Tools
Sorted by:
Try your query at:
 |
 |
 |
 |
 |
 |
Results 11 - 20
of
4,283
The Q-curve Construction for Endomorphism-Accelerated Elliptic Curves
"... Abstract. We give a detailed account of the use of Q-curve reductions to construct elliptic curves over Fp2 with efficiently computable endo-morphisms, which can be used to accelerate elliptic curve-based cryp-tosystems in the same way as Gallant–Lambert–Vanstone (GLV) and Galbraith–Lin–Scott (GLS) ..."
Abstract
-
Cited by 2 (0 self)
- Add to MetaCart
-secure curves. We con-struct several one-parameter families of elliptic curves over Fp2 equipped with efficient endomorphisms for every p> 3, and exhibit examples of twist-secure 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 ..."
Abstract
-
Cited by 16 (2 self)
- Add to MetaCart
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 ..."
Abstract
- Add to MetaCart
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 ..."
Abstract
-
Cited by 184 (4 self)
- Add to MetaCart
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 ..."
Abstract
-
Cited by 51 (1 self)
- Add to MetaCart
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 ..."
Abstract
-
Cited by 4 (0 self)
- Add to MetaCart
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 public-key cryptography is often considered to be too computationally expensive for small devices if not accelerated by crypto-graphic hardware. We revisited this statement and implemented elliptic curve point multiplication for 160-bit, 192-bit, and 224-bit NIST/SECG curves over GF ..."
Abstract
-
Cited by 189 (2 self)
- Add to MetaCart
in processor word size and the increase in key size. 3. Elliptic curves over fields using pseudo-Mersenne primes as standardized by NIST and SECG allow for high performance implementations and show no perfor-mance disadvantage over optimal extension fields or prime fields selected specifically for a particular
Results 11 - 20
of
4,283
