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The Qcurve Construction for EndomorphismAccelerated Elliptic Curves
"... Abstract. We give a detailed account of the use of Qcurve reductions to construct elliptic curves over Fp2 with efficiently computable endomorphisms, which can be used to accelerate elliptic curvebased cryptosystems in the same way as Gallant–Lambert–Vanstone (GLV) and Galbraith–Lin–Scott (GLS) ..."
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Cited by 2 (0 self)
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secure curves. We construct several oneparameter families of elliptic curves over Fp2 equipped with efficient endomorphisms for every p> 3, and exhibit examples of twistsecure curves over Fp2 for the efficient Mersenne prime p = 2127−1.
Constructive and destructive facets of Weil descent on elliptic curves
 JOURNAL OF CRYPTOLOGY
, 2002
"... ..."
Efficient Construction of Cryptographically Strong Elliptic Curves
"... We present a very efficient algorithm which given a negative integer , 1 mod 8, not divisible by 3, finds a prime number p and a cryptographically strong elliptic curve E over the prime field F p whose endomorphism ring is the quadratic order O of discriminant . If the class number of O is 200, then ..."
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We present a very efficient algorithm which given a negative integer , 1 mod 8, not divisible by 3, finds a prime number p and a cryptographically strong elliptic curve E over the prime field F p whose endomorphism ring is the quadratic order O of discriminant . If the class number of O is 200
Introducing Ramanujan’s Class Polynomials in the Generation of Prime Order Elliptic Curves
, 804
"... Complex Multiplication (CM) method is a frequently used method for the generation of prime order elliptic curves (ECs) over a prime field Fp. The most demanding and complex step of this method is the computation of the roots of a special type of class polynomials, called Hilbert polynomials. These p ..."
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Complex Multiplication (CM) method is a frequently used method for the generation of prime order elliptic curves (ECs) over a prime field Fp. The most demanding and complex step of this method is the computation of the roots of a special type of class polynomials, called Hilbert polynomials
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
, 1998
"... Elliptic curve cryptosystems, proposed by Koblitz ([11]) and Miller ([15]), can be constructed over a smaller field of definition than the ElGamal cryptosystems ([5]) or the RSA cryptosystems ([19]). This is why elliptic curve cryptosystems have begun to attract notice. In this paper, we investigate ..."
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Cited by 184 (4 self)
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Elliptic curve cryptosystems, proposed by Koblitz ([11]) and Miller ([15]), can be constructed over a smaller field of definition than the ElGamal cryptosystems ([5]) or the RSA cryptosystems ([19]). This is why elliptic curve cryptosystems have begun to attract notice. In this paper, we
Elliptic Curves Suitable for Pairing Based Cryptography
 Designs, Codes and Cryptography
, 2003
"... We give a method for constructing ordinary elliptic curves over finite prime field Fp with small security parameter k with respect to a prime l dividing the group order #E(Fp) such that p << l² ..."
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Cited by 51 (1 self)
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We give a method for constructing ordinary elliptic curves over finite prime field Fp with small security parameter k with respect to a prime l dividing the group order #E(Fp) such that p << l²
Reductions of an elliptic curve with almost prime orders
"... 1 Let E be an elliptic curve over Q. For a prime p of good reduction, let Ep be the reduction of E modulo p. We investigate Koblitz’s Conjecture about the number of primes p for which Ep(Fp) has prime order. More precisely, our main result is that if E is with Complex Multiplication, then there exis ..."
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1 Let E be an elliptic curve over Q. For a prime p of good reduction, let Ep be the reduction of E modulo p. We investigate Koblitz’s Conjecture about the number of primes p for which Ep(Fp) has prime order. More precisely, our main result is that if E is with Complex Multiplication
Comparing elliptic curve cryptography and RSA on 8bit CPUs
 in Proc. of the Sixth Workshop on Crypto graphic Hardware and Embedded Systems (CHES’04
, 2004
"... Abstract. Strong publickey cryptography is often considered to be too computationally expensive for small devices if not accelerated by cryptographic hardware. We revisited this statement and implemented elliptic curve point multiplication for 160bit, 192bit, and 224bit NIST/SECG curves over GF ..."
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Cited by 189 (2 self)
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in processor word size and the increase in key size. 3. Elliptic curves over fields using pseudoMersenne primes as standardized by NIST and SECG allow for high performance implementations and show no performance disadvantage over optimal extension fields or prime fields selected specifically for a particular
Results 11  20
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4,283