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Twisted Edwards Curves
, 2008
"... This paper introduces “twisted Edwards curves,” a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies; presents ..."
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Cited by 70 (7 self)
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This paper introduces “twisted Edwards curves,” a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies
Twisted Edwards Curves Revisited
, 2008
"... This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses 1 8M for suitably selected curve constants. In compa ..."
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Cited by 35 (2 self)
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This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses 1 8M for suitably selected curve constants
Twisting Edwards curves with isogenies
"... Edwards ’ elliptic curve form is popular in modern cryptographic implementations thanks to their fast, strongly unified addition formulas. Twisted Edwards curves with a = −1 are slightly faster, but their addition formulas are not complete over Fp where p ≡ 3 (mod 4). In this short note, we propose ..."
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Edwards ’ elliptic curve form is popular in modern cryptographic implementations thanks to their fast, strongly unified addition formulas. Twisted Edwards curves with a = −1 are slightly faster, but their addition formulas are not complete over Fp where p ≡ 3 (mod 4). In this short note, we propose
DIVISION POLYNOMIALS FOR TWISTED EDWARDS CURVES
, 809
"... Abstract. This paper presents division polynomials for twisted Edwards curves. Their chief property is that they characterise the ntorsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these polynomials, which may aid computation. 1. ..."
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Cited by 1 (0 self)
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Abstract. This paper presents division polynomials for twisted Edwards curves. Their chief property is that they characterise the ntorsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these polynomials, which may aid computation. 1.
SkewFrobenius map on twisted Edwards curve ∗
"... In this paper, we consider the Frobenius endomorphism on twisted Edwards curve and give the characteristic polynomial of the map. Applying the Frobenius endomorphism on twisted Edwards curve, we construct a skewFrobenius map defined on the quadratic twist of an twisted Edwards curve. Our results sh ..."
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Cited by 1 (0 self)
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In this paper, we consider the Frobenius endomorphism on twisted Edwards curve and give the characteristic polynomial of the map. Applying the Frobenius endomorphism on twisted Edwards curve, we construct a skewFrobenius map defined on the quadratic twist of an twisted Edwards curve. Our results
Two Kinds of Division Polynomials For Twisted Edwards Curves
, 2009
"... This paper presents two kinds of division polynomials for twisted Edwards curves. Their chief property is that they characterise the ntorsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these polynomials, which may aid computation. 1 ..."
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Cited by 2 (0 self)
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This paper presents two kinds of division polynomials for twisted Edwards curves. Their chief property is that they characterise the ntorsion points of a given twisted Edwards curve. We also present results concerning the coefficients of these polynomials, which may aid computation. 1
A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem
"... Abstract. This paper presents implementation results of a reconfigurable elliptic curve processor defined over prime fields GF(p). We use this processor to compare a new algorithm for point addition and point doubling operations on the twisted Edwards curves, against a current standard algorithm in ..."
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Cited by 3 (1 self)
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Abstract. This paper presents implementation results of a reconfigurable elliptic curve processor defined over prime fields GF(p). We use this processor to compare a new algorithm for point addition and point doubling operations on the twisted Edwards curves, against a current standard algorithm
Mean value formulas for twisted Edwards curves Dustin Moody
, 2010
"... R. Feng, and H. Wu recently established a certain meanvalue formula for the xcoordinates of the ndivision points on an elliptic curve given in Weierstrass form (A mean value formula for elliptic curves, 2010, available at ..."
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R. Feng, and H. Wu recently established a certain meanvalue formula for the xcoordinates of the ndivision points on an elliptic curve given in Weierstrass form (A mean value formula for elliptic curves, 2010, available at
VLSI implementation of doublebase scalar multiplication on a twisted edwards curve with an efficiently computable endomorphism. Cryptology ePrint Archive: Report 2015/421
, 2015
"... Abstract. The verification of an ECDSA signature requires a doublebase scalar multiplication, an operation of the form k ·G+ l ·Q where G is a generator of a large elliptic curve group of prime order n, Q is an arbitrary element of said group, and k, l are two integers in the range of [1, n − 1]. W ..."
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Cited by 1 (0 self)
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]. We introduce in this paper an areaoptimized VLSI design of a PrimeField Arithmetic Unit (PFAU) that can serve as a looselycoupled or tightlycoupled hardware accelerator in a systemonchip to speed up the execution of doublebase scalar multiplication. Our design is optimized for twisted Edwards
Faster point scalar multiplication on NIST elliptic curves over
"... GF(p) using (twisted) Edwards curves over GF(p3) ..."
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