Results 31 to 40 of about 2,272,026 (278)
Regulators of rank one quadratic twists [PDF]
, 2008 We investigate the regulators of elliptic curves with rank 1 in some families of quadratic twists of a fixed elliptic curve. In particular, we formulate some conjectures on the average size of these regulators.
Delaunay, Christophe +1 more
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Efficient Unified Arithmetic for Hardware Cryptography [PDF]
, 2008 The basic arithmetic operations (i.e. addition, multiplication, and inversion) in finite fields, GF(q), where q = pk and p is a prime integer, have several applications in cryptography, such as RSA algorithm, Diffie-Hellman key exchange algorithm [1 ...
Koc, Cetin Kaya +3 more
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Triangles and elliptic curves, V [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994 The author continues his work on elliptic curves associated to triangles as described in part I, ibid. 70, No. 4, 106-108; part II, ibid., No. 7, 223-225; and part III, ibid., No. 10, 311-314 (1994); see respectively Zbl 0824.14028 and 14029 and Zbl 0832.14021).
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Ranks of elliptic curves [PDF]
Bulletin of the American Mathematical Society, 2002 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 Swinnerton-Dyer Conjecture, the Parity Conjecture, ranks in families of quadratic twists, and ways to search for elliptic curves of large rank.
Alice Silverberg, Karl Rubin
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On families of 9-congruent elliptic curves [PDF]
, 2015 We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over Q, i.e.
Fisher, Tom
core +1 more source
On tea, donuts and non-commutative geometry [PDF]
Surveys in Mathematics and its Applications, 2018 As many will agree, it feels good to complement a cup of tea by a donut or two. This sweet relationship is also a guiding principle of non-commutative geometry known as Serre Theorem.
Igor V. Nikolaev
doaj
Visualising Sha[2] in Abelian Surfaces [PDF]
, 2002 Given an elliptic curve E1 over a number field and an element s in its 2-Selmer group, we give two different ways to construct infinitely many Abelian surfaces A such that the homogeneous space representing s occurs as a fibre of A over another elliptic ...
Bruin, Nils
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Multi-Functional Resource-Constrained Elliptic Curve Cryptographic Processor
IEEE Access, 2023 With the rising data evolution, the demand for secured communications over networks is rising immensely. Elliptic Curve Cryptography (ECC) provides an attractive solution to fulfill the requirements of modern network applications.
Binh Kieu Do-Nguyen +4 more
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Methods for using elliptic curves in cryptography [PDF]
E3S Web of ConferencesElliptic Curve Cryptography (ECC), a significant modern cryptography, is more secure and robust than most others due to its construction using an elliptic curve and the application of mathematical operations for encryption and key generation. Furthermore,
Obukhov Vadim +4 more
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Upper bound for the height of S-integral points on elliptic curves [PDF]
, 2012 We establish new upper bounds for the height of the S-integral points of an elliptic curve. This bound is explicitly given in terms of the set S of places of the number field K involved, but also in terms of the degree of K, as well as the rank, the ...
Bosser, Vincent, Surroca, Andrea
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