Trading Inversions for Multiplications in Elliptic Curve Cryptography

[1]  José Felipe Voloch,et al.  Homogeneous weights and exponential sums , 2003 .

[2]  P. L. Montgomery,et al.  Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation , 2002, CT-RSA.

[3]  C.K. Koc,et al.  Architectures for unified field inversion with applications in elliptic curve cryptography , 2002, 9th International Conference on Electronics, Circuits and Systems.

[4]  Róbert Lórencz,et al.  New Algorithm for Classical Modular Inverse , 2002, CHES.

[5]  Régis Blache.  Lifts of points on curves and exponential sums , 2002, math/0202206.

[6]  Gilberto Bini,et al.  Finite commutative rings and their applications , 2002 .

[7]  Scott A. Vanstone,et al.  Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms , 2001, CRYPTO.

[8]  Alfred Menezes,et al.  Software Implementation of the NIST Elliptic Curves Over Prime Fields , 2001, CT-RSA.

[9]  Kouichi Sakurai,et al.  Efficient Scalar Multiplications on Elliptic Curves with Direct Computations of Several Doublings , 2001 .

[10]  Erkay Savas,et al.  The Montgomery Modular Inverse-Revisited , 2000, IEEE Trans. Computers.

[11]  Marcus Greferath,et al.  Gray isometries for finite chain rings and a nonlinear ternary (36, 312, 15) code , 1999, IEEE Trans. Inf. Theory.

[12]  Ian F. Blake,et al.  Elliptic curves in cryptography , 1999 .

[13]  W. Li,et al.  Character Sums overp-adic Fields , 1999 .

[14]  Atsuko Miyaji,et al.  Efficient Elliptic Curve Exponentiation Using Mixed Coordinates , 1998, ASIACRYPT.

[15]  Ricardo Dahab,et al.  Improved Algorithms for Elliptic Curve Arithmetic in GF(2n) , 1998, Selected Areas in Cryptography.

[16]  Daniel M. Gordon,et al.  A Survey of Fast Exponentiation Methods , 1998, J. Algorithms.

[17]  Christof Paar,et al.  Efficient Algorithms for Elliptic Curve Cryptosystems , 1997, CRYPTO.

[18]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[19]  Tor Helleseth,et al.  Universal Hash Functions from Exponential Sums over Finite Fields and Galois Rings , 1996, CRYPTO.

[20]  Tor Helleseth,et al.  Exponential sums over Galois rings and their applications , 1996 .

[21]  Burton S. Kaliski,et al.  The Montgomery Inverse and Its Applications , 1995, IEEE Trans. Computers.

[22]  Chae Hoon Lim,et al.  More Flexible Exponentiation with Precomputation , 1994, CRYPTO.

[23]  N. J. A. Sloane,et al.  The Z4-linearity of Kerdock, Preparata, Goethals, and related codes , 1994, IEEE Trans. Inf. Theory.

[24]  Douglas R. Stinson,et al.  Universal hashing and authentication codes , 1991, Des. Codes Cryptogr..

[25]  M. V. Vlugt,et al.  Artin-Schreier curves and codes , 1991 .

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

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

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

[29]  P. L. Montgomery.  Modular multiplication without trial division , 1985 .

[30]  Gustavus J. Simmons,et al.  Authentication Theory/Coding Theory , 1985, CRYPTO.

[31]  T. Elgamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

[32]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.