Huff's Model for Elliptic Curves

This paper revisits a model for elliptic curves over ℚ introduced by Huff in 1948 to study a diophantine problem. Huff’s model readily extends over fields of odd characteristic. Every elliptic curve over such a field and containing a copy of ℤ/4ℤ ×ℤ/2ℤ is birationally equivalent to a Huff curve over the original field.

[1]  Gerald B. Huff.  Diophantine problems in geometry and elliptic ternary forms , 1948 .

[2]  Paulo S. L. M. Barreto,et al.  Efficient Implementation of Pairing-Based Cryptosystems , 2004, Journal of Cryptology.

[3]  H. Edwards.  A normal form for elliptic curves , 2007 .

[4]  N. Koblitz.  Elliptic curve cryptosystems , 1987 .

[5]  François Morain,et al.  Primality Proving Using Elliptic Curves: An Update , 1998, ANTS.

[6]  Ian F. Blake,et al.  Advances in Elliptic Curve Cryptography: Frontmatter , 2005 .

[7]  Joseph H. Silverman,et al.  The arithmetic of elliptic curves , 1986, Graduate texts in mathematics.

[8]  Ed Dawson,et al.  Twisted Edwards Curves Revisited , 2008, IACR Cryptol. ePrint Arch..

[9]  Paulo S. L. M. Barreto,et al.  On the Selection of Pairing-Friendly Groups , 2003, Selected Areas in Cryptography.

[10]  Victor S. Miller,et al.  The Weil Pairing, and Its Efficient Calculation , 2004, Journal of Cryptology.

[11]  Victor S. Miller,et al.  Use of Elliptic Curves in Cryptography , 1985, CRYPTO.

[12]  Tanja Lange,et al.  Faster Addition and Doubling on Elliptic Curves , 2007, ASIACRYPT.

[13]  Tanja Lange,et al.  Faster computation of Tate pairings , 2009 .

[14]  Antoine Joux,et al.  Another Approach to Pairing Computation in Edwards Coordinates , 2008, INDOCRYPT.

[15]  Tanja Lange,et al.  Inverted Edwards Coordinates , 2007, AAECC.

[16]  P. L. Montgomery.  Speeding the Pollard and elliptic curve methods of factorization , 1987 .

[17]  Tanja Lange,et al.  Binary Edwards Curves , 2008, CHES.

[18]  Joe Kilian,et al.  Primality testing using elliptic curves , 1999, JACM.

[19]  Palash Sarkar,et al.  Pairing Computation on Twisted Edwards Form Elliptic Curves , 2008, Pairing.

[20]  W. D. Peeples.  Elliptic curves and rational distance sets , 1954 .

[21]  Jacques Calmet,et al.  Algebraic Algorithms and Error-Correcting Codes , 1985, Lecture Notes in Computer Science.

[22]  H. W. Lenstra,et al.  Factoring integers with elliptic curves , 1987 .

[23]  Nigel P. Smart,et al.  Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series) , 2005 .

[24]  A. Atkin,et al.  ELLIPTIC CURVES AND PRIMALITY PROVING , 1993 .

[25]  Alfred Menezes,et al.  Elliptic Curve Cryptography: The Serpentine Course of a Paradigm Shift , 2011, IACR Cryptol. ePrint Arch..

[26]  Tanja Lange,et al.  Faster Computation of the Tate Pairing , 2009, IACR Cryptol. ePrint Arch..

[27]  Tanja Lange,et al.  Twisted Edwards Curves , 2008, AFRICACRYPT.