Enhanced Doubling Attacks on Signed-All-Bits Set Recoding

In cryptographic devices like a smart card whose computing ability and memory are limited, cryptographic algorithms should be performed efficiently. However, the issue of efficiency sometimes raises vulnerabilities against side channel attacks (SCAs). In elliptic curve cryptosystems, one of main operations is the scalar multiplication. Thus it must be constructed in safety against SCAs. Recently, Hedabou et al. proposed a signed-all-bits set (sABS) recoding as simple power analysis countermeasure, which is also secure against doubling attack (DA). In this paper we propose enhanced doubling attacks which break Hedabou's countermeasure based on sABS recoding, and then show the statistical approach of noise reduction to experiment on the proposed attacks in actuality. We also introduce a countermeasure based on a projective coordinate.

[1]  Christophe Clavier,et al.  Universal Exponentiation Algorithm , 2001, CHES.

[2]  Alfred Menezes,et al.  Elliptic curve crypto systems , 1995 .

[3]  C. Paar,et al.  Universal Exponentiation Algorithm – A First Step Towards Provable SPA-resistance – , 2001 .

[4]  Frédéric Valette,et al.  The Doubling Attack - Why Upwards Is Better than Downwards , 2003, CHES.

[5]  Marc Joye,et al.  Cryptographic Hardware and Embedded Systems - CHES 2004 , 2004, Lecture Notes in Computer Science.

[6]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

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

[8]  David Naccache,et al.  Cryptographic Hardware and Embedded Systems — CHES 2001 , 2001 .

[9]  Siva Sai Yerubandi,et al.  Differential Power Analysis , 2002 .

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

[11]  Seungjoo Kim,et al.  A Countermeasure against One Physical Cryptanalysis May Benefit Another Attack , 2001, ICISC.

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

[13]  Kwangjo Kim,et al.  Information Security and Cryptology — ICISC 2001 , 2002, Lecture Notes in Computer Science.

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

[15]  Yvo Desmedt.  Public Key Cryptography — PKC 2003 , 2002, Lecture Notes in Computer Science.

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

[17]  Alfred Menezes,et al.  The Elliptic Curve Digital Signature Algorithm (ECDSA) , 2001, International Journal of Information Security.

[18]  Mustapha Hedabou,et al.  Countermeasures for Preventing Comb Method Against SCA Attacks , 2005, ISPEC.

[19]  Louis Goubin,et al.  A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems , 2003, Public Key Cryptography.

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

[21]  Eli Biham,et al.  Differential Fault Analysis of Secret Key Cryptosystems , 1997, CRYPTO.

[22]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[23]  Christof Paar,et al.  Cryptographic Hardware and Embedded Systems - CHES 2003 , 2003, Lecture Notes in Computer Science.

[24]  Atsuko Miyaji,et al.  Efficient Countermeasures against RPA, DPA, and SPA , 2004, CHES.

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