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.