A secure exponentiation algorithm resistant to a combined attack on RSA implementation

Abstract

Because two types of side-channel attacks, namely passive information leakages and active fault injections, are considered separate implementation threats to cryptographic modules, most countermeasures against these attacks have been independently developed. However, Amiel et al. demonstrated that a fault injection combined with a simple power analysis (SPA) can break such a classical Rivest, Shamir, and Adelman (RSA) system implementation. In this paper, we show that this combined attack (CA) can be applied to the Boscher, Naciri, and Prouff algorithm, which is an SPA/fault attack (FA)-resistant exponentiation method for RSA implementation. Furthermore, this paper proposes a novel exponentiation algorithm resistant to power analysis and an FA as well as to the CA. The proposed exponentiation algorithm can be employed for secure Chinese remainder theorem-RSA implementation. In addition, the paper presents some experimental results of an SPA under the assumption of a successful fault injection.

Keywords:

• side-channel attack
• fault attack
• combined attack
• exponentiation
• CRT-RSA algorithm

2010 AMS Subject Classifications:

• 94A60
• 68P25
• 14G50

Acknowledgements

This work was supported by the KLA-SCARF project, the ICT R&D program of ETRI (Research on Key Leakage Analysis and Response Technologies).

Notes

[1] The URL regarding the KLA-SCARF evaluation board is http://www.k-scarf.or.kr