On the importance of protecting Δ in SFLASH against side channel attacks

SFLASH was chosen as one of the final selection of the NESSIE project in 2003. It is one of the most efficient digital signature schemes and is suitable for implementation on memory-constrained devices such as smartcards. Side channel attacks (SCA) are a serious threat to memory-constrained devices. If the implementation on them is careless, we are able to break the secret key. We experimentally analyze the effectiveness of a side channel attack on SFLASH. There are two different secret keys for SFLASH, namely the proper secret key (s, t) and the random seed Δ used for the hash function SHA-1. Whereas many papers discussed the security of (s, t), little is known about that of Δ. Steinwandt et al. proposed a theoretical DPA on finding Δ by observing the XOR operations. We propose another DPA on Δ using the addition operation modulo 2³², and present an experimental result of the DPA. After obtaining the secret key Δ, the underlying problem of SFLASH can be reduced to the C* problem broken by Patarin. From our simulation, about 1408 pairs of messages and signatures are needed to break SFLASH. Consequently, we have to carefully implement SHA-1 in order to resist SCA on SFLASH.