Protections against Differential Analysis for Elliptic Curve Cryptography

We propose several new methods to protect the scalar multiplication on an elliptic curve against Differential Analysis. The basic idea consists in transforming the curve through various random morphisms to provide a non-deterministic execution of the algorithm.

[1]  Paul C. Kocher,et al.  Differential Power Analysis , 1999, CRYPTO.

[2]  Jerome A. Solinas.  An Improved Algorithm for Arithmetic on a Family of Elliptic Curves , 1997, CRYPTO.

[3]  Paul C. Kocher,et al.  Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems , 1996, CRYPTO.

[4]  Joan Feigenbaum,et al.  Advances in Cryptology-Crypto 91 , 1992 .

[5]  Ernest F. Brickell,et al.  Advances in Cryptology — CRYPTO’ 92 , 2001, Lecture Notes in Computer Science.

[6]  Neal Koblitz,et al.  Advances in Cryptology — CRYPTO ’96 , 2001, Lecture Notes in Computer Science.

[7]  Willi Meier,et al.  Efficient Multiplication on Certain Nonsupersingular Elliptic Curves , 1992, CRYPTO.

[8]  Atsuko Miyaji,et al.  Efficient elliptic curve exponentiation , 1997, ICICS.

[9]  Henri Cohen,et al.  A course in computational algebraic number theory , 1993, Graduate texts in mathematics.

[10]  Kazuo Ohta,et al.  Advances in Cryptology — ASIACRYPT’98 , 2002, Lecture Notes in Computer Science.

[11]  D. Chudnovsky,et al.  Sequences of numbers generated by addition in formal groups and new primality and factorization tests , 1986 .

[12]  Burton S. Kaliski.  Advances in Cryptology - CRYPTO '97 , 1997 .

[13]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[14]  Neal Koblitz,et al.  CM-Curves with Good Cryptographic Properties , 1991, CRYPTO.

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

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

[17]  Jean-Sébastien Coron,et al.  Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems , 1999, CHES.

[18]  Alfred Menezes,et al.  Elliptic curve public key cryptosystems , 1993, The Kluwer international series in engineering and computer science.

[19]  Christof Paar,et al.  Cryptographic Hardware and Embedded Systems - CHES 2006, 8th International Workshop, Yokohama, Japan, October 10-13, 2006, Proceedings , 2006, CHES.

[20]  M. Anwar Hasan.  Power Analysis Attacks and Algorithmic Approaches to their Countermeasures for Koblitz Curve Cryptosystems , 2000, CHES.