On isogeny classes of Edwards curves over finite fields
Tài liệu tham khảo
Auer, 2002, Legendre elliptic curves over finite fields, J. Number Theory, 95, 303, 10.1016/S0022-314X(01)92760-X
Bernstein, 2008, Twisted Edwards curves, vol. 5023, 389
Bernstein, 2007, Faster addition and doubling on elliptic curves, vol. 4833, 29
2005, vol. 317
Castryck, 2011, Toric forms of elliptic curves and their arithmetic, J. Symbolic Comput., 46, 943, 10.1016/j.jsc.2011.02.003
Chudnovsky, 1986, Sequences of numbers generated by addition in formal groups and new primality and factorization tests, Adv. in Appl. Math., 7, 385, 10.1016/0196-8858(86)90023-0
Edwards, 2007, A normal form for elliptic curves, Bull. Amer. Math. Soc. (N.S.), 44, 393, 10.1090/S0273-0979-07-01153-6
Farashahi, 2010, On the number of distinct elliptic curves in some families, Des. Codes Cryptogr., 54, 83, 10.1007/s10623-009-9310-2
Huff, 1948, Diophantine problems in geometry and elliptic ternary forms, Duke Math. J., 15, 443, 10.1215/S0012-7094-48-01543-9
Joye, 2010, Huffʼs model for elliptic curves, vol. 6197, 234
Katz, 2009, Lang–Trotter revisited, Bull. Amer. Math. Soc. (N.S.), 46, 413, 10.1090/S0273-0979-09-01257-9
Katz, 2010, 2, 3, 5, Legendre: ± trace ratios in families of elliptic curves, Experiment. Math., 19, 267, 10.1080/10586458.2010.10390623
Dustin Moody, Daniel Shumow, Analogues of Veluʼs formulas for isogenies on alternate models of elliptic curves, Cryptology ePrint Archive, Report 2011/430, http://eprint.iacr.org/, 2011.
François Morain, Edwards curves and CM curves, ArXiv e-prints April 2009.
Needham, 1997
Silverman, 1992, The Arithmetic of Elliptic Curves, vol. 106
Tate, 1966, Endomorphisms of abelian varieties over finite fields, Invent. Math., 2, 134, 10.1007/BF01404549
Vélu, 1971, Isogénies entre courbes elliptiques, C. R. Acad. Sci. Paris Sér. A–B, 273, A238
Wang, 1989
Washington, 2003, Elliptic Curves: Number Theory and Cryptography
Williams, 1970, Finite transformation formulae involving the Legendre symbol, Pacific J. Math., 34, 559, 10.2140/pjm.1970.34.559
Hongfeng Wu, Rongquan Feng, Elliptic curves in Huffʼs model, Cryptology ePrint Archive, Report 2010/390, http://eprint.iacr.org/ 2010.