynomial variable are used. The parallel computation provides regular and low-cost structure with low critical path delay. In addition, the pipelining technique is applied to the proposed structures to shorten the critical path and to perform the computation in two clock cycles. The implementations of the proposed methods over the binary extension fields GF(2163) and GF(2233) have been successfully verified and synthesized using Xilinx ISE 11 by Virtex-4, XC4VLX200 FPGA. [ABSTRACT FROM AUTHOR]

Published
2015

30. Efficient Pseudorandom Generators Based on the DDH Assumption.

Author

Hutchison, David, Kanade, Takeo, Kittler, Josef, Kleinberg, Jon M., Mattern, Friedemann, Mitchell, John C., Naor, Moni, Nierstrasz, Oscar, Rangan, C. Pandu, Steffen, Bernhard, Sudan, Madhu, Terzopoulos, Demetri, Tygar, Doug, Vardi, Moshe Y., Weikum, Gerhard, Okamoto, Tatsuaki, Wang, Xiaoyun, Farashahi, Reza Rezaeian, Schoenmakers, Berry, and Sidorenko, Andrey

Abstract

A family of pseudorandom generators based on the decisional Diffie-Hellman assumption is proposed. The new construction is a modified and generalized version of the Dual Elliptic Curve generator proposed by Barker and Kelsey. Although the original Dual Elliptic Curve generator is shown to be insecure, the modified version is provably secure and very efficient in comparison with the other pseudorandom generators based on discrete log assumptions. Our generator can be based on any group of prime order provided that an additional requirement is met (i.e., there exists an efficiently computable function that in some sense enumerates the elements of the group). Two specific instances are presented. The techniques used to design the instances, for example, the new probabilistic randomness extractor are of independent interest for other applications. [ABSTRACT FROM AUTHOR]

Published
2007
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31. The Quadratic Extension Extractor for (Hyper)Elliptic Curves in Odd Characteristic.

Author

Hutchison, David, Kanade, Takeo, Kittler, Josef, Kleinberg, Jon M., Mattern, Friedemann, Mitchell, John C., Naor, Moni, Nierstrasz, Oscar, Rangan, C. Pandu, Steffen, Bernhard, Sudan, Madhu, Terzopoulos, Demetri, Tygar, Doug, Vardi, Moshe Y., Weikum, Gerhard, Carlet, Claude, Sunar, Berk, Farashahi, Reza Rezaeian, and Pellikaan, Ruud

Abstract

We propose a simple and efficient deterministic extractor for the (hyper)elliptic curve $\mathcal{C}$, defined over $\mathbb{F}_{q^2}$, where q is some power of an odd prime. Our extractor, for a given point P on $\mathcal{C}$, outputs the first $\mathbb{F}_{q}$-coefficient of the abscissa of the point P. We show that if a point P is chosen uniformly at random in $\mathcal{C}$, the element extracted from the point P is indistinguishable from a uniformly random variable in $\mathbb{F}_q$. [ABSTRACT FROM AUTHOR]

Published
2007
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32. Extractors for Jacobian of Hyperelliptic Curves of Genus 2 in Odd Characteristic.

Author

Hutchison, David, Kanade, Takeo, Kittler, Josef, Kleinberg, Jon M., Mattern, Friedemann, Mitchell, John C., Naor, Moni, Nierstrasz, Oscar, Pandu Rangan, C., Steffen, Bernhard, Sudan, Madhu, Terzopoulos, Demetri, Tygar, Doug, Vardi, Moshe Y., Weikum, Gerhard, Galbraith, Steven D., and Farashahi, Reza Rezaeian

Abstract

We propose two simple and efficient deterministic extractors for $J(\mathbb{F}_q)$, the Jacobian of a genus 2 hyperelliptic curve H defined over $\mathbb{F}_q$, for some odd q. Our first extractor, $\texttt{SEJ}$, called sum extractor, for a given point D on $J(\mathbb{F}_q)$, outputs the sum of abscissas of rational points on H in the support of D, considering D as a reduced divisor. Similarly the second extractor, $\texttt{PEJ}$, called product extractor, for a given point D on the $J(\mathbb{F}_q)$, outputs the product of abscissas of rational points in the support of D. Provided that the point D is chosen uniformly at random in $J(\mathbb{F}_q)$, the element extracted from the point D is indistinguishable from a uniformly random variable in $\mathbb{F}_q$. Thanks to the Kummer surface $\mathcal{K}$, that is associated to the Jacobian of H over $\mathbb{F}_q$, we propose the sum and product extractors, $\texttt{SEK}$ and $\texttt{PEK}$, for $\mathcal{K}(\mathbb{F}_q)$. These extractors are the modified versions of the extractors $\texttt{SEJ}$ and $\texttt{PEJ}$. Provided a point K is chosen uniformly at random in $\mathcal{K}$, the element extracted from the point K is statistically close to a uniformly random variable in $\mathbb{F}_q$. [ABSTRACT FROM AUTHOR]

Published
2007
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