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Ranks of elliptic curves
 Bull. Amer. Math. Soc. (N.S
, 1973
"... Abstract. This paper gives a general survey of ranks of elliptic curves over the field of rational numbers. The rank is a measure of the size of the set of rational points. The paper includes discussions of the Birch and SwinnertonDyer Conjecture, the Parity Conjecture, ranks in families of quadrat ..."
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Cited by 52 (1 self)
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Abstract. This paper gives a general survey of ranks of elliptic curves over the field of rational numbers. The rank is a measure of the size of the set of rational points. The paper includes discussions of the Birch and SwinnertonDyer Conjecture, the Parity Conjecture, ranks in families
ELLIPTIC CURVES
"... The object of this article is to construct certain classes of arithmetically significant, holomorphic Siegel cusp forms F of genus 2, which are neither of SaitoKurokawa type, in which case the degree 4 spinor Lfunction L(s, F) is divisible by an abelian Lfunction, nor of Yoshida type, in which ca ..."
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The object of this article is to construct certain classes of arithmetically significant, holomorphic Siegel cusp forms F of genus 2, which are neither of SaitoKurokawa type, in which case the degree 4 spinor Lfunction L(s, F) is divisible by an abelian Lfunction, nor of Yoshida type, in which case L(s, F) is a product of Lseries of a
Efficient Elliptic Curve Exponentiation
, 1997
"... Elliptic curve cryptosystems, proposed by Koblitz([8]) and Miller([11]), can be constructed over a smaller definition field than the ElGamal cryptosystems([5]) or the RSA cryptosystems([16]). This is why elliptic curve cryptosystems have be un to attract notice. There are mainly two types in ellipti ..."
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Cited by 46 (1 self)
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Elliptic curve cryptosystems, proposed by Koblitz([8]) and Miller([11]), can be constructed over a smaller definition field than the ElGamal cryptosystems([5]) or the RSA cryptosystems([16]). This is why elliptic curve cryptosystems have be un to attract notice. There are mainly two types
Remark on the rank of elliptic curves
 Osaka J. Math
"... A covariant functor on elliptic curves with complex multiplication is constructed. The functor takes values in noncommutaive tori with real multiplication. A conjecture on the rank of elliptic curve is formulated. Key words and phrases: complex tori, noncommutative tori ..."
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Cited by 10 (10 self)
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A covariant functor on elliptic curves with complex multiplication is constructed. The functor takes values in noncommutaive tori with real multiplication. A conjecture on the rank of elliptic curve is formulated. Key words and phrases: complex tori, noncommutative tori
Application of Elliptic Curve . . .
, 2012
"... Application of Elliptic Curve Method (ECM) in cryptography popularly known as Elliptic Curve Cryptography (ECC) has been discussed in this paper. Finally the performance of ECC in security and moreover, its recent trends has been discussed. ..."
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Application of Elliptic Curve Method (ECM) in cryptography popularly known as Elliptic Curve Cryptography (ECC) has been discussed in this paper. Finally the performance of ECC in security and moreover, its recent trends has been discussed.
Elliptic Curve Paillier Schemes
, 2001
"... . This paper is concerned with generalisations of Paillier's probabilistic encryption scheme from the integers modulo a square to elliptic curves over rings. Paillier himself described two public key encryption schemes based on anomalous elliptic curves over rings. It is argued that these schem ..."
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Cited by 21 (1 self)
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. This paper is concerned with generalisations of Paillier's probabilistic encryption scheme from the integers modulo a square to elliptic curves over rings. Paillier himself described two public key encryption schemes based on anomalous elliptic curves over rings. It is argued
Results 11  20
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